cryptocol/random/
random.rs

1// Copyright 2024, 2025, 2026 PARK Youngho.
2//
3// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
4// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
5// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your option.
6// This file may not be copied, modified, or distributed
7// except according to those terms.
8
9//! The module that contains a random number generator struct
10
11#![allow(missing_docs)]
12// #![allow(rustdoc::missing_doc_code_examples)]
13
14
15use std::ptr::copy_nonoverlapping;
16use std::time::{ SystemTime, UNIX_EPOCH };
17use std::collections::hash_map::RandomState;
18use std::collections::VecDeque;
19use std::hash::{ BuildHasher, Hasher };
20use std::sync::atomic::{ AtomicBool, Ordering };
21use std::sync::Mutex;
22use std::thread::{ available_parallelism, scope };
23
24#[cfg(not(target_family = "windows"))] use std::fs::File;
25#[cfg(not(target_family = "windows"))] use std::io::Read;
26
27use crate::number::{ SmallUInt, LongUnion, LongerUnion, BigUInt, BigUInt_Prime, A_LIST };
28use crate::random::{ Random, Random_Engine };
29
30
31pub(super) const SECURE_COUNT: u128 = u16::MAX as u128;
32
33/// RandGen is the Random_Generic with the generic parameter u16::MAX which is 65535.
34pub type RandGen = Random_Generic<SECURE_COUNT>;
35
36/// AnyGen is the Random_Generic with the default generic parameter.
37pub type AnyGen = Random_Generic;
38
39/// SlapdashGen is the Random_Generic with the default generic parameter.
40pub type SlapdashGen = Random_Generic<{u64::MAX as u128}>;
41
42
43pub(crate) const COLUMN: usize = 100;
44pub(crate) const ROW: usize = 5;
45pub(crate) const NUM_STR: [[&str; COLUMN]; ROW] = [
46    [
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555    ],
556];
557
558
559
560/// This generic struct `Random_Generic` is the struct for implementing a
561/// pseudo-random number generator both for primitive unsigned integers
562/// such as `u8`, `u16`, `u32`, `u64`, `u128`, and `usize`, and for `BigUInt`.
563/// Depending on the engine object, it uses hash algorithms or symmetric-key
564/// cryptographic algorithm to generate pseudo random numbers.
565/// 
566/// # Generic Parameters
567/// - COUNT: The length of the period of pseudo-random number sequence.
568///   If `COUNT` is `1000`, a new seed will be used every `1000` pseudo-random
569///   numbers, for example. The default value of `COUNT` is `u128::MAX`.
570/// - NTR: How many bytes of the true random numbers to be used as a seed.
571///   If `NTR` is `32`, thirty-two bytes of the true random number will be
572///   used as a seed. The default value of `NTR` is `64`.
573///   `NTR` cannot exceed `64`. Even if `NTR` is `100`, only sixty-four bytes
574///   of the true random numbers will be used, for example.
575/// 
576/// # Feature
577/// - The generic parameter `COUNT` should be `1` ~ `u128::MAX` inclusively.
578/// - The default value of `COUNT` is `340282366920938463463374607431768211455`
579///   which is `u128::MAX` and far less than theoretical period of pseudo-random
580///   numbers recursively generated by 512-bit hash algorithms. `COUNT is the
581///   limited number of pseudo-random numbers generated from a seed.
582/// - After it generates pseudo-random numbers `COUNT` times, it finds a new
583///   seed from a system automatically and generates next pseudo-random numbers
584///   with a new seed. In other words, it uses new seeds every `COUNT` times of
585///   generation of pseudo-random numbers.
586/// 
587/// # Panics
588/// If `COUNT` is `0`, the constructor methods
589/// such as `new()` and `new_with_seeds()` will panic!
590/// 
591/// # Predetermined Provided Specific `struct`s
592/// - Random_BIG_KECCAK_1024: uses a hash algorithm BIG_KECCAK_1024,
593///   and is cryptographically secure.
594/// - Random_SHA3_512: uses a hash algorithm SHA3_512, and is cryptographically
595///   secure and uses true random numbers far more frequently than
596///   `Any_SHA3_512` does.
597/// - Random_SHA2_512: uses a hash algorithm SHA2_512, and is cryptographically
598///   secure and uses true random numbers far more frequently than
599///   `Any_SHA2_512` does.
600/// - Any_SHAKE_256: uses a hash algorithm SHAKE_256,
601///   and is cryptographically secure.
602/// - Any_SHAKE_128: uses a hash algorithm SHAKE_128,
603///   and is cryptographically secure.
604/// - Any_SHA3_512: uses a hash algorithm SHA3_512, and is cryptographically
605///   secure and uses true random numbers far less often than `Random_SHA3_512`
606///   does.
607/// - Any_SHA3_256: uses a hash algorithm SHA3_256, and is cryptographically
608///   secure and uses true random numbers far less often than `Random_SHA3_256`
609///   does.
610/// - Any_SHA2_512: uses a hash algorithm SHA2_512, and is cryptographically
611///   secure and uses true random numbers far less often than `Random_SHA2_512`
612///   does.
613/// - Any_SHA2_256: uses a hash algorithm SHA2_256,
614///   and is cryptographically secure.
615/// - Slapdash_SHA1: uses a hash algorithm SHA1,
616///   and is NOT cryptographically secure.
617/// - Slapdash_SHA0: uses a hash algorithm SHA0,
618///   and is NOT cryptographically secure.
619/// - Slapdash_Num_C: uses a pseudo-random number generator algorithm of the
620///   function rand() of C standard library,
621///   and is NOT cryptographically secure.
622/// - Slapdash_MD5: uses a hash algorithm MD5,
623///   and is NOT cryptographically secure.
624/// - Slapdash_MD4: uses a hash algorithm MD4,
625///   and is NOT cryptographically secure.
626/// - Random_Rijndael: uses a symmetric-key encryption algorithm Rijndael,
627///   and is cryptographically secure and uses true random numbers far more
628///   frequently than `Any_Rijndael` does..
629/// - Any_Rijndael: uses a symmetric-key encryption algorithm Rijndael,
630///   and is cryptographically secure and uses true random numbers far less
631///   often than `Random_Rijndael` does.
632/// - Slapdash_DES: uses a symmetric-key encryption algorithm DES,
633///   and is NOT cryptographically secure.
634/// 
635/// - Random: a synonym of `Random_BIG_KECCAK_1024` at the moment, and is
636///   cryptographically secure and uses true random numbers far more frequently
637///   than `Any` does.
638/// - Any: a synonym of `Any_SHA2_512` at the moment, and is cryptographically
639///   secure and uses true random numbers far less often than `Random` does.
640/// - Slapdash: a synonym of `Slapdash_Num_C` at the moment,
641///   and is NOT cryptographically secure.
642/// - Random_* are cryptographically secure and uses true random numbers far
643///   more frequently than `Any_*` do.
644/// - Any_* are cryptographically secure and uses true random numbers far
645///   less often than `Random_*` do.
646/// 
647/// # QUICK START
648/// You can use either struct `Random` or `Any` or `Slapdash` depending on your
649/// purpose. `Random` and `Any` are for cryptographical purpose while Slapdash`
650/// is for non-cryptographical purpose. Look into the following examples.
651/// 
652/// ## Example
653/// ```
654/// use cryptocol::number::BigUInt_Prime;
655/// use cryptocol::random::Random;
656/// use cryptocol::define_utypes_with;
657/// define_utypes_with!(u64);
658/// 
659/// let mut rand = Random::new();
660/// // let mut rand = Any::new();
661/// println!("Random number = {}", rand.random_u128());
662/// println!("Random number = {}", rand.random_u64());
663/// println!("Random number = {}", rand.random_u32());
664/// println!("Random number = {}", rand.random_u16());
665/// println!("Random number = {}", rand.random_u8());
666/// 
667/// if let Some(num) = rand.random_under_uint(1234567890123456_u64)
668///     { println!("Random number u64 = {}", num); }
669/// 
670/// if let Some(num) = rand.random_minmax_uint(1234_u16, 6321)
671///     { println!("Random number u16 = {}", num); }
672/// 
673/// println!("Random odd number usize = {}", rand.random_odd_uint::<usize>());
674/// if let Some(num) = rand.random_odd_under_uint(1234_u16)
675///     { println!("Random odd number u16 = {}", num); }
676/// 
677/// println!("Random 128-bit number u128 = {}", rand.random_with_msb_set_uint::<u128>());
678/// println!("Random 16-bit odd number u16 = {}", rand.random_with_msb_set_uint::<u16>());
679/// println!("Random prime number u64 = {}", rand.random_prime_using_miller_rabin_uint::<u64>(5));
680/// println!("Random usize-sized prime number usize = {}", rand.random_prime_with_msb_set_using_miller_rabin_uint::<usize>(5));
681/// 
682/// let num: [u128; 20] = rand.random_array();
683/// for i in 0..20
684///     { println!("Random number {} => {}", i, num[i]); }
685/// 
686/// let mut num = [0_u64; 32];
687/// rand.put_random_in_array(&mut num);
688/// for i in 0..32
689///     { println!("Random number {} => {}", i, num[i]); }
690/// 
691/// let mut biguint: U512 = rand.random_biguint();
692/// println!("Random Number: {}", biguint);
693/// 
694/// let mut ceiling = U1024::max().wrapping_div_uint(3_u8);
695/// if let Some(r) = rand.random_under_biguint(&ceiling)
696/// {
697///     println!("Random Number less than {} is\n{}", ceiling, r);
698///     assert!(r < ceiling);
699/// }
700/// 
701/// ceiling = U1024::max().wrapping_div_uint(5_u8);
702/// let r = rand.random_under_biguint_(&ceiling);
703/// println!("Random Number less than {} is\n{}", ceiling, r);
704/// assert!(r < ceiling);
705/// 
706/// ceiling = U1024::max().wrapping_div_uint(4_u8);
707/// if let Some(r) = rand.random_odd_under_biguint(&ceiling)
708/// {
709///     println!("Random odd Number less than {} is\n{}", ceiling, r);
710///     assert!(r < ceiling);
711/// }
712/// 
713/// biguint = rand.random_with_msb_set_biguint();
714/// println!("Random Number: {}", biguint);
715/// 
716/// biguint = rand.random_odd_with_msb_set_biguint();
717/// println!("512-bit Random Odd Number = {}", biguint);
718/// assert!(biguint > U512::halfmax());
719/// assert!(biguint.is_odd());
720/// 
721/// biguint = rand.random_prime_using_miller_rabin_biguint(5);
722/// println!("Random Prime Number = {}", biguint);
723/// assert!(biguint.is_odd());
724/// 
725/// biguint = rand.random_prime_with_msb_set_using_miller_rabin_biguint(5);
726/// println!("512-bit Random Prime Number = {}", biguint);
727/// assert!(biguint.is_odd());
728/// ```
729#[allow(non_camel_case_types)]
730pub struct Random_Generic<const COUNT: u128 = {u128::MAX}>
731{
732    original_seed: [u64; 8],
733    original_aux: [u64; 8],
734    main_state: [u64; 8],
735    aux_state: [u64; 8],
736    count: u128,
737    collect_seed: fn() -> [u64; 8],
738    main_generator: Box<dyn Random_Engine>,
739    aux_generator: Box<dyn Random_Engine>,
740}
741
742impl<const COUNT: u128> Random_Generic<COUNT>
743{
744    // pub fn new_with<SG, AG>(mut main_generator: SG, mut aux_generator: AG) -> Self
745    /// Constructs a new `Random_Generic` object
746    /// with two random number generator engines.
747    /// 
748    /// # Arguments
749    /// - `main_generator` is a main random number generator engine
750    ///   which is of `Random_Engine`-type and
751    ///   for generating main pseudo-random numbers.
752    /// - `aux_generator` is an auxiliary random number generator engine
753    ///   which is of `Random_Engine`-type and
754    ///   for generating auxiliary pseudo-random numbers to use in
755    ///   generating the main pseudo-random numbers.
756    /// 
757    /// # Output
758    /// It returns a new object of `Random_Generic`.
759    /// 
760    /// # Panics
761    /// If `COUNT` is `0`, this method will panic!
762    /// 
763    /// # Cryptographical Security
764    /// - If you use either `Random_*` or `Any_*`, it is considered to be
765    ///   cryptographically secure.
766    /// - If you use `Slapdash_*`, it is considered that it may be
767    ///   cryptographically insecure.
768    /// 
769    /// # Example 1 for BIG_KECCAK_1024
770    /// ```
771    /// use cryptocol::random::RandGen;
772    /// use cryptocol::hash::BIG_KECCAK_1024;
773    /// use cryptocol::define_utypes_with;
774    /// define_utypes_with!(u64);
775    /// 
776    /// let mut rand = RandGen::new_with(BIG_KECCAK_1024::new(), BIG_KECCAK_1024::new());
777    /// let num: U512 = rand.random_prime_with_msb_set_using_miller_rabin_biguint(5);
778    /// println!("Random number = {}", num);
779    /// ```
780    /// 
781    /// # For more examples,
782    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.new_with)
783    pub fn new_with<SG, AG>(mut main_generator: SG, mut aux_generator: AG) -> Self
784    where SG: Random_Engine + 'static, AG: Random_Engine + 'static
785    {
786        if COUNT == 0
787            { panic!("COUNT should be greater than 0."); }
788
789        let original_seed = Self::collect_seed();
790        let original_aux = Self::collect_seed();
791        let mut state = original_aux.clone();
792        for i in 0..4
793            { state[i << 1] = original_seed[i]; }
794        let main_state = state.clone();
795        for i in 0..8
796            { state[i] = !state[7-i]; }
797        let aux_state = state;
798        main_generator.sow_array(&main_state, &original_seed);
799        aux_generator.sow_array(&aux_state, &original_aux);
800        Self
801        {
802            original_seed,
803            original_aux,
804            main_state,
805            aux_state,
806            count: COUNT,
807            collect_seed: Self::collect_seed,
808            main_generator: Box::new(main_generator),
809            aux_generator: Box::new(aux_generator),
810        }
811    }
812
813    // pub fn new_with_generators_seeds<SG, AG>(mut main_generator: SG, mut aux_generator: AG, seed: u64, aux: u64) -> Self
814    /// Constructs a new `Random_Generic` object with
815    /// two random number generator engines and two seeds of type `u64` given.
816    /// 
817    /// # Arguments
818    /// - `main_generator` is a main random number generator engine
819    ///   which is of `Random_Engine`-type and
820    ///   for generating main pseudo-random numbers.
821    /// - `aux_generator` is an auxiliary random number generator engine
822    ///   which is of `Random_Engine`-type and
823    ///   for generating auxiliary pseudo-random numbers to use in
824    ///   generating the main pseudo-random numbers.
825    /// - `seed` is the seed number of `u64`.
826    /// - `aux` is the seed number of `u64`.
827    /// 
828    /// # Output
829    /// It returns a new object of `Random_Generic`.
830    /// 
831    /// # Panics
832    /// If `COUNT` is `0`, this method will panic!
833    /// 
834    /// # Cryptographical Security
835    /// - If you use either `Random_*` or `Any_*`, it is considered to be
836    ///   cryptographically secure.
837    /// - If you use `Slapdash_*`, it is considered that it may be
838    ///   cryptographically insecure.
839    /// - You are highly recommended to use the method
840    ///   `new_with_generators_seed_arrays()` rather than this method
841    ///   for security reason. It is because the default seed collector function
842    ///   collects 1024 bits as a seed. If you use this method, it results that
843    ///   you give only '128' bits (= '64' bits + '64' bits) as a seed and the
844    ///   other '896' bits will be made out of the '128' bits that you provided.
845    /// 
846    /// # Example 1 for BIG_KECCAK_1024
847    /// ```
848    /// use cryptocol::random::RandGen;
849    /// use cryptocol::hash::BIG_KECCAK_1024;
850    /// use cryptocol::define_utypes_with;
851    /// define_utypes_with!(u64);
852    /// 
853    /// let mut rand = RandGen::new_with_generators_seeds(BIG_KECCAK_1024::new(), BIG_KECCAK_1024::new(), 10500872879054459758_u64, 15887751380961987625_u64);
854    /// let num: U512 = rand.random_prime_with_msb_set_using_miller_rabin_biguint(5);
855    /// println!("Random number = {}", num);
856    /// ```
857    /// 
858    /// # For more examples,
859    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.new_with_generators_seeds)
860    pub fn new_with_generators_seeds<SG, AG>(mut main_generator: SG, mut aux_generator: AG, seed: u64, aux: u64) -> Self
861    where SG: Random_Engine + 'static, AG: Random_Engine + 'static
862    {
863        if COUNT == 0
864            { panic!("COUNT should be greater than 0."); }
865
866        let mut main_state = [0_u64; 8];
867        main_state[1] = 1;
868        main_state[2] = seed;
869        main_state[3] = aux;
870        for i in 4..8
871            { main_state[i] = main_state[i-1].wrapping_add(main_state[i-2]); }
872        let original_seed = [seed, aux, aux.wrapping_add(0xfedcba0987654321), seed.wrapping_add(0xfedcba0987654321), aux.wrapping_sub(0xfedcba0987654321), seed.wrapping_sub(0xfedcba0987654321), seed.wrapping_add(0x1234567890abcdef), aux.wrapping_add(0x1234567890abcdef)];
873        main_generator.sow_array(&main_state, &original_seed);
874
875        let mut aux_state = [0_u64; 8];
876        aux_state[0] = 1;
877        aux_state[2] = aux;
878        aux_state[3] = seed;
879        for i in 4..8
880            { aux_state[i] = !aux_state[i-4]; }
881        let original_aux = [aux, !seed, !seed.wrapping_sub(0xfedcba0987654321), !aux.wrapping_sub(0xfedcba0987654321), !seed.wrapping_add(0xfedcba0987654321), !aux.wrapping_add(0xfedcba0987654321), !aux.wrapping_sub(0x1234567890abcdef), !seed.wrapping_sub(0x1234567890abcdef)];
882        aux_generator.sow_array(&aux_state, &original_aux);
883        Self
884        {
885            original_seed,
886            original_aux,
887            main_state,
888            aux_state,
889            count: COUNT,
890            collect_seed: Self::collect_seed,
891            main_generator: Box::new(main_generator),
892            aux_generator: Box::new(aux_generator),
893        }
894    }
895
896    // pub fn new_with_generators_seed_arrays<SG, AG>(mut main_generator: SG, mut aux_generator: AG, seed: [u64; 8], aux: [u64; 8]) -> Self
897    /// Constructs a new `Random_Generic` object with two random
898    /// number generator engines and two seed arrays of type `u64` given.
899    /// 
900    /// # Arguments
901    /// - `main_generator` is a main random number generator engine
902    ///   which is of `Random_Engine`-type and
903    ///   for generating main pseudo-random numbers.
904    /// - `aux_generator` is an auxiliary random number generator engine
905    ///   which is of `Random_Engine`-type and
906    ///   for generating auxiliary pseudo-random numbers to use in
907    ///   generating the main pseudo-random numbers.
908    /// - `seed` is the seed array and is of `[u64; 8]`.
909    /// - `aux` is the seed array and is of `[u64; 8]`.
910    /// 
911    /// # Output
912    /// It returns a new object of `Random_Generic`.
913    /// 
914    /// # Panics
915    /// If `COUNT` is `0`, this method will panic!
916    /// 
917    /// # Cryptographical Security
918    /// - If you use either `Random_*` or `Any_*`, it is considered to be
919    ///   cryptographically secure.
920    /// - If you use `Slapdash_*`, it is considered that it may be
921    ///   cryptographically insecure.
922    /// - You are highly recommended to use this method rather than the method
923    ///   new_with_generators_seeds for security reason. It is because the
924    ///   default seed collector function collects 1024 bits as a seed. If you
925    ///   use this method, it results that you give full '1024' bits (= '64'
926    ///   bits X '8' X '2') as a seed and it is equivalent to use a seed
927    ///   collector function.
928    /// 
929    /// # Example 1 for BIG_KECCAK_1024
930    /// ```
931    /// use cryptocol::random::{ RandGen, AnyGen, SlapdashGen };
932    /// use cryptocol::define_utypes_with;
933    /// define_utypes_with!(u64);
934    /// 
935    /// use cryptocol::hash::BIG_KECCAK_1024;
936    /// let seed = [10500872879054459758_u64, 14597581050087285790, 10790544591050087758, 17281050044597905758, 15900810579072854758, 10572800879059744558, 13758728710500905448, 15054105075808728459];
937    /// let aux = [10500054459758872879_u64, 15810500854459728790, 10790877585445910500, 10044597872810905758, 10579072855900814758, 14410572800879059558, 17105448597050095872, 18087279054105078459];
938    /// let mut rand = RandGen::new_with_generators_seed_arrays(BIG_KECCAK_1024::new(), BIG_KECCAK_1024::new(), seed, aux);
939    /// let num: U512 = rand.random_prime_with_msb_set_using_miller_rabin_biguint(5);
940    /// println!("Random number = {}", num);
941    /// ```
942    /// 
943    /// # For more examples,
944    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.new_with_generators_seed_arrays)
945    pub fn new_with_generators_seed_arrays<SG, AG>(mut main_generator: SG, mut aux_generator: AG, seed: [u64; 8], aux: [u64; 8]) -> Self
946    where SG: Random_Engine + 'static, AG: Random_Engine + 'static
947    {
948        if COUNT == 0
949            { panic!("COUNT should be greater than 0."); }
950
951        let main_state = seed.clone();
952        main_generator.sow_array(&main_state, &seed);
953
954        let aux_state = aux.clone();
955        aux_generator.sow_array(&aux_state, &aux);
956        Self
957        {
958            original_seed: seed,
959            original_aux: aux,
960            main_state,
961            aux_state,
962            count: COUNT,
963            collect_seed: Self::collect_seed,
964            main_generator: Box::new(main_generator),
965            aux_generator: Box::new(aux_generator),
966        }
967    }
968
969    // pub fn new_with_generators_seed_collector<SG, AG>(mut main_generator: SG, mut aux_generator: AG, seed_collector: fn() -> [u64; 8]) -> Self
970    /// Constructs a new `Random_Generic` object
971    /// with two random number generator engines and a seed collector method.
972    /// 
973    /// # Arguments
974    /// - `main_generator` is a main random number generator engine
975    ///   which is of `Random_Engine`-type and
976    ///   for generating main pseudo-random numbers.
977    /// - `aux_generator` is an auxiliary random number generator engine
978    ///   which is of `Random_Engine`-type and
979    ///   for generating auxiliary pseudo-random numbers to use in
980    ///   generating the main pseudo-random numbers.
981    /// - `seed_collector` is a seed collector function to collect seeds, and
982    ///   is of the type `fn() -> [u64; 8]`.
983    /// 
984    /// # Output
985    /// It returns a new object of `Random_Generic`.
986    /// 
987    /// # Features
988    /// - The default seed collector function is provided in this module,
989    ///   but it is optimized for Unix/Linux though it works under Windows too.
990    /// - If you use this crate under Windows and/or you have a better one,
991    ///   you can use your own seed collector function by replacing the default
992    ///   seed collector function with your own one. 
993    /// 
994    /// # Panics
995    /// If `COUNT` is `0`, this method will panic!
996    /// 
997    /// # Cryptographical Security
998    /// - If you use either `Random_*` or `Any_*`, it is considered to be
999    ///   cryptographically secure.
1000    /// - If you use `Slapdash_*`, it is considered that it may be
1001    ///   cryptographically insecure.
1002    /// 
1003    /// # Example 1 for BIG_KECCAK_1024
1004    /// ```
1005    /// use cryptocol::hash::BIG_KECCAK_1024;
1006    /// use cryptocol::random::RandGen;
1007    /// use cryptocol::define_utypes_with;
1008    /// define_utypes_with!(u64);
1009    /// 
1010    /// fn seed_collector() -> [u64; 8]
1011    /// {
1012    ///     use std::time::{ SystemTime, UNIX_EPOCH };
1013    ///     use cryptocol::number::LongerUnion;
1014    /// 
1015    ///     let ptr = seed_collector as *const fn() -> [u64; 8] as u64;
1016    ///     let mut seed_buffer = [ptr; 8];
1017    ///     for i in 0..8
1018    ///         { seed_buffer[i] ^= ptr.swap_bytes().rotate_left(i as u32); }
1019    /// 
1020    ///     if let Ok(nanos) = SystemTime::now().duration_since(UNIX_EPOCH)
1021    ///     {
1022    ///         let common = LongerUnion::new_with(nanos.as_nanos());
1023    ///         for i in 0..4
1024    ///         {
1025    ///             let j = i << 1;
1026    ///             seed_buffer[j] = common.get_ulong_(0);
1027    ///             seed_buffer[j + 1] = common.get_ulong_(1);
1028    ///         }
1029    ///     }
1030    ///     seed_buffer
1031    /// }
1032    /// 
1033    /// let mut rand = RandGen::new_with_generators_seed_collector(BIG_KECCAK_1024::new(), BIG_KECCAK_1024::new(), seed_collector);
1034    /// let num: U512 = rand.random_prime_with_msb_set_using_miller_rabin_biguint(5);
1035    /// println!("Random number = {}", num);
1036    /// ```
1037    /// 
1038    /// # For more examples,
1039    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.new_with_generators_seed_collector)
1040    pub fn new_with_generators_seed_collector<SG, AG>(mut main_generator: SG, mut aux_generator: AG, seed_collector: fn() -> [u64; 8]) -> Self
1041    where SG: Random_Engine + 'static, AG: Random_Engine + 'static
1042    {
1043        if COUNT == 0
1044            { panic!("COUNT should be greater than 0."); }
1045
1046        let original_seed = seed_collector();
1047        let original_aux = seed_collector();
1048        let mut state = original_aux.clone();
1049        for i in 0..4
1050            { state[i << 1] = original_seed[i]; }
1051        let main_state = state.clone();
1052        for i in 0..8
1053            { state[i] = !state[7-i]; }
1054        let aux_state = state;
1055        main_generator.sow_array(&main_state, &original_seed);
1056        aux_generator.sow_array(&aux_state, &original_aux);
1057        Self
1058        {
1059            original_seed,
1060            original_aux,
1061            main_state,
1062            aux_state,
1063            count: COUNT,
1064            collect_seed: seed_collector,
1065            main_generator: Box::new(main_generator),
1066            aux_generator: Box::new(aux_generator),
1067        }
1068    }
1069
1070    // pub fn new_with_generators_seed_collector_seeds<SG, AG>(mut main_generator: SG, mut aux_generator: AG, seed_collector: fn() -> [u64; 8], seed: u64, aux: u64) -> Self
1071    /// Constructs a new `Random_Generic` object with two random number
1072    /// generator engines, a seed collector function, and two seeds
1073    /// of type `u64` given.
1074    /// 
1075    /// # Arguments
1076    /// - `main_generator` is a main random number generator engine
1077    ///   which is of `Random_Engine`-type and
1078    ///   for generating main pseudo-random numbers.
1079    /// - `aux_generator` is an auxiliary random number generator engine
1080    ///   which is of `Random_Engine`-type and
1081    ///   for generating auxiliary pseudo-random numbers to use in
1082    ///   generating the main pseudo-random numbers.
1083    /// - `seed_collector` is a seed collector function to collect seeds, and
1084    ///   is of the type `fn() -> [u64; 8]`.
1085    /// - `seed` is the seed number of `u64`.
1086    /// - `aux` is the seed number of `u64`.
1087    /// 
1088    /// # Output
1089    /// It returns a new object of `Random_Generic`.
1090    /// 
1091    /// # Features
1092    /// - The default seed collector function is provided in this module,
1093    ///   but it is optimized for Unix/Linux though it works under Windows too.
1094    /// - If you use this crate under Windows and/or you have a better one,
1095    ///   you can use your own seed collector function by replacing the default
1096    ///   seed collector function with your own one.
1097    /// 
1098    /// # Panics
1099    /// If `COUNT` is `0`, this method will panic!
1100    /// 
1101    /// # Cryptographical Security
1102    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1103    ///   cryptographically secure.
1104    /// - If you use `Slapdash_*`, it is considered that it may be
1105    ///   cryptographically insecure.
1106    /// - You are highly recommended to use the method
1107    ///   `new_with_generators_seed_collector_seed_arrays()` rather than this
1108    ///   method for security reason. It is because the default seed collector
1109    ///   function collects 1024 bits as a seed. If you use this method, it
1110    ///   results that you give only '128' bits (= '64' bits + '64' bits) as a
1111    ///   seed and the other '896' bits will be made out of the '128' bits that
1112    ///   you provided.
1113    /// 
1114    /// # Example 1 for BIG_KECCAK_1024
1115    /// ```
1116    /// use cryptocol::hash::BIG_KECCAK_1024;
1117    /// use cryptocol::random::RandGen;
1118    /// use cryptocol::define_utypes_with;
1119    /// define_utypes_with!(u64);
1120    /// 
1121    /// fn seed_collector() -> [u64; 8]
1122    /// {
1123    ///     use std::time::{ SystemTime, UNIX_EPOCH };
1124    ///     use cryptocol::number::LongerUnion;
1125    /// 
1126    ///     let ptr = seed_collector as *const fn() -> [u64; 8] as u64;
1127    ///     let mut seed_buffer = [ptr; 8];
1128    ///     for i in 0..8
1129    ///         { seed_buffer[i] ^= ptr.swap_bytes().rotate_left(i as u32); }
1130    /// 
1131    ///     if let Ok(nanos) = SystemTime::now().duration_since(UNIX_EPOCH)
1132    ///     {
1133    ///         let common = LongerUnion::new_with(nanos.as_nanos());
1134    ///         for i in 0..4
1135    ///         {
1136    ///             let j = i << 1;
1137    ///             seed_buffer[j] = common.get_ulong_(0);
1138    ///             seed_buffer[j + 1] = common.get_ulong_(1);
1139    ///         }
1140    ///     }
1141    ///     seed_buffer
1142    /// }
1143    /// 
1144    /// let mut rand = RandGen::new_with_generators_seed_collector_seeds(BIG_KECCAK_1024::new(), BIG_KECCAK_1024::new(), seed_collector, 10500872879054459758_u64, 15887751380961987625_u64);
1145    /// let num: U512 = rand.random_prime_with_msb_set_using_miller_rabin_biguint(5);
1146    /// println!("Random number = {}", num);
1147    /// ```
1148    /// 
1149    /// # For more examples,
1150    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.new_with_generators_seed_collector_seeds)
1151    pub fn new_with_generators_seed_collector_seeds<SG, AG>(mut main_generator: SG, mut aux_generator: AG, seed_collector: fn() -> [u64; 8], seed: u64, aux: u64) -> Self
1152    where SG: Random_Engine + 'static, AG: Random_Engine + 'static
1153    {
1154        if COUNT == 0
1155            { panic!("COUNT should be greater than 0."); }
1156
1157        let mut main_state = [0_u64; 8];
1158        main_state[1] = 1;
1159        main_state[2] = seed;
1160        main_state[3] = aux;
1161        for i in 4..8
1162            { main_state[i] = main_state[i-1].wrapping_add(main_state[i-2]); }
1163        let original_seed = [seed, aux, aux.wrapping_add(0xfedcba0987654321), seed.wrapping_add(0xfedcba0987654321), aux.wrapping_sub(0xfedcba0987654321), seed.wrapping_sub(0xfedcba0987654321), seed.wrapping_add(0x1234567890abcdef), aux.wrapping_add(0x1234567890abcdef)];
1164        main_generator.sow_array(&main_state, &original_seed);
1165
1166        let mut aux_state = [0_u64; 8];
1167        aux_state[0] = 1;
1168        aux_state[2] = aux;
1169        aux_state[3] = seed;
1170        for i in 4..8
1171            { aux_state[i] = !aux_state[i-4]; }
1172        let original_aux = [aux, !seed, !seed.wrapping_sub(0xfedcba0987654321), !aux.wrapping_sub(0xfedcba0987654321), !seed.wrapping_add(0xfedcba0987654321), !aux.wrapping_add(0xfedcba0987654321), !aux.wrapping_sub(0x1234567890abcdef), !seed.wrapping_sub(0x1234567890abcdef)];
1173        aux_generator.sow_array(&aux_state, &original_aux);
1174        Self
1175        {
1176            original_seed,
1177            original_aux,
1178            main_state,
1179            aux_state,
1180            count: COUNT,
1181            collect_seed: seed_collector,
1182            main_generator: Box::new(main_generator),
1183            aux_generator: Box::new(aux_generator),
1184        }
1185    }
1186
1187    // pub fn new_with_generators_seed_collector_seed_arrays<SG, AG>(mut main_generator: SG, mut aux_generator: AG, seed_collector: fn() -> [u64; 8], seed: [u64; 8], aux: [u64; 8]) -> Self
1188    /// Constructs a new `Random_Generic` object with two random
1189    /// number generator engines and two seed arrays of type `u64`.
1190    /// 
1191    /// # Arguments
1192    /// - `main_generator` is a main random number generator engine
1193    ///   which is of `Random_Engine`-type and
1194    ///   for generating main pseudo-random numbers.
1195    /// - `aux_generator` is an auxiliary random number generator engine
1196    ///   which is of `Random_Engine`-type and
1197    ///   for generating auxiliary pseudo-random numbers to use in
1198    ///   generating the main pseudo-random numbers.
1199    /// - `seed_collector` is a seed collector function to collect seeds, and
1200    ///   is of the type `fn() -> [u64; 8]`.
1201    /// - `seed` is the seed array and is of `[u64; 8]`.
1202    /// - `aux` is the seed array and is of `[u64; 8]`.
1203    /// 
1204    /// # Output
1205    /// It returns a new object of `Random_Generic`.
1206    /// 
1207    /// # Features
1208    /// - The default seed collector function is provided in this module,
1209    ///   but it is optimized for Unix/Linux though it works under Windows too.
1210    /// - If you use this crate under Windows and/or you have a better one,
1211    ///   you can use your own seed collector function by replacing the default
1212    ///   seed collector function with your own one.
1213    /// - You are highly recommended to use this method rather than the method
1214    ///   new_with_generators_seed_collector_seeds for security reason. It is
1215    ///   because the default seed collector function collects 1024 bits as a
1216    ///   seed. If you use this method, it results that you give full '1024'
1217    ///   bits (= '64' bits X '8' X '2') as a seed and it is equivalent to use
1218    ///   a seed collector function
1219    /// 
1220    /// # Panics
1221    /// If `COUNT` is `0`, this method will panic!
1222    /// 
1223    /// # Cryptographical Security
1224    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1225    ///   cryptographically secure.
1226    /// - If you use `Slapdash_*`, it is considered that it may be
1227    ///   cryptographically insecure.
1228    /// 
1229    /// # Example 1 for BIG_KECCAK_1024
1230    /// ```
1231    /// use cryptocol::hash::BIG_KECCAK_1024;
1232    /// use cryptocol::random::RandGen;
1233    /// use cryptocol::define_utypes_with;
1234    /// define_utypes_with!(u64);
1235    /// 
1236    /// fn seed_collector() -> [u64; 8]
1237    /// {
1238    ///     use std::time::{ SystemTime, UNIX_EPOCH };
1239    ///     use cryptocol::number::LongerUnion;
1240    /// 
1241    ///     let ptr = seed_collector as *const fn() -> [u64; 8] as u64;
1242    ///     let mut seed_buffer = [ptr; 8];
1243    ///     for i in 0..8
1244    ///         { seed_buffer[i] ^= ptr.swap_bytes().rotate_left(i as u32); }
1245    /// 
1246    ///     if let Ok(nanos) = SystemTime::now().duration_since(UNIX_EPOCH)
1247    ///     {
1248    ///         let common = LongerUnion::new_with(nanos.as_nanos());
1249    ///         for i in 0..4
1250    ///         {
1251    ///             let j = i << 1;
1252    ///             seed_buffer[j] = common.get_ulong_(0);
1253    ///             seed_buffer[j + 1] = common.get_ulong_(1);
1254    ///         }
1255    ///     }
1256    ///     seed_buffer
1257    /// }
1258    /// 
1259    /// let seed = [10500872879054459758_u64, 14597581050087285790, 10790544591050087758, 17281050044597905758, 15900810579072854758, 10572800879059744558, 13758728710500905448, 15054105075808728459];
1260    /// let aux = [10500054459758872879_u64, 15810500854459728790, 10790877585445910500, 10044597872810905758, 10579072855900814758, 14410572800879059558, 17105448597050095872, 18087279054105078459];
1261    /// let mut rand = RandGen::new_with_generators_seed_collector_seed_arrays(BIG_KECCAK_1024::new(), BIG_KECCAK_1024::new(), seed_collector, seed, aux);
1262    /// let num: U512 = rand.random_prime_with_msb_set_using_miller_rabin_biguint(5);
1263    /// println!("Random number = {}", num);
1264    /// ```
1265    /// 
1266    /// # For more examples,
1267    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.new_with_generators_seed_collector_seed_arrays)
1268    pub fn new_with_generators_seed_collector_seed_arrays<SG, AG>(mut main_generator: SG, mut aux_generator: AG, seed_collector: fn() -> [u64; 8], seed: [u64; 8], aux: [u64; 8]) -> Self
1269    where SG: Random_Engine + 'static, AG: Random_Engine + 'static
1270    {
1271        if COUNT == 0
1272            { panic!("COUNT should be greater than 0."); }
1273
1274        let main_state = seed.clone();
1275        main_generator.sow_array(&main_state, &seed);
1276
1277        let aux_state = aux.clone();
1278        aux_generator.sow_array(&aux_state, &aux);
1279        Self
1280        {
1281            original_seed: seed,
1282            original_aux: aux,
1283            main_state,
1284            aux_state,
1285            count: COUNT,
1286            collect_seed: seed_collector,
1287            main_generator: Box::new(main_generator),
1288            aux_generator: Box::new(aux_generator),
1289        }
1290    }
1291
1292    // fn collect_seed() -> [u64; 8]
1293    /// Collects seed from a system.
1294    /// 
1295    /// # Output
1296    /// It returns a random number array `[u64; 8]` as seeds.
1297    fn collect_seed() -> [u64; 8]
1298    {
1299        let mut seed_buffer = [0_u64; 8];
1300        let mut read_long = 0_usize;
1301        #[cfg(not(target_family = "windows"))]
1302        {
1303            if let Ok(mut file) = File::open("/dev/random")
1304            {
1305                // let mut buffer = [0u8; 64];
1306                // if let Ok(n) = file.read(&mut buffer)
1307                if let Ok(n) = file.read(unsafe { &mut *(seed_buffer.as_mut_ptr() as *mut u8 as *mut [u8; 64]) }) //buffer)
1308                {
1309                    let n = if n >= 64 {64} else {n};
1310                    // unsafe { copy_nonoverlapping(buffer.as_ptr(), seed_buffer.as_mut_ptr() as *mut u8, n); }
1311                    read_long = n >> 3;
1312                    if (n & 0b111) != 0
1313                        { read_long += 1; }
1314                }
1315            }
1316        }
1317        if read_long < 8
1318        {
1319            if let Ok(nanos) = SystemTime::now().duration_since(UNIX_EPOCH)
1320            {
1321                let common = LongerUnion::new_with(nanos.as_nanos());
1322                seed_buffer[read_long] = common.get_ulong_(0);
1323                read_long += 1;
1324                if read_long < 8
1325                {
1326                    seed_buffer[read_long] = common.get_ulong_(1);
1327                    read_long += 1;
1328                }
1329            }
1330        }
1331        for i in read_long..8
1332            { seed_buffer[i] = RandomState::new().build_hasher().finish(); }
1333        seed_buffer
1334    }
1335
1336    // fn collect_seed_u64() -> u64
1337    /// Collects eight-byte seed from a system.
1338    /// 
1339    /// # Output
1340    /// It returns a true random number `u64` made as a seed.
1341    pub(super) fn collect_seed_u64() -> u64
1342    {
1343        #[cfg(not(target_family = "windows"))]
1344        {
1345            if let Ok(mut file) = File::open("/dev/random")
1346            {
1347                let mut buffer = [0u8; 8];
1348                if let Ok(_) = file.read(&mut buffer)
1349                {
1350                    let seed = LongUnion::new_with_ubytes(buffer);
1351                    return seed.get();
1352                }
1353            }
1354        }
1355        if let Ok(nanos) = SystemTime::now().duration_since(UNIX_EPOCH)
1356        {
1357            let common = LongerUnion::new_with(nanos.as_nanos());
1358            let idx = (common.get_ulong_(0) & 1) as usize;
1359            common.get_ulong_(idx)
1360        }
1361        else
1362        {
1363            let common = LongUnion::new_with(RandomState::new().build_hasher().finish());
1364            common.get()
1365        }
1366    }
1367
1368    // fn produce_main_state(&mut self) -> [u64; 8]
1369    /// Runs the registered pseudo-random number generator to prepare for
1370    /// generating a random number for main_state.
1371    fn produce_main_state(&mut self)
1372    {
1373        self.change_count();
1374        for i in 0..8
1375            { self.main_state[i] ^= self.original_seed[i]; }
1376        let xor = self.count ^ (self.original_aux[0] as u128 | (self.original_aux[1] as u128) << 64);
1377        let count = if (self.count == 0) || (xor == 0) {self.count} else {xor};
1378        self.main_state = self.main_generator.harvest(count, &self.main_state);
1379    }
1380
1381    // fn produce_aux_state(&mut self) -> [u64; 8]
1382    /// Runs the registered pseudo-random number generator to prepare for
1383    /// generating a random number for aux_state.
1384    fn produce_aux_state(&mut self)
1385    {
1386        self.change_count();
1387        for i in 0..8
1388            { self.aux_state[i] ^= self.original_aux[i]; }
1389        let xor = self.count ^ (self.original_seed[0] as u128 | (self.original_seed[1] as u128) << 64);
1390        let count = if (self.count == 0) || (xor == 0) {self.count} else {xor};
1391        self.aux_state = self.aux_generator.harvest(count, &self.aux_state);
1392    }
1393
1394    // fn change_count(&mut self)
1395    /// Changes`self.count` and `self.sugar` when `self.count` becomes `0`,
1396    /// changes the seeds for both generators when `self.sugar` becomes `true`.
1397    /// Otherwise, subracts `1` from `self.count`.
1398    fn change_count(&mut self)
1399    {
1400        if self.is_restarted()
1401        {
1402            self.count = COUNT;
1403        }
1404        self.count = self.count.wrapping_sub(1);
1405        if self.is_restarted()
1406        {
1407            self.original_seed = (self.collect_seed)();
1408            self.original_aux = (self.collect_seed)();
1409            for i in 0..8
1410            {
1411                self.main_state[i] ^= self.original_aux[i];
1412                self.aux_state[i] ^= self.original_seed[i];
1413            }
1414            self.main_generator.sow_array(&self.main_state, &self.original_seed);
1415            self.aux_generator.sow_array(&self.aux_state, &self.original_aux);
1416        }
1417    }
1418
1419    #[inline]
1420    fn is_restarted(&self) -> bool    { self.count == 0 }
1421
1422    // pub fn get_seed_collector(&self) -> fn() -> [u64; 8]
1423    /// Returns the function pointer to the current seed collector function.
1424    /// 
1425    /// # Output
1426    /// It returns the function pointer to the current seed collector function,
1427    /// and is of the type `fn() -> [u64; 8]`.
1428    /// 
1429    /// # Example 1 for Random
1430    /// ```
1431    /// use cryptocol::random::Random;
1432    /// let rand = Random::new();
1433    /// let seed = rand.get_seed_collector()();
1434    /// print!("seed = ");
1435    /// for i in 0..8
1436    ///     { print!("{} ", seed[i]); }
1437    /// ```
1438    /// 
1439    /// # For more examples,
1440    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.get_seed_collector)
1441    #[inline]
1442    pub fn get_seed_collector(&self) -> fn() -> [u64; 8]
1443    {
1444        self.collect_seed
1445    }
1446
1447    // pub fn set_seed_collector(&mut self, collect_seed: fn() -> [u64; 8])
1448    /// Replaces the default seed collector function
1449    /// with new seed collector function.
1450    /// 
1451    /// # Arguments
1452    /// `collect_seed` is a new seed collector function to replace the default
1453    /// seed collector function, and is of the type `fn() -> [u64; 8]`.
1454    /// 
1455    /// # Example 1 for Random
1456    /// ```
1457    /// use cryptocol::random::Random;
1458    /// fn seed_collector() -> [u64; 8]
1459    /// {
1460    ///     use std::time::{ SystemTime, UNIX_EPOCH };
1461    ///     use cryptocol::number::LongerUnion;
1462    /// 
1463    ///     let ptr = seed_collector as *const fn() -> [u64; 8] as u64;
1464    ///     let mut seed_buffer = [ptr; 8];
1465    ///     for i in 0..8
1466    ///         { seed_buffer[i] ^= ptr.swap_bytes().rotate_left(i as u32); }
1467    /// 
1468    ///     if let Ok(nanos) = SystemTime::now().duration_since(UNIX_EPOCH)
1469    ///     {
1470    ///         let common = LongerUnion::new_with(nanos.as_nanos());
1471    ///         for i in 0..4
1472    ///         {
1473    ///             let j = i << 1;
1474    ///             seed_buffer[j] = common.get_ulong_(0);
1475    ///             seed_buffer[j + 1] = common.get_ulong_(1);
1476    ///         }
1477    ///     }
1478    ///     seed_buffer
1479    /// }
1480    /// type Func = *const fn() -> [u64; 8];
1481    /// 
1482    /// let mut rand = Random::new();
1483    /// rand.set_seed_collector(seed_collector);
1484    /// assert_eq!(seed_collector as Func, rand.get_seed_collector() as Func);
1485    /// println!("seed = {}", rand.random_u128());
1486    /// ```
1487    /// 
1488    /// # For more examples,
1489    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.set_seed_collector)
1490    #[inline]
1491    pub fn set_seed_collector(&mut self, seed_collector: fn() -> [u64; 8])
1492    {
1493        self.collect_seed = seed_collector;
1494    }
1495
1496    // pub fn reset_seed_collector(&mut self)
1497    /// Replace the current seed collector function
1498    /// with the default seed collector function.
1499    /// 
1500    /// # Features
1501    /// After this method is performed, the previous seed collector function
1502    /// will be lost.
1503    /// 
1504    /// # Example 1 for Random
1505    /// ```
1506    /// fn seed_collector() -> [u64; 8]
1507    /// {
1508    ///     [0_u64; 8]
1509    /// }
1510    /// type Func = *const fn() -> [u64; 8];
1511    /// 
1512    /// use cryptocol::random::Random;
1513    /// let mut rand = Random::new();
1514    /// let collector = rand.get_seed_collector();
1515    /// rand.set_seed_collector(seed_collector);
1516    /// assert_eq!(seed_collector as Func, rand.get_seed_collector() as Func);
1517    /// rand.reset_seed_collector();
1518    /// assert_eq!(collector as Func, rand.get_seed_collector() as Func);
1519    /// ```
1520    /// 
1521    /// # For more examples,
1522    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.reset_seed_collector)
1523    #[inline]
1524    pub fn reset_seed_collector(&mut self)
1525    {
1526        self.collect_seed = Self::collect_seed;
1527    }
1528
1529    // pub fn random_u8(&mut self) -> u8
1530    /// Generates random numbers of type `u8`.
1531    /// 
1532    /// # Output
1533    /// It returns a random number of type `u8`.
1534    /// 
1535    /// # Cryptographical Security
1536    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1537    ///   cryptographically secure.
1538    /// - If you use `Slapdash_*`, it is considered that it may be
1539    ///   cryptographically insecure.
1540    /// 
1541    /// # Example 1 for Random
1542    /// ```
1543    /// use cryptocol::random::Random;
1544    /// let mut rand = Random::new();
1545    /// for i in 0..10
1546    ///     { println!("{} Random number (Random) = {}", i, rand.random_u8()); }
1547    /// ```
1548    /// 
1549    /// # For more examples,
1550    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_u8)
1551    pub fn random_u8(&mut self) -> u8
1552    {
1553        self.produce_aux_state();
1554        self.produce_main_state();
1555        let mut i = self.main_state[0] as usize & 0b111;
1556        let mut j = self.main_state[1] as usize & 0b111;
1557        i = self.aux_state[i] as usize & 0b111;
1558        j = self.aux_state[j] as usize & 0b111;
1559        LongUnion::new_with(self.main_state[i]).get_ubyte_(j)
1560    }
1561
1562    // pub fn random_u16(&mut self) -> u16
1563    /// Generates random numbers of type `u16`.
1564    /// 
1565    /// # Output
1566    /// It returns a random number of type `u16`.
1567    /// 
1568    /// # Cryptographical Security
1569    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1570    ///   cryptographically secure.
1571    /// - If you use `Slapdash_*`, it is considered that it may be
1572    ///   cryptographically insecure.
1573    /// 
1574    /// # Example 1 for Random
1575    /// ```
1576    /// use cryptocol::random::Random;
1577    /// let mut rand = Random::new();
1578    /// for i in 0..10
1579    ///     { println!("{} Random number (Random) = {}", i, rand.random_u16()); }
1580    /// ```
1581    /// 
1582    /// # For more examples,
1583    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_u16)
1584    pub fn random_u16(&mut self) -> u16
1585    {
1586        self.produce_aux_state();
1587        self.produce_main_state();
1588        let mut i = self.main_state[2] as usize & 0b111;
1589        let mut j = self.main_state[3] as usize & 0b111;
1590        i = self.aux_state[i] as usize & 0b111;
1591        j = self.aux_state[j] as usize & 0b11;
1592        LongUnion::new_with(self.main_state[i]).get_ushort_(j)
1593    }
1594
1595    // pub fn random_u32(&mut self) -> u32
1596    /// Generates random numbers of type `u32`.
1597    /// 
1598    /// # Output
1599    /// It returns a random number of type `u32`.
1600    /// 
1601    /// # Cryptographical Security
1602    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1603    ///   cryptographically secure.
1604    /// - If you use `Slapdash_*`, it is considered that it may be
1605    ///   cryptographically insecure.
1606    /// 
1607    /// # Example 1 for Random
1608    /// ```
1609    /// use cryptocol::random::Random;
1610    /// let mut rand = Random::new();
1611    /// for i in 0..10
1612    ///     { println!("{} Random number (Random) = {}", i, rand.random_u32()); }
1613    /// ```
1614    /// 
1615    /// # For more examples,
1616    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_u32)
1617    pub fn random_u32(&mut self) -> u32
1618    {
1619        self.produce_aux_state();
1620        self.produce_main_state();
1621        let mut i = self.main_state[4] as usize & 0b111;
1622        let mut j = self.main_state[5] as usize & 0b111;
1623        i = self.aux_state[i] as usize & 0b111;
1624        j = self.aux_state[j] as usize & 1;
1625        LongUnion::new_with(self.main_state[i]).get_uint_(j)
1626    }
1627
1628    // pub fn random_u64(&mut self) -> u64
1629    /// Generates random numbers of type `u64`.
1630    /// 
1631    /// # Output
1632    /// It returns a random number of type `u64`.
1633    /// 
1634    /// # Cryptographical Security
1635    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1636    ///   cryptographically secure.
1637    /// - If you use `Slapdash_*`, it is considered that it may be
1638    ///   cryptographically insecure.
1639    /// 
1640    /// # Example 1 for Random
1641    /// ```
1642    /// use cryptocol::random::Random;
1643    /// let mut rand = Random::new();
1644    /// for i in 0..10
1645    ///     { println!("{} Random number (Random) = {}", i, rand.random_u64()); }
1646    /// ```
1647    /// 
1648    /// # For more examples,
1649    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_u64)
1650    pub fn random_u64(&mut self) -> u64
1651    {
1652        self.produce_aux_state();
1653        self.produce_main_state();
1654        let mut i = self.main_state[0] as usize & 0b111;
1655        i = self.aux_state[i] as usize & 0b111;
1656        self.main_state[i]
1657    }
1658
1659    // pub fn random_u128(&mut self) -> u128
1660    /// Generates random numbers of type `u128`.
1661    /// 
1662    /// # Output
1663    /// It returns a random number of type `u128`.
1664    /// 
1665    /// # Cryptographical Security
1666    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1667    ///   cryptographically secure.
1668    /// - If you use `Slapdash_*`, it is considered that it may be
1669    ///   cryptographically insecure.
1670    /// 
1671    /// # Example 1 for Random
1672    /// ```
1673    /// use cryptocol::random::Random;
1674    /// let mut rand = Random::new();
1675    /// for i in 0..10
1676    ///     { println!("{} Random number (Random) = {}", i, rand.random_u128()); }
1677    /// ```
1678    /// 
1679    /// # For more examples,
1680    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_u128)
1681    pub fn random_u128(&mut self) -> u128
1682    {
1683        self.produce_aux_state();
1684        self.produce_main_state();
1685        let mut i = self.main_state[6] as usize & 0b111;
1686        let mut j = self.main_state[7] as usize & 0b111;
1687        i = self.aux_state[i] as usize & 0b111;
1688        j = self.aux_state[j] as usize & 0b111;
1689        let mut res = LongerUnion::new();
1690        res.set_ulong(0, self.main_state[i]);
1691        res.set_ulong(1, self.main_state[j]);
1692        res.get()
1693    }
1694
1695    // pub fn random_usize(&mut self) -> usize
1696    /// Generates random numbers of type `usize`.
1697    /// 
1698    /// # Output
1699    /// It returns a random number of type `usize`.
1700    /// 
1701    /// # Cryptographical Security
1702    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1703    ///   cryptographically secure.
1704    /// - If you use `Slapdash_*`, it is considered that it may be
1705    ///   cryptographically insecure.
1706    /// 
1707    /// # Example 1 for Random
1708    /// ```
1709    /// use cryptocol::random::Random;
1710    /// let mut rand = Random::new();
1711    /// for i in 0..10
1712    ///     { println!("{} Random number (Random) = {}", i, rand.random_usize()); }
1713    /// ```
1714    /// 
1715    /// # For more examples,
1716    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_usize)
1717    #[inline]
1718    pub fn random_usize(&mut self) -> usize
1719    {
1720        // #[cfg(target_pointer_width = "8")]      return self.random_u8().into_usize();
1721        #[cfg(target_pointer_width = "16")]     return self.random_u16().into_usize();
1722        #[cfg(target_pointer_width = "32")]     return self.random_u32().into_usize();
1723        #[cfg(target_pointer_width = "64")]     return self.random_u64().into_usize();
1724        // #[cfg(target_pointer_width = "128")]    return self.random_u128().into_usize();
1725    }
1726
1727    // pub fn random_uint<T>(&mut self) -> T
1728    /// Generates random numbers of type `T`.
1729    /// 
1730    /// # Output
1731    /// It returns a random number of type `T`.
1732    /// 
1733    /// # Cryptographical Security
1734    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1735    ///   cryptographically secure.
1736    /// - If you use `Slapdash_*`, it is considered that it may be
1737    ///   cryptographically insecure.
1738    /// 
1739    /// # Example 1 for Random
1740    /// ```
1741    /// use cryptocol::random::Random;
1742    /// let mut rand = Random::new();
1743    /// for i in 0..10
1744    ///     { println!("{} Random number (Random) = {}", i, rand.random_uint::<u8>()); }
1745    /// ```
1746    /// 
1747    /// # For more examples,
1748    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_uint)
1749    pub fn random_uint<T>(&mut self) -> T
1750    where T: SmallUInt
1751    {
1752        match T::size_in_bytes()
1753        {
1754            1 => T::u8_as_smalluint(self.random_u8()),
1755            2 => T::u16_as_smalluint(self.random_u16()),
1756            4 => T::u32_as_smalluint(self.random_u32()),
1757            8 => T::u64_as_smalluint(self.random_u64()),
1758            _ => T::u128_as_smalluint(self.random_u128()),
1759        }
1760    }
1761
1762    // pub fn random_under_uint<T>(&mut self, ceiling: T) -> Option<T>
1763    /// Generates random numbers of type `T` less than `ceiling`.
1764    /// 
1765    /// # Argument
1766    /// The argument `ceiling` is the upper limitation which the generated
1767    /// random number should be less than, and is of the type `T`.
1768    /// 
1769    /// # Output
1770    /// It returns a random number of type `T` less than `ceiling`
1771    /// wrapped by enum `Some` of `Option`.
1772    /// 
1773    /// # Features
1774    /// If `ceiling` is `0`, it returns `None`. Otherwise, it returns a
1775    /// random number of type `T` wrapped by enum `Some` of `Option`.
1776    /// 
1777    /// # Cryptographical Security
1778    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1779    ///   cryptographically secure.
1780    /// - If you use `Slapdash_*`, it is considered that it may be
1781    ///   cryptographically insecure.
1782    /// 
1783    /// # Example 1 for Random
1784    /// ```
1785    /// use cryptocol::random::Random;
1786    /// let mut rand = Random::new();
1787    /// if let Some(num) = rand.random_under_uint(12_u8)
1788    ///     { println!("Random number u8 = {}", num); }
1789    /// ```
1790    /// 
1791    /// # For more examples,
1792    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_under_uint)
1793    #[inline]
1794    pub fn random_under_uint<T>(&mut self, ceiling: T) -> Option<T>
1795    where T: SmallUInt
1796    {
1797        if ceiling != T::zero() { Some(self.random_under_uint_::<T>(ceiling)) } else { None }
1798    }
1799
1800    // pub fn random_under_uint_<T>(&mut self, ceiling: T) -> T
1801    /// Generates random numbers of type `T` less than `ceiling`.
1802    /// 
1803    /// # Argument
1804    /// The argument `ceiling` is the upper limitation which the generated
1805    /// random number should be less than, and is of the type `T`.
1806    /// 
1807    /// # Output
1808    /// It returns a random number of type `T` less than `ceiling`.
1809    /// 
1810    /// # Panics
1811    /// If `ceiling` is `0`, it will panic.
1812    /// 
1813    /// # Caution
1814    /// Use only when `ceiling` is not `0`.
1815    /// 
1816    /// # Cryptographical Security
1817    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1818    ///   cryptographically secure.
1819    /// - If you use `Slapdash_*`, it is considered that it may be
1820    ///   cryptographically insecure.
1821    /// 
1822    /// # Example 1 for Random
1823    /// ```
1824    /// use cryptocol::random::Random;
1825    /// let mut rand = Random::new();
1826    /// let num = rand.random_under_uint_(12_u8);
1827    /// println!("Random number u8 = {}", num);
1828    /// ```
1829    /// 
1830    /// # For more examples,
1831    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_under_uint_)
1832    #[inline]
1833    pub fn random_under_uint_<T>(&mut self, ceiling: T) -> T
1834    where T: SmallUInt
1835    {
1836        self.random_uint::<T>() % ceiling
1837    }
1838
1839    // pub fn random_minmax_uint<T>(&mut self, from: T, ceiling: T) -> Option<T>
1840    /// Generates random numbers of type `T` less than `ceiling` exclusively
1841    /// and greater than or equal to `from` inclusively.
1842    /// 
1843    /// # Arguments
1844    /// - `from` is the lower limitation which the generated random number
1845    ///   should be greater than or equal to, and is of the type `T`..
1846    /// - `ceiling` is the upper limitation which the generated random number
1847    ///   should be less than, and is of the type `T`.
1848    /// 
1849    /// # Output
1850    /// If `ceiling` is `0` or `from` is greater than or equal to `ceiling`,
1851    /// it returns a random number of type `T` less than `ceiling` and greater
1852    /// than or equal to `from`, and the returned random number is wrapped by
1853    /// enum `Some` of `Option`. Otherwise, it returns enum `None` of `Option`.
1854    /// 
1855    /// # Cryptographical Security
1856    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1857    ///   cryptographically secure.
1858    /// - If you use `Slapdash_*`, it is considered that it may be
1859    ///   cryptographically insecure.
1860    /// 
1861    /// # Example 1
1862    /// ```
1863    /// use cryptocol::random::Random;
1864    /// let mut rand = Random::new();
1865    /// if let Some(num) = rand.random_minmax_uint(12_u8, 21)
1866    ///     { println!("Random number u8 = {}", num); }
1867    /// ```
1868    /// 
1869    /// # For more examples,
1870    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_minmax_uint)
1871    #[inline]
1872    pub fn random_minmax_uint<T>(&mut self, from: T, ceiling: T) -> Option<T>
1873    where T: SmallUInt
1874    {
1875        if ceiling > from { Some(self.random_minmax_uint_(from, ceiling)) } else { None }
1876    }
1877
1878    // pub fn random_minmax_uint_<T>(&mut self, from: T, ceiling: T) -> T
1879    /// Generates random numbers of type `T` less than `ceiling` exclusively
1880    /// and greater than or equal to `from` inclusively.
1881    /// 
1882    /// # Arguments
1883    /// - `from` is the lower limitation which the generated random number
1884    ///   should be greater than or equal to, and is of the type `T`..
1885    /// - `ceiling` is the upper limitation which the generated random number
1886    ///   should be less than, and is of the type `T`.
1887    /// 
1888    /// # Output
1889    /// It returns a random number of type `T` less than `ceiling`
1890    /// and greater than or equal to `from`.
1891    /// 
1892    /// # Panics
1893    /// If `ceiling` is `0` or `from` is greater than or equal to `ceiling`,
1894    /// it will panic.
1895    /// 
1896    /// # Caution
1897    /// Use this method only when you are sure that `ceiling` is not `0`
1898    /// and `from` is less than `ceiling`.
1899    /// 
1900    /// # Cryptographical Security
1901    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1902    ///   cryptographically secure.
1903    /// - If you use `Slapdash_*`, it is considered that it may be
1904    ///   cryptographically insecure.
1905    /// 
1906    /// # Example 1 for Random
1907    /// ```
1908    /// use cryptocol::random::Random;
1909    /// let mut rand = Random::new();
1910    /// let num = rand.;random_minmax_uint_(12_u8, 21)
1911    /// println!("Random number u8 = {}", num);
1912    /// ```
1913    /// 
1914    /// # For more examples,
1915    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_minmax_uint_)
1916    #[inline]
1917    pub fn random_minmax_uint_<T>(&mut self, from: T, ceiling: T) -> T
1918    where T: SmallUInt
1919    {
1920        self.random_under_uint_(ceiling - from) + from
1921    }
1922
1923    // pub fn random_odd_uint<T>(&mut self) -> T
1924    /// Generates random odd numbers of type `T`.
1925    /// 
1926    /// # Output
1927    /// It returns a random odd number of type `T`.
1928    /// 
1929    /// # Cryptographical Security
1930    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1931    ///   cryptographically secure.
1932    /// - If you use `Slapdash_*`, it is considered that it may be
1933    ///   cryptographically insecure.
1934    /// 
1935    /// # Example 1 for Random
1936    /// ```
1937    /// use cryptocol::random::Random;
1938    /// let mut rand = Random::new();
1939    /// println!("Random odd number u8 = {}", rand.random_odd_uint::<u8>());
1940    /// println!("Random odd number u16 = {}", rand.random_odd_uint::<u16>());
1941    /// println!("Random odd number u32 = {}", rand.random_odd_uint::<u32>());
1942    /// println!("Random odd number u64 = {}", rand.random_odd_uint::<u64>());
1943    /// println!("Random odd number u128 = {}", rand.random_odd_uint::<u128>());
1944    /// println!("Random odd number usize = {}", rand.random_odd_uint::<usize>());
1945    /// ```
1946    /// 
1947    /// # For more examples,
1948    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_odd_uint)
1949    pub fn random_odd_uint<T>(&mut self) -> T
1950    where T: SmallUInt
1951    {
1952        let mut res = self.random_uint::<T>();
1953        res.set_lsb();
1954        res
1955    }
1956
1957    // pub fn random_odd_under_uint<T>(&mut self, ceiling: T) -> Option<T>
1958    /// Generates random odd numbers of type `T` less than `ceiling`.
1959    /// 
1960    /// # Argument
1961    /// The argument `ceiling` is the upper limitation which the generated
1962    /// random number should be less than, and is of the type `T`.
1963    /// 
1964    /// # Output
1965    /// It returns a random odd numbers of type `T` less than `ceiling`
1966    /// wrapped by enum `Some` of `Option`.
1967    /// 
1968    /// # Features
1969    /// If `ceiling` is less than `2`, it returns `None`. Otherwise, it returns
1970    /// a random odd numbers of type `T` wrapped by enum `Some` of `Option`.
1971    /// 
1972    /// # Cryptographical Security
1973    /// - If you use either `Random_*` or `Any_*`, it is considered to be
1974    ///   cryptographically secure.
1975    /// - If you use `Slapdash_*`, it is considered that it may be
1976    ///   cryptographically insecure.
1977    /// 
1978    /// # Example 1 for Random
1979    /// ```
1980    /// use cryptocol::random::Random;
1981    /// let mut rand = Random::new();
1982    /// if let Some(num) = rand.random_odd_under_uint(12_u8)
1983    ///     { println!("Random odd number u8 = {}", num); }
1984    /// if let Some(num) = rand.random_odd_under_uint(1234_u16)
1985    ///     { println!("Random odd number u16 = {}", num); }
1986    /// if let Some(num) = rand.random_odd_under_uint(12345678_u32)
1987    ///     { println!("Random odd number u32 = {}", num); }
1988    /// if let Some(num) = rand.random_odd_under_uint(1234567890123456_u64)
1989    ///     { println!("Random odd number u64 = {}", num); }
1990    /// if let Some(num) = rand.random_odd_under_uint(12345678901234567890_u128)
1991    ///     { println!("Random odd number u128 = {}", num); }
1992    /// if let Some(num) = rand.random_odd_under_uint(123456789_usize)
1993    ///     { println!("Random odd number usize = {}", num); }
1994    /// if let Some(num) = rand.random_odd_under_uint(0_usize)
1995    ///     { println!("Random odd number usize = {}", num); }
1996    /// else
1997    ///     { println!("No random unsigned odd number under 0!"); }
1998    /// ```
1999    /// 
2000    /// # For more examples,
2001    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_odd_under_uint)
2002    #[inline]
2003    pub fn random_odd_under_uint<T>(&mut self, ceiling: T) -> Option<T>
2004    where T: SmallUInt
2005    {
2006        if ceiling.is_zero_or_one() { None } else { Some(self.random_odd_under_uint_(ceiling)) }
2007    }
2008
2009    // pub fn random_odd_under_uint_<T>(&mut self, ceiling: T) -> T
2010    /// Generates random odd numbers of type `T` less than `ceiling`.
2011    /// 
2012    /// # Argument
2013    /// The argument `ceiling` is the upper limitation which the generated
2014    /// random number should be less than, and is of the type `T`.
2015    /// 
2016    /// # Output
2017    /// It returns a random odd numbers of type `T` less than `ceiling`.
2018    /// 
2019    /// # Panics
2020    /// If `ceiling` is less than `2`, it will panic.
2021    /// 
2022    /// # Caution
2023    /// Use this method only when `ceiling` is greater than `1`.
2024    /// 
2025    /// # Cryptographical Security
2026    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2027    ///   cryptographically secure.
2028    /// - If you use `Slapdash_*`, it is considered that it may be
2029    ///   cryptographically insecure.
2030    /// 
2031    /// # Example 1 for Random
2032    /// ```
2033    /// use cryptocol::random::Random;
2034    /// let mut rand = Random::new();
2035    /// 
2036    /// let num = rand.random_odd_under_uint_(12_u8);
2037    /// println!("Random odd number u8 = {}", num);
2038    /// 
2039    /// let num = rand.random_odd_under_uint_(1234_u16);
2040    /// println!("Random odd number u16 = {}", num);
2041    /// 
2042    /// let num = rand.random_odd_under_uint_(12345678_u32);
2043    /// println!("Random odd number u32 = {}", num);
2044    /// 
2045    /// let num = rand.random_odd_under_uint_(1234567890123456_u64);
2046    /// println!("Random odd number u64 = {}", num);
2047    /// 
2048    /// let num = rand.random_odd_under_uint_(12345678901234567890_u128);
2049    /// println!("Random odd number u128 = {}", num);
2050    /// 
2051    /// let num = rand.random_odd_under_uint_(123456789_usize);
2052    /// println!("Random odd number usize = {}", num);
2053    /// ```
2054    /// 
2055    /// # For more examples,
2056    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_odd_under_uint_)
2057    pub fn random_odd_under_uint_<T>(&mut self, mut ceiling: T) -> T
2058    where T: SmallUInt
2059    {
2060        if ceiling.is_zero_or_one()
2061            { panic!(); }
2062        ceiling.reset_lsb();
2063        let mut res = self.random_under_uint_(ceiling);
2064        res.set_lsb();
2065        res
2066    }
2067
2068    // pub fn random_with_msb_set_uint<T>(&mut self) -> T
2069    /// Generates random numbers of type `T` and of maximum size of `T`.
2070    /// 
2071    /// # Output
2072    /// It returns random numbers of type `T` and of maximum size of `T`.
2073    /// 
2074    /// # Cryptographical Security
2075    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2076    ///   cryptographically secure.
2077    /// - If you use `Slapdash_*`, it is considered that it may be
2078    ///   cryptographically insecure.
2079    /// 
2080    /// # Example 1 for Random
2081    /// ```
2082    /// use cryptocol::random::Random;
2083    /// let mut rand = Random::new();
2084    /// println!("Random 8-bit number = {}", rand.random_with_msb_set_uint::<u8>());
2085    /// println!("Random 16-bit number = {}", rand.random_with_msb_set_uint::<u16>());
2086    /// println!("Random 32-bit number = {}", rand.random_with_msb_set_uint::<u32>());
2087    /// println!("Random 64-bit number = {}", rand.random_with_msb_set_uint::<u64>());
2088    /// println!("Random 128-bit number = {}", rand.random_with_msb_set_uint::<u128>());
2089    /// println!("Random usize-sized number = {}", rand.random_with_msb_set_uint::<usize>());
2090    /// ```
2091    /// 
2092    /// # For more examples,
2093    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_with_msb_set_uint)
2094    pub fn random_with_msb_set_uint<T>(&mut self) -> T
2095    where T: SmallUInt
2096    {
2097        let mut res = self.random_uint::<T>();
2098        res.set_msb();
2099        res
2100    }
2101
2102    // pub fn random_odd_with_msb_set_uint<T>(&mut self) -> T
2103    /// Generates random odd numbers of type `T` and of maximum size of `T`.
2104    /// 
2105    /// # Output
2106    /// It returns random odd numbers of type `T` and of maximum size of `T`.
2107    /// 
2108    /// # Cryptographical Security
2109    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2110    ///   cryptographically secure.
2111    /// - If you use `Slapdash_*`, it is considered that it may be
2112    ///   cryptographically insecure.
2113    /// 
2114    /// # Example 1 for Random
2115    /// ```
2116    /// use cryptocol::random::Random;
2117    /// let mut rand = Random::new();
2118    /// println!("Random 8-bit odd number = {}", rand.random_odd_with_msb_set_uint::<u8>());
2119    /// println!("Random 16-bit odd number = {}", rand.random_odd_with_msb_set_uint::<u16>());
2120    /// println!("Random 32-bit odd number = {}", rand.random_odd_with_msb_set_uint::<u32>());
2121    /// println!("Random 64-bit odd number = {}", rand.random_odd_with_msb_set_uint::<u64>());
2122    /// println!("Random 128-bit odd number = {}", rand.random_odd_with_msb_set_uint::<u128>());
2123    /// println!("Random usize-sized odd number = {}", rand.random_odd_with_msb_set_uint::<usize>());
2124    /// ```
2125    /// 
2126    /// # For more examples,
2127    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_odd_with_msb_set_uint)
2128    pub fn random_odd_with_msb_set_uint<T>(&mut self) -> T
2129    where T: SmallUInt
2130    {
2131        let mut res = self.random_odd_uint::<T>();
2132        res.set_msb();
2133        res
2134    }
2135
2136    // pub fn random_prime_using_miller_rabin_uint<T>(&mut self, repetition: usize) -> T
2137    /// Returns a random prime number.
2138    /// 
2139    /// # Argument
2140    /// The argument `repetition` defines how many times it tests whether or not
2141    /// the generated random number is prime. Usually, `repetition` is given to
2142    /// be 5 to have 99.9% hit rate.
2143    /// 
2144    /// # Output
2145    /// A random prime number whose range is from 2 up to T::max() inclusively.
2146    /// 
2147    /// # Features
2148    /// - It uses
2149    ///   [Miller Rabin algorithm](https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test).
2150    /// - If this test results in composite number, the tested number is surely
2151    ///   a composite number. If this test results in notprime number, the
2152    ///   probability that the tested number is not a prime number is 1/4 (= 25%).
2153    ///   So, if the test results in prime number twice, the probability that the
2154    ///   tested number is not a prime number is 1/16 (= 1/4 * 1/4 = 6.25%).
2155    ///   Therefore, if you test any number 5 times and they all result in a prime
2156    ///   number, the probability that the tested number is not a prime number is
2157    ///   1/1024 = (= 1/4 * 1/4 * 1/4 * 1/4 * 1/4 = 0.09765625%). In other words,
2158    ///   it is about 99.9% that the number is a prime number.
2159    /// - The random prime numbers that may or may not be cryptographically
2160    ///   secure depending on what pseudo-random number generator is used.
2161    /// 
2162    /// # Cryptographical Security
2163    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2164    ///   cryptographically secure.
2165    /// - If you use `Slapdash_*`, it is considered that it may be
2166    ///   cryptographically insecure.
2167    /// 
2168    /// # Counterpart Methods
2169    /// If you want to use a `(sizeof::<T>() * 8)`-bit long random prime
2170    /// number, you are highly recommended to use the method
2171    /// [random_prime_with_msb_set_using_miller_rabin_uint()](struct@Random_Generic#method.random_prime_with_msb_set_using_miller_rabin_uint)
2172    /// rather than this method.
2173    /// 
2174    /// # Example 1 for Random
2175    /// ```
2176    /// use cryptocol::random::Random;
2177    /// let mut rand = Random::new();
2178    /// println!("Random 8-bit prime number = {}", rand.random_prime_using_miller_rabin_uint::<u8>(5));
2179    /// println!("Random 16-bit prime number = {}", rand.random_prime_using_miller_rabin_uint::<u16>(5));
2180    /// println!("Random 32-bit prime number = {}", rand.random_prime_using_miller_rabin_uint::<u32>(5));
2181    /// println!("Random 64-bit prime number = {}", rand.random_prime_using_miller_rabin_uint::<u64>(5));
2182    /// println!("Random 128-bit prime number = {}", rand.random_prime_using_miller_rabin_uint::<u128>(5));
2183    /// println!("Random usize-sized prime number = {}", rand.random_prime_using_miller_rabin_uint::<usize>(5));
2184    /// ```
2185    /// 
2186    /// # For more examples,
2187    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_prime_using_miller_rabin_uint)
2188    pub fn random_prime_using_miller_rabin_uint<T>(&mut self, repetition: usize) -> T
2189    where T: SmallUInt
2190    {
2191        let mut res = self.random_odd_uint::<T>();
2192        while !res.is_prime_using_miller_rabin(repetition)
2193            { res = self.random_odd_uint::<T>(); }
2194        res
2195    }
2196
2197    // pub fn random_prime_with_msb_set_using_miller_rabin_uint<T>(&mut self, repetition: usize) -> T
2198    /// Returns a full-sized random prime number, which is its MSB (Most
2199    /// Segnificant Bit) is set `1`.
2200    /// 
2201    /// # Argument
2202    /// The argument `repetition` defines how many times it tests whether or not
2203    /// the generated random number is prime. Usually, `repetition` is given to
2204    /// be 5 to have 99.9% hit rate.
2205    /// 
2206    /// # Output
2207    /// A full-sized random prime number, which is its MSB (Most Segnificant
2208    /// Bit) is set `1` and whose range is from 2 up to T::max() inclusively.
2209    /// 
2210    /// # Features
2211    /// - This method generates a random number, and then simply sets its MSB
2212    /// (Most Significant Bit) to be one, and then checks whether or not the
2213    /// generated random number is prime number, and then it repeats until it
2214    /// will generate a prime number.
2215    /// - It uses
2216    /// [Miller Rabin algorithm](https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test).
2217    /// - If this test results in composite number, the tested number is surely
2218    /// a composite number. If this test results in notprime number, the
2219    /// probability that the tested number is not a prime number is 1/4 (= 25%).
2220    /// So, if the test results in prime number twice, the probability that the
2221    /// tested number is not a prime number is 1/16 (= 1/4 * 1/4 = 6.25%).
2222    /// Therefore, if you test any number 5 times and they all result in a prime
2223    /// number, the probability that the tested number is not a prime number is
2224    /// 1/1024 = (= 1/4 * 1/4 * 1/4 * 1/4 * 1/4 = 0.09765625%). In other words,
2225    /// it is about 99.9% that the number is a prime number.
2226    /// - The random prime numbers that may or may not be cryptographically
2227    /// secure depending on what pseudo-random number generator is used.
2228    /// 
2229    /// # Cryptographical Security
2230    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2231    ///   cryptographically secure.
2232    /// - If you use `Slapdash_*`, it is considered that it may be
2233    ///   cryptographically insecure.
2234    /// 
2235    /// # Counterpart Methods
2236    /// - If you want to use a normal random prime number, you are highly
2237    /// recommended to use the method
2238    /// [random_prime_using_miller_rabin_uint()](struct@Random_Generic#method.random_prime_using_miller_rabin_uint)
2239    /// rather than this method.
2240    /// 
2241    /// # Example 1 for Random
2242    /// ```
2243    /// use cryptocol::random::Random;
2244    /// let mut rand = Random::new();
2245    /// println!("Random 8-bit prime number = {}", rand.random_prime_with_msb_set_using_miller_rabin_uint::<u8>(5));
2246    /// println!("Random 16-bit prime number = {}", rand.random_prime_with_msb_set_using_miller_rabin_uint::<u16>(5));
2247    /// println!("Random 32-bit prime number = {}", rand.random_prime_with_msb_set_using_miller_rabin_uint::<u32>(5));
2248    /// println!("Random 64-bit prime number = {}", rand.random_prime_with_msb_set_using_miller_rabin_uint::<u64>(5));
2249    /// println!("Random 128-bit prime number = {}", rand.random_prime_with_msb_set_using_miller_rabin_uint::<u128>(5));
2250    /// println!("Random usize-sized prime number = {}", rand.random_prime_with_msb_set_using_miller_rabin_uint::<usize>(5));
2251    /// ```
2252    /// 
2253    /// # For more examples,
2254    /// click [here](./documentation/random_random_smalluint/struct.Random_Generic.html#method.random_prime_with_msb_set_using_miller_rabin_uint)
2255    pub fn random_prime_with_msb_set_using_miller_rabin_uint<T>(&mut self, repetition: usize) -> T
2256    where T: SmallUInt
2257    {
2258        let mut res = self.random_odd_with_msb_set_uint::<T>();
2259        while !res.is_prime_using_miller_rabin(repetition)
2260            { res = self.random_odd_with_msb_set_uint::<T>(); }
2261        res
2262    }
2263
2264    // pub fn random_array<T, const N: usize>(&mut self) -> [T; N]
2265    /// Returns random number array [T; N].
2266    /// 
2267    /// # Output
2268    /// A random number array [T; N] each element of which has a range from
2269    /// `0` up to `T::max()` inclusively for both ends.
2270    /// 
2271    /// # Features
2272    /// The random numbers that may or may not be cryptographically secure
2273    /// depending on what pseudo-random number generator is used.
2274    /// 
2275    /// # Cryptographical Security
2276    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2277    ///   cryptographically secure.
2278    /// - If you use `Slapdash_*`, it is considered that it may be
2279    ///   cryptographically insecure.
2280    /// 
2281    /// # Counterpart Methods
2282    /// If you want random BigUInt, you are highly recommended
2283    /// to use the method
2284    /// [random_biguint()](struct@Random_Generic#method.random_biguint)
2285    /// rather than this method.
2286    /// 
2287    /// # Example 1 for Random
2288    /// ```
2289    /// use cryptocol::random::Random;
2290    /// let mut rand = Random::new();
2291    /// let num: [u128; 5] = rand.random_array();
2292    /// for i in 0..5
2293    ///     { println!("Random number {} => {}", i, num[i]); }
2294    /// ```
2295    /// 
2296    /// # For more examples,
2297    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.random_array)
2298    pub fn random_array<T, const N: usize>(&mut self) -> [T; N]
2299    where T: SmallUInt
2300    {
2301        let mut res = [T::zero(); N];
2302        self.put_random_in_array(&mut res);
2303        res
2304    }
2305
2306    // pub fn put_random_in_array<T, const N: usize>(&mut self, out: &mut [T; N])
2307    /// Puts random number array [T; N] in `out`.
2308    /// 
2309    /// # Argument
2310    /// `out` is a random number array [T; N] each element of which has
2311    /// a range from `0` up to `T::max()` inclusively for both ends.
2312    /// 
2313    /// # Features
2314    /// The random numbers that may or may not be cryptographically secure
2315    /// depending on what pseudo-random number generator is used.
2316    /// 
2317    /// # Cryptographical Security
2318    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2319    ///   cryptographically secure.
2320    /// - If you use `Slapdash_*`, it is considered that it may be
2321    ///   cryptographically insecure.
2322    /// 
2323    /// # Counterpart Methods
2324    /// If you want random BigUInt, you are highly recommended
2325    /// to use the method
2326    /// [random_biguint()](struct@Random_Generic#method.random_biguint)
2327    /// rather than this method.
2328    /// 
2329    /// # Example 1 for Random
2330    /// ```
2331    /// use cryptocol::random::Random;
2332    /// let mut rand = Random::new();
2333    /// let mut num = [0_u128; 5];
2334    /// rand.put_random_in_array(&mut num);
2335    /// for i in 0..5
2336    ///     { println!("Random number {} => {}", i, num[i]); }
2337    /// ```
2338    /// 
2339    /// # For more examples,
2340    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.put_random_in_array)
2341    pub fn put_random_in_array<T, const N: usize>(&mut self, out: &mut [T; N])
2342    where T: SmallUInt
2343    {
2344        self.produce_aux_state();
2345        self.produce_main_state();
2346        let mut tsize = T::size_in_bytes() as usize * N;
2347        const ASIZE: usize = 8 * 8; // = U64::size_in_bytes() as usize * 8;
2348        let mut j = 0_usize;
2349        let mut array = self.aux_state.clone();
2350        while tsize > 0
2351        {
2352            for i in 0..8
2353                { array[i] ^= self.main_state[i]; }
2354            let count = if tsize < ASIZE { tsize } else { ASIZE };
2355            unsafe { copy_nonoverlapping(array.as_ptr() as *const u8, (out.as_mut_ptr() as *mut u8).add(ASIZE * j), count); }
2356            self.produce_main_state();
2357            tsize -= count;
2358            j += 1;
2359        }
2360    }
2361
2362    // pub fn random_biguint<T, const N: usize>(&mut self) -> BigUInt<T, N>
2363    /// Constucts a new `BigUInt<T, N>`-type object which has the random value.
2364    /// 
2365    /// # Output
2366    /// A random number whose range is from `0` up to `BigUInt::max()`
2367    /// inclusively for both ends.
2368    /// 
2369    /// # Features
2370    /// The random numbers that may or may not be cryptographically secure
2371    /// depending on what pseudo-random number generator is used.
2372    /// 
2373    /// # Cryptographical Security
2374    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2375    ///   cryptographically secure.
2376    /// - If you use `Slapdash_*`, it is considered that it may be
2377    ///   cryptographically insecure.
2378    /// 
2379    /// # Counterpart Methods
2380    /// - If you want to use a random number less than a certain value, you are
2381    ///   highly recommended to use the method
2382    ///   [random_under_biguint()](struct@Random_Generic#method.random_under_biguint)
2383    ///   rather than this method.
2384    /// - If you want to use a random odd number, you are highly recommended to
2385    ///   use the method
2386    ///   [random_odd_biguint()](struct@Random_Generic#method.random_odd_biguint)
2387    ///   rather than this method.
2388    /// - If you want to use a random odd number less than a certain value,
2389    ///   you are highly recommended to use the method
2390    ///   [ranodm_odd_under_biguint()](struct@Random_Generic#method.ranodm_odd_under_biguint)
2391    ///   rather than this method.
2392    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random
2393    ///   number, you are highly recommended to use the method
2394    ///   [random_with_msb_set_biguint()](struct@Random_Generic#method.random_with_msb_set_biguint)
2395    ///   rather than this method.
2396    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random odd
2397    ///   number, you are highly recommended to
2398    ///   use the method [random_odd_with_msb_set_biguint()](struct@Random_Generic#method.random_odd_with_msb_set_biguint)
2399    ///   rather than this method.
2400    /// - If you want to use a normal random prime number, you are highly recommended to
2401    ///   use the method [random_prime_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_using_miller_rabin_biguint)
2402    ///   rather than this method.
2403    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random prime
2404    ///   number, you are highly recommended to
2405    ///   use the method [random_prime_with_msb_set_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_with_msb_set_using_miller_rabin_biguint)
2406    ///   rather than this method.
2407    /// 
2408    /// # Example 1 for Random
2409    /// ```
2410    /// use cryptocol::random::Random;
2411    /// use cryptocol::define_utypes_with;
2412    /// define_utypes_with!(u128);
2413    /// 
2414    /// let mut rand = Random::new();
2415    /// let biguint: U256 = rand.random_biguint();
2416    /// println!("Random Number: {}", biguint);
2417    /// ```
2418    /// 
2419    /// # For more examples,
2420    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.random_biguint)
2421    #[inline]
2422    pub fn random_biguint<T, const N: usize>(&mut self) -> BigUInt<T, N>
2423    where T: SmallUInt
2424    {
2425        BigUInt::<T, N>::from_array(self.random_array::<T, N>()                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    )
2426    }
2427
2428    // pub fn random_under_biguint<T, const N: usize>(&mut self, ceiling: &BigUInt<T, N>) -> Option<BigUInt<T, N>>
2429    /// Constucts a new `BigUInt<T, N>`-type object which has the random
2430    /// value less than a certain value, wrapped by enum `Some` of `Option`.
2431    /// 
2432    /// # Argument
2433    /// The argument `ceiling` is the upper limitation which the generated
2434    /// random number should be less than, and is of type `&BigUInt<T, N>`.
2435    /// 
2436    /// # Output
2437    /// A random number wrapped by enum `Some` of `Option`, whose range is
2438    /// between 0 inclusively and the certain value exclusively when `ceiling`
2439    /// is not zero. If `ceiling` is zero, `None` will be returned.
2440    /// 
2441    /// # Features
2442    /// - This method generates a random number, and then simply divides it by
2443    ///   the certain value to get its remainder.
2444    /// - The random numbers that may or may not be cryptographically
2445    ///   secure depending on what pseudo-random number generator is used.
2446    /// 
2447    /// # Cryptographical Security
2448    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2449    ///   cryptographically secure.
2450    /// - If you use `Slapdash_*`, it is considered that it may be
2451    ///   cryptographically insecure.
2452    /// 
2453    /// # Counterpart Methods
2454    /// - If you want to use a normal random number, you are highly recommended
2455    ///   to use the method
2456    ///   [random_biguint()](struct@Random_Generic#method.random_biguint)
2457    ///   rather than this method.
2458    /// - If you want to use a random odd number, you are highly recommended to
2459    ///   use the method
2460    ///   [random_odd_biguint()](struct@Random_Generic#method.random_odd_biguint)
2461    ///   rather than this method.
2462    /// - If you want to use a random odd number less than a certain value,
2463    ///   you are highly recommended to use the method
2464    ///   [ranodm_odd_under_biguint()](struct@Random_Generic#method.ranodm_odd_under_biguint)
2465    ///   rather than this method.
2466    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random
2467    ///   number, you are highly recommended to use the method
2468    ///   [random_with_msb_set_biguint()](struct@Random_Generic#method.random_with_msb_set_biguint)
2469    ///   rather than this method.
2470    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random odd
2471    ///   number, you are highly recommended to use the method
2472    ///   [random_odd_with_msb_set_biguint()](struct@Random_Generic#method.random_odd_with_msb_set_biguint)
2473    ///   rather than this method.
2474    /// - If you want to use a normal random prime number, you are highly
2475    ///   recommended to use the method
2476    ///   [random_prime_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_using_miller_rabin_biguint)
2477    ///   rather than this method.
2478    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random prime
2479    ///   number, you are highly recommended to use the method
2480    ///   [random_prime_with_msb_set_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_with_msb_set_using_miller_rabin_biguint)
2481    ///   rather than this method.
2482    /// 
2483    /// # Example 1 for Random
2484    /// ```
2485    /// use cryptocol::random::Random;
2486    /// use cryptocol::define_utypes_with;
2487    /// define_utypes_with!(u64);
2488    /// 
2489    /// let mut rand = Random::new();
2490    /// let ceiling = U16384::max().wrapping_div_uint(3_u8);
2491    /// if let Some(r) = rand.random_under_biguint(&ceiling)
2492    /// {
2493    ///     println!("Random Number less than {} is\n{}", ceiling, r);
2494    ///     assert!(r < ceiling);
2495    /// }
2496    /// ```
2497    /// 
2498    /// # For more examples,
2499    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.random_under_biguint)
2500    #[inline]
2501    pub fn random_under_biguint<T, const N: usize>(&mut self, ceiling: &BigUInt<T, N>) -> Option<BigUInt<T, N>>
2502    where T: SmallUInt
2503    {
2504        if ceiling.eq_uint(0_u8) {None} else {Some(self.random_under_biguint_::<T, N>(ceiling))}
2505    }
2506
2507    // pub fn random_under_biguint_<T, const N: usize>(&mut self, ceiling: &BigUInt<T, N>) -> BigUInt<T, N>
2508    /// Constucts a new `BigUInt<T, N>`-type object which has the random
2509    /// value less than a certain value.
2510    /// 
2511    /// # Argument
2512    /// The argument `ceiling` is the upper limitation which the generated
2513    /// random number should be less than, and is of type `&BigUInt<T, N>`.
2514    /// 
2515    /// # Output
2516    /// The random number whose range is between 0 inclusively
2517    /// and the certain value exclusively.
2518    /// 
2519    /// # Features
2520    /// - This method generates a random number, and then simply divides it by
2521    ///   the certain value to get its remainder.
2522    /// - The random numbers that may or may not be cryptographically
2523    ///   secure depending on what pseudo-random number generator is used.
2524    /// 
2525    /// # Panics
2526    /// If `ceiling` is zero, this method will panic.
2527    /// 
2528    /// # Caution
2529    /// Use this method only when you are sure that `ceiling` is not zero.
2530    /// 
2531    /// # Cryptographical Security
2532    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2533    ///   cryptographically secure.
2534    /// - If you use `Slapdash_*`, it is considered that it may be
2535    ///   cryptographically insecure.
2536    /// 
2537    /// # Counterpart Methods
2538    /// - If you want to use a normal random number, you are highly recommended
2539    ///   to use the method
2540    ///   [random_biguint()](struct@Random_Generic#method.random_biguint)
2541    ///   rather than this method.
2542    /// - If you want to use a random odd number, you are highly recommended to
2543    ///   use the method
2544    ///   [random_odd_biguint()](struct@Random_Generic#method.random_odd_biguint)
2545    ///   rather than this method.
2546    /// - If you want to use a random odd number less than a certain value,
2547    ///   you are highly recommended to use the method
2548    ///   [ranodm_odd_under_biguint()](struct@Random_Generic#method.ranodm_odd_under_biguint)
2549    ///   rather than this method.
2550    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random
2551    ///   number, you are highly recommended to use the method
2552    ///   [random_with_msb_set_biguint()](struct@Random_Generic#method.random_with_msb_set_biguint)
2553    ///   rather than this method.
2554    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random odd
2555    ///   number, you are highly recommended to use the method
2556    ///   [random_odd_with_msb_set_biguint()](struct@Random_Generic#method.random_odd_with_msb_set_biguint)
2557    ///   rather than this method.
2558    /// - If you want to use a normal random prime number, you are highly
2559    ///   recommended to use the method
2560    ///   [random_prime_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_using_miller_rabin_biguint)
2561    ///   rather than this method.
2562    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random prime
2563    ///   number, you are highly recommended to use the method
2564    ///   [random_prime_with_msb_set_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_with_msb_set_using_miller_rabin_biguint)
2565    ///   rather than this method.
2566    /// 
2567    /// # Example 1 for Random
2568    /// ```
2569    /// use cryptocol::random::Random;
2570    /// use cryptocol::define_utypes_with;
2571    /// define_utypes_with!(u32);
2572    /// 
2573    /// let mut rand = Random::new();
2574    /// let ceiling = U16384::max().wrapping_div_uint(3_u8);
2575    /// let r = rand.random_under_biguint_(&ceiling);
2576    /// println!("Random Number less than {} is\n{}", ceiling, r);
2577    /// assert!(r < ceiling);
2578    /// ```
2579    /// 
2580    /// # For more examples,
2581    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.random_under_biguint_)
2582    #[inline]
2583    pub fn random_under_biguint_<T, const N: usize>(&mut self, ceiling: &BigUInt<T, N>) -> BigUInt<T, N>
2584    where T: SmallUInt
2585    {
2586        self.random_biguint::<T, N>().wrapping_rem(ceiling)
2587    }
2588
2589    // pub fn random_odd_biguint<T, const N: usize>(&mut self) -> BigUInt<T, N>
2590    /// Constucts a new `BigUInt<T, N>`-type object which has the random odd
2591    /// value.
2592    /// 
2593    /// # Argument
2594    /// The argument `ceiling` is the upper limitation which the generated
2595    /// random number should be less than, and is of type `&BigUInt<T, N>`.
2596    /// 
2597    /// # Output
2598    /// The random number that this method `any_odd()` returns is a pure
2599    /// random odd number whose range is from `1` up to `BigUInt::max()`
2600    /// inclusively for both ends.
2601    /// 
2602    /// # Features
2603    /// - This method generates a random number, and then simply set the LSB
2604    /// (Least Significant Bit).
2605    /// - The random numbers that may or may not be cryptographically
2606    /// secure depending on what pseudo-random number generator is used.
2607    /// 
2608    /// # Cryptographical Security
2609    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2610    ///   cryptographically secure.
2611    /// - If you use `Slapdash_*`, it is considered that it may be
2612    ///   cryptographically insecure.
2613    /// 
2614    /// # Counterpart Methods
2615    /// - If you want to use a normal random number, you are highly recommended
2616    ///   to use the method
2617    ///   [random_biguint()](struct@Random_Generic#method.random_biguint)
2618    ///   rather than this method.
2619    /// - If you want to use a random number less than a certain value, you are
2620    ///   highly recommended to use the method
2621    ///   [random_under_biguint()](struct@Random_Generic#method.random_under_biguint)
2622    ///   rather than this method.
2623    /// - If you want to use a random odd number, you are highly recommended to
2624    ///   use the method
2625    ///   [random_odd_biguint()](struct@Random_Generic#method.random_odd_biguint)
2626    ///   rather than this method.
2627    /// - If you want to use a random odd number less than a certain value,
2628    ///   you are highly recommended to use the method
2629    ///   [ranodm_odd_under_biguint()](struct@Random_Generic#method.ranodm_odd_under_biguint)
2630    ///   rather than this method.
2631    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random number,
2632    ///   you are highly recommended to use the method
2633    ///   [random_with_msb_set_biguint()](struct@Random_Generic#method.random_with_msb_set_biguint)
2634    ///   rather than this method.
2635    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random odd
2636    ///   number, you are highly recommended to use the method
2637    ///   [random_odd_with_msb_set_biguint()](struct@Random_Generic#method.random_odd_with_msb_set_biguint)
2638    ///   rather than this method.
2639    /// - If you want to use a normal random prime number, you are highly
2640    ///   recommended to use the method
2641    ///   [random_prime_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_using_miller_rabin_biguint)
2642    ///   rather than this method.
2643    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random prime
2644    ///   number, you are highly recommended to use the method
2645    ///   [random_prime_with_msb_set_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_with_msb_set_using_miller_rabin_biguint)
2646    ///   rather than this method.
2647    /// 
2648    /// # Example 1 for Random
2649    /// ```
2650    /// use cryptocol::random::Random;
2651    /// use cryptocol::define_utypes_with;
2652    /// define_utypes_with!(u16);
2653    /// 
2654    /// let mut rand = Random::new();
2655    /// let r: U16384 = rand.random_odd_biguint();
2656    /// println!("Random odd number is {}.", r);
2657    /// assert!(r.is_odd());
2658    /// ```
2659    /// 
2660    /// # For more examples,
2661    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.random_odd_biguint)
2662    pub fn random_odd_biguint<T, const N: usize>(&mut self) -> BigUInt<T, N>
2663    where T: SmallUInt
2664    {
2665        let mut res = self.random_biguint::<T, N>();
2666        res.set_lsb();
2667        res
2668    }
2669
2670    // pub fn random_odd_under_biguint<T, const N: usize>(&mut self, ceiling: &BigUInt<T, N>) -> Option<BigUInt<T, N>>
2671    /// Constucts a new `BigUInt<T, N>`-type object which has the random odd
2672    /// value less than a certain value, wrapped by enum `Some` of `Option`.
2673    /// 
2674    /// # Argument
2675    /// The argument `ceiling` is the upper limitation which the generated
2676    /// random number should be less than, and is of type `&BigUInt<T, N>`.
2677    /// 
2678    /// # Output
2679    /// The random odd number whose range is between 0 inclusively and the
2680    /// certain value exclusively, wrapped by enum `Some` of `Option` if
2681    /// `ceiling` is not zero. If `ceiling` is zero, `None` will be returned.
2682    /// 
2683    /// # Features
2684    /// - This method generates a random number, and then simply divides it
2685    ///   by the certain value to get its remainder and then simply set the LSB
2686    ///   (Least Significant Bit).
2687    /// - The random numbers that may or may not be cryptographically
2688    ///   secure depending on what pseudo-random number generator is used.
2689    /// 
2690    /// # Cryptographical Security
2691    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2692    ///   cryptographically secure.
2693    /// - If you use `Slapdash_*`, it is considered that it may be
2694    ///   cryptographically insecure.
2695    /// 
2696    /// # Counterpart Methods
2697    /// - If you want to use a normal random number, you are highly recommended
2698    ///   to use the method
2699    ///   [random_biguint()](struct@Random_Generic#method.random_biguint)
2700    ///   rather than this method.
2701    /// - If you want to use a random number less than a certain value, you are
2702    ///   highly recommended to use the method
2703    ///   [random_under_biguint()](struct@Random_Generic#method.random_under_biguint)
2704    ///   rather than this method.
2705    /// - If you want to use a random odd number, you are highly recommended to
2706    ///   use the method
2707    ///   [random_odd_biguint()](struct@Random_Generic#method.random_odd_biguint)
2708    ///   rather than this method.
2709    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random
2710    ///   number, you are highly recommended to use the method
2711    ///   [random_with_msb_set_biguint()](struct@Random_Generic#method.random_with_msb_set_biguint)
2712    ///   rather than this method.
2713    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random odd
2714    ///   number, you are highly recommended to use the method
2715    ///   [random_odd_with_msb_set_biguint()](struct@Random_Generic#method.random_odd_with_msb_set_biguint)
2716    ///   rather than this method.
2717    /// - If you want to use a normal random prime number, you are highly
2718    ///   recommended to use the method
2719    ///   [random_prime_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_using_miller_rabin_biguint)
2720    ///   rather than this method.
2721    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random prime
2722    ///   number, you are highly recommended to use the method
2723    ///   [random_prime_with_msb_set_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_with_msb_set_using_miller_rabin_biguint)
2724    ///   rather than this method.
2725    /// 
2726    /// # Example 1 for Random
2727    /// ```
2728    /// use cryptocol::random::Random;
2729    /// use cryptocol::define_utypes_with;
2730    /// define_utypes_with!(u8);
2731    /// 
2732    /// let mut rand = Random::new();
2733    /// let ceiling = U16384::max().wrapping_div_uint(3_u8);
2734    /// if let Some(r) = rand.random_odd_under_biguint(&ceiling)
2735    /// {
2736    ///     println!("Random odd number less than {} is\n{}", ceiling, r);
2737    ///     assert!(r < ceiling);
2738    ///     assert!(r.is_odd());
2739    /// }
2740    /// ```
2741    /// 
2742    /// # For more examples,
2743    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.random_odd_under_biguint)
2744    #[inline]
2745    pub fn random_odd_under_biguint<T, const N: usize>(&mut self, ceiling: &BigUInt<T, N>) -> Option<BigUInt<T, N>>
2746    where T: SmallUInt
2747    {
2748        if ceiling.is_zero_or_one() { None } else { Some(self.random_odd_under_biguint_(ceiling)) }
2749    }
2750
2751    // pub fn random_odd_under_biguint_<T, const N: usize>(&mut self, ceiling: &BigUInt<T, N>) -> BigUInt<T, N>
2752    /// Constucts a new `BigUInt<T, N>`-type object which has the random odd
2753    /// value less than a certain value.
2754    /// 
2755    /// # Argument
2756    /// The argument `ceiling` is the upper limitation which the generated
2757    /// random number should be less than, and is of type `&BigUInt<T, N>`.
2758    /// 
2759    /// # Output
2760    /// The random odd number whose range is between 0 inclusively and the
2761    /// certain value exclusively.
2762    /// 
2763    /// # Features
2764    /// - This method generates a random number, and then simply divides it
2765    ///   by the certain value to get its remainder and then simply set the LSB
2766    ///   (Least Significant Bit).
2767    /// - The random numbers that may or may not be cryptographically
2768    ///   secure depending on what pseudo-random number generator is used.
2769    /// 
2770    /// # Panics
2771    /// If `ceiling` is zero, this method will panic.
2772    /// 
2773    /// # Caution
2774    /// Use this method only when you are sure that `ceiling` is not zero.
2775    /// 
2776    /// # Cryptographical Security
2777    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2778    ///   cryptographically secure.
2779    /// - If you use `Slapdash_*`, it is considered that it may be
2780    ///   cryptographically insecure.
2781    /// 
2782    /// # Counterpart Methods
2783    /// - If you want to use a normal random number, you are highly recommended
2784    ///   to use the method
2785    ///   [random_biguint()](struct@Random_Generic#method.random_biguint)
2786    ///   rather than this method.
2787    /// - If you want to use a random number less than a certain value, you are
2788    ///   highly recommended to use the method
2789    ///   [random_under_biguint()](struct@Random_Generic#method.random_under_biguint)
2790    ///   rather than this method.
2791    /// - If you want to use a random odd number, you are highly recommended to
2792    ///   use the method
2793    ///   [random_odd_biguint()](struct@Random_Generic#method.random_odd_biguint)
2794    ///   rather than this method.
2795    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random
2796    ///   number, you are highly recommended to use the method
2797    ///   [random_with_msb_set_biguint()](struct@Random_Generic#method.random_with_msb_set_biguint)
2798    ///   rather than this method.
2799    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random odd
2800    ///   number, you are highly recommended to
2801    ///   use the method [random_odd_with_msb_set_biguint()](struct@Random_Generic#method.random_odd_with_msb_set_biguint)
2802    ///   rather than this method.
2803    /// - If you want to use a normal random prime number, you are highly
2804    ///   recommended to use the method
2805    ///   [random_prime_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_using_miller_rabin_biguint)
2806    ///   rather than this method.
2807    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random prime
2808    ///   number, you are highly recommended to use the method
2809    ///   [random_prime_with_msb_set_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_with_msb_set_using_miller_rabin_biguint)
2810    ///   rather than this method.
2811    /// 
2812    /// # Example 1 for Random
2813    /// ```
2814    /// use cryptocol::random::Random;
2815    /// use cryptocol::define_utypes_with;
2816    /// define_utypes_with!(u128);
2817    /// 
2818    /// let mut rand = Random::new();
2819    /// let ceiling = U16384::max().wrapping_div_uint(3_u8);
2820    /// let r = rand.random_odd_under_biguint_(&ceiling);
2821    /// println!("Random odd number less than {} is\n{}", ceiling, r);
2822    /// assert!(r < ceiling);
2823    /// assert!(r.is_odd());
2824    /// ```
2825    /// 
2826    /// # For more examples,
2827    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.random_odd_under_biguint_)
2828    #[inline]
2829    pub fn random_odd_under_biguint_<T, const N: usize>(&mut self, ceiling: &BigUInt<T, N>) -> BigUInt<T, N>
2830    where T: SmallUInt
2831    {
2832        if ceiling.is_zero_or_one()
2833            { panic!(); }
2834        let mut ceiling = ceiling.clone();
2835        ceiling.reset_lsb();
2836        let mut res = self.random_under_biguint_(&ceiling);
2837        res.set_lsb();
2838        res
2839    }
2840
2841    // pub fn random_with_msb_set_biguint<T, const N: usize>(&mut self) -> BigUInt<T, N>
2842    /// Constucts a new `BigUInt<T, N>`-type object which has the random value
2843    /// with `(N * sizeof::<T>() * 8)`-bit length.
2844    /// 
2845    /// # Output
2846    /// The random number whose range is from !(BigUInt::max() >> 1) up to
2847    /// BigUInt::max() inclusively.
2848    /// 
2849    /// # Features
2850    /// - This method generates a random number, and then simply set the MSB
2851    ///   (Most Significant Bit).
2852    /// - The random numbers that may or may not be cryptographically
2853    ///   secure depending on what pseudo-random number generator is used.
2854    /// 
2855    /// # Cryptographical Security
2856    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2857    ///   cryptographically secure.
2858    /// - If you use `Slapdash_*`, it is considered that it may be
2859    ///   cryptographically insecure.
2860    /// 
2861    /// # Counterpart Methods
2862    /// - If you want to use a normal random number, you are highly recommended
2863    ///   to use the method
2864    ///   [random_biguint()](struct@Random_Generic#method.random_biguint)
2865    ///   rather than this method.
2866    /// - If you want to use a random number less than a certain value, you are
2867    ///   highly recommended to use the method
2868    ///   [random_under_biguint()](struct@Random_Generic#method.random_under_biguint)
2869    ///   rather than this method.
2870    /// - If you want to use a random odd number, you are highly recommended to
2871    ///   use the method
2872    ///   [random_odd_biguint()](struct@Random_Generic#method.random_odd_biguint)
2873    ///   rather than this method.
2874    /// - If you want to use a random odd number less than a certain value,
2875    ///   you are highly recommended to use the method
2876    ///   [ranodm_odd_under_biguint()](struct@Random_Generic#method.ranodm_odd_under_biguint)
2877    ///   rather than this method.
2878    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random odd
2879    ///   number, you are highly recommended to
2880    ///   use the method [random_odd_with_msb_set_biguint()](struct@Random_Generic#method.random_odd_with_msb_set_biguint)
2881    ///   rather than this method.
2882    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random odd
2883    ///   number, you are highly recommended to
2884    ///   use the method [random_odd_with_msb_set_biguint()](struct@Random_Generic#method.random_odd_with_msb_set_biguint)
2885    ///   rather than this method.
2886    /// - If you want to use a normal random prime number, you are highly
2887    ///   recommended to use the method
2888    ///   [random_prime_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_using_miller_rabin_biguint)
2889    ///   rather than this method.
2890    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random prime
2891    ///   number, you are highly recommended to use the method
2892    ///   [random_prime_with_msb_set_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_with_msb_set_using_miller_rabin_biguint)
2893    ///   rather than this method.
2894    /// 
2895    /// # Example 1 for Random
2896    /// ```
2897    /// use cryptocol::random::Random;
2898    /// use cryptocol::define_utypes_with;
2899    /// define_utypes_with!(u64);
2900    /// 
2901    /// let mut rand = Random::new();
2902    /// let r: u64384 = rand.random_with_msb_set_biguint();
2903    /// println!("Random number is {}.", r);
2904    /// assert!(r > u64384::halfmax());
2905    /// ```
2906    /// 
2907    /// # For more examples,
2908    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.random_with_msb_set_biguint)
2909    #[inline]
2910    pub fn random_with_msb_set_biguint<T, const N: usize>(&mut self) -> BigUInt<T, N>
2911    where T: SmallUInt
2912    {
2913        let mut res = self.random_biguint::<T, N>();
2914        res.set_msb();
2915        res
2916    }
2917
2918    // pub fn random_odd_with_msb_set_biguint<T, const N: usize>(&mut self) -> BigUInt<T, N>
2919    /// Constucts a new `BigUInt<T, N>`-type object which has the random odd
2920    /// value with `(N * sizeof::<T>() * 8)`-bit length
2921    /// 
2922    /// # Output
2923    /// The random number that this method random_odd_with_msb_set() returns is
2924    /// a random odd number whose range is from !(BigUInt::max() >> 1) + 1 up to
2925    /// BigUInt::max() inclusively.
2926    /// 
2927    /// # Features
2928    /// - This method generates a random number, and then simply set the MSB
2929    ///   (Most Significant Bit) and LSB (Least Significant Bit).
2930    /// - The random numbers that may or may not be cryptographically
2931    ///   secure depending on what pseudo-random number generator is used.
2932    /// 
2933    /// # Cryptographical Security
2934    /// - If you use either `Random_*` or `Any_*`, it is considered to be
2935    ///   cryptographically secure.
2936    /// - If you use `Slapdash_*`, it is considered that it may be
2937    ///   cryptographically insecure.
2938    /// 
2939    /// # Counterpart Methods
2940    /// - If you want to use a normal random number, you are highly recommended
2941    ///   to use the method
2942    ///   [random_biguint()](struct@Random_Generic#method.random_biguint)
2943    ///   rather than this method.
2944    /// - If you want to use a random number less than a certain value, you are
2945    ///   highly recommended to use the method
2946    ///   [random_under_biguint()](struct@Random_Generic#method.random_under_biguint)
2947    ///   rather than this method.
2948    /// - If you want to use a random odd number, you are highly recommended to
2949    ///   use the method
2950    ///   [random_odd_biguint()](struct@Random_Generic#method.random_odd_biguint)
2951    ///   rather than this method.
2952    /// - If you want to use a random odd number less than a certain value,
2953    ///   you are highly recommended to use the method
2954    ///   [ranodm_odd_under_biguint()](struct@Random_Generic#method.ranodm_odd_under_biguint)
2955    ///   rather than this method.
2956    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random
2957    ///   number, you are highly recommended to use the method
2958    ///   [random_with_msb_set_biguint()](struct@Random_Generic#method.random_with_msb_set_biguint)
2959    ///   rather than this method.
2960    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random
2961    ///   number, you are highly recommended to use the method
2962    ///   [random_with_msb_set_biguint()](struct@Random_Generic#method.random_with_msb_set_biguint)
2963    ///   rather than this method.
2964    /// - If you want to use a normal random prime number, you are highly
2965    ///   recommended to use the method
2966    ///   [random_prime_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_using_miller_rabin_biguint)
2967    ///   rather than this method.
2968    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random prime
2969    ///   number, you are highly recommended to use the method
2970    ///   [random_prime_with_msb_set_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_with_msb_set_using_miller_rabin_biguint)
2971    ///   rather than this method.
2972    /// 
2973    /// # Example 1 for Random
2974    /// ```
2975    /// use cryptocol::random::Random;
2976    /// use cryptocol::define_utypes_with;
2977    /// define_utypes_with!(u32);
2978    /// 
2979    /// let mut rand = Random::new();
2980    /// let r: U16384 = rand.random_odd_with_msb_set_biguint();
2981    /// println!("Random number is {}.", r);
2982    /// assert!(r > U16384::halfmax());
2983    /// assert!(r.is_odd());
2984    /// ```
2985    /// 
2986    /// # For more examples,
2987    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.random_odd_with_msb_set_biguint)
2988    pub fn random_odd_with_msb_set_biguint<T, const N: usize>(&mut self) -> BigUInt<T, N>
2989    where T: SmallUInt
2990    {
2991        let mut r = self.random_with_msb_set_biguint();
2992        r.set_lsb();
2993        r
2994    }
2995
2996    // pub fn random_prime_using_miller_rabin_biguint<T, const N: usize>(&mut self, repetition: usize) -> BigUInt<T, N>
2997    /// Constucts a new `BigUInt<T, N>`-type object which represents a random
2998    /// prime number.
2999    /// 
3000    /// # Argument
3001    /// The argument `repetition` defines how many times it tests whether the
3002    /// generated random number is prime. Usually, `repetition` is given to be
3003    /// `5` for 99.9% accuracy or `7` for 99.99% accuracy.
3004    /// 
3005    /// # Output
3006    /// The random prime number that this method random_prime_Miller_Rabin()
3007    /// returns is a random prime number whose range is from
3008    /// 2 up to BigUInt::max() inclusively.
3009    /// 
3010    /// # Features
3011    /// - It uses
3012    ///   [Miller Rabin algorithm](https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test).
3013    /// - If this test results in composite number, the tested number is surely
3014    ///   a composite number. If this test results in prime number, the
3015    ///   probability that the tested number is not a prime number is 1/4. So,
3016    ///   if the test results in prime number twice, the probability that the
3017    ///   tested number is not a prime number is 1/16 (= 1/4 * 1/4). Therefore,
3018    ///   if you test any number 5 times and they all result in a prime number,
3019    ///   it is 99.9% that the number is a prime number.
3020    /// - The random prime numbers that may or may not be cryptographically
3021    ///   secure depending on what pseudo-random number generator is used.
3022    /// 
3023    /// # Counterpart Methods
3024    /// - If you want to use a normal random number, you are highly recommended
3025    ///   to use the method
3026    ///   [random_biguint()](struct@Random_Generic#method.random_biguint)
3027    ///   rather than this method.
3028    /// - If you want to use a random number less than a certain value, you are
3029    ///   highly recommended to use the method
3030    ///   [random_under_biguint()](struct@Random_Generic#method.random_under_biguint)
3031    ///   rather than this method.
3032    /// - If you want to use a random odd number, you are highly recommended to
3033    ///   use the method
3034    ///   [random_odd_biguint()](struct@Random_Generic#method.random_odd_biguint)
3035    ///   rather than this method.
3036    /// - If you want to use a random odd number less than a certain value,
3037    ///   you are highly recommended to use the method
3038    ///   [ranodm_odd_under_biguint()](struct@Random_Generic#method.ranodm_odd_under_biguint)
3039    ///   rather than this method.
3040    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random
3041    ///   number, you are highly recommended to use the method
3042    ///   [random_with_msb_set_biguint()](struct@Random_Generic#method.random_with_msb_set_biguint)
3043    ///   rather than this method.
3044    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random odd
3045    ///   number, you are highly recommended to use the method
3046    ///   [random_odd_with_msb_set_biguint()](struct@Random_Generic#method.random_odd_with_msb_set_biguint)
3047    ///   rather than this method.
3048    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random prime
3049    ///   number, you are highly recommended to use the method
3050    ///   [random_prime_with_msb_set_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_with_msb_set_using_miller_rabin_biguint)
3051    ///   rather than this method.
3052    /// 
3053    /// # Example 1 for Random
3054    /// ```
3055    /// use cryptocol::random::Random;
3056    /// use cryptocol::define_utypes_with;
3057    /// define_utypes_with!(u16);
3058    /// 
3059    /// let mut rand = Random::new();
3060    /// let prime: U256 = rand.random_prime_using_miller_rabin_biguint(5);
3061    /// println!("Random prime number: {}", prime);
3062    /// ```
3063    /// 
3064    /// # For more examples,
3065    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.random_prime_using_miller_rabin_biguint)
3066    pub fn random_prime_using_miller_rabin_biguint<T, const N: usize>(&mut self, repetition: usize) -> BigUInt<T, N>
3067    where T: SmallUInt
3068    {
3069        let mut res = self.random_odd_biguint::<T, N>();
3070        while !res.is_prime_using_miller_rabin(repetition)
3071            { res = self.random_odd_biguint::<T, N>(); }
3072        res
3073    }
3074
3075    pub(crate) fn random_prime_candidate_with_msb_set_biguint<T, const N: usize>(&mut self) -> BigUInt<T, N>
3076    where T: SmallUInt
3077    {
3078        let mut candidate = self.random_odd_with_msb_set_biguint::<T, N>();
3079        while candidate.filter_out_composite_number()
3080        {
3081            candidate = self.random_odd_with_msb_set_biguint::<T, N>();
3082        }
3083        candidate
3084    }
3085
3086    pub(crate) fn random_prime_candidate_with_half_length_biguint<T, const N: usize>(&mut self) -> BigUInt<T, N>
3087    where T: SmallUInt
3088    {
3089        let half = T::BITS * N as u32;
3090        let mut candidate = self.random_odd_with_msb_set_biguint::<T, N>();
3091        candidate.shift_right_assign(half);
3092        candidate.set_lsb();
3093        while candidate.filter_out_composite_number()
3094        {
3095            candidate = self.random_odd_with_msb_set_biguint::<T, N>();
3096            candidate.shift_right_assign(half);
3097            candidate.set_lsb();
3098        }
3099        candidate
3100    }
3101
3102    // pub fn random_prime_with_msb_set_using_miller_rabin_biguint<T, const N: usize>(&mut self, repetition: usize) -> BigUInt<T, N>
3103    /// Constucts a new `BigUInt<T, N>`-type object which represents a random
3104    /// prime number of full-size of BigUInt<T, N>.
3105    /// 
3106    /// # Argument
3107    /// The argument `repetition` defines how many times it tests whether the
3108    /// generated random number is prime. Usually, `repetition` is given to be
3109    /// `5` for 99.9% accuracy or `7` for 99.99% accuracy.
3110    /// 
3111    /// # Output
3112    /// The random prime numbers which ranges from
3113    /// BigUInt::halfmax() up to BigUInt::max() inclusively.
3114    /// 
3115    /// # Features
3116    /// - This method uses concurrency.
3117    /// - This method generates a random number, and then simply sets its MSB
3118    ///   (Most Significant Bit) to be one, and then checks whether or not the
3119    ///   generated random number is prime number, and then it repeats until it
3120    ///   will generate a prime number.
3121    /// - It uses [Miller Rabin algorithm](https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test).
3122    /// - If this test results in composite number, the tested number is surely
3123    ///   a composite number. If this test results in prime number, the
3124    ///   probability that the tested number is not a prime number is 1/4. So,
3125    ///   if the test results in prime number twice, the probability that the
3126    ///   tested number is not a prime number is 1/16 (= 1/4 * 1/4). Therefore,
3127    ///   if you test any number 5 times and they all result in a prime number,
3128    ///   it is 99.9% that the number is a prime number.
3129    /// 
3130    /// # Counterpart Methods
3131    /// - If you want to use a normal random number, you are highly recommended
3132    ///   to use the method
3133    ///   [random_biguint()](struct@Random_Generic#method.random_biguint)
3134    ///   rather than this method.
3135    /// - If you want to use a random number less than a certain value, you are
3136    ///   highly recommended to use the method
3137    ///   [random_under_biguint()](struct@Random_Generic#method.random_under_biguint)
3138    ///   rather than this method.
3139    /// - If you want to use a random odd number, you are highly recommended to
3140    ///   use the method
3141    ///   [random_odd_biguint()](struct@Random_Generic#method.random_odd_biguint)
3142    ///   rather than this method.
3143    /// - If you want to use a random odd number less than a certain value,
3144    ///   you are highly recommended to use the method
3145    ///   [ranodm_odd_under_biguint()](struct@Random_Generic#method.ranodm_odd_under_biguint)
3146    ///   rather than this method.
3147    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random
3148    ///   number, you are highly recommended to use the method
3149    ///   [random_with_msb_set_biguint()](struct@Random_Generic#method.random_with_msb_set_biguint)
3150    ///   rather than this method.
3151    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random odd
3152    ///   number, you are highly recommended to use the method
3153    ///   [random_odd_with_msb_set_biguint()](struct@Random_Generic#method.random_odd_with_msb_set_biguint)
3154    ///   rather than this method.
3155    /// - If you want to use a normal random prime number, you are highly
3156    ///   recommended to use the method
3157    ///   [random_prime_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_using_miller_rabin_biguint)
3158    ///   rather than this method.
3159    /// 
3160    /// # Example 1 for Random
3161    /// ```
3162    /// use cryptocol::random::Random;
3163    /// use cryptocol::define_utypes_with;
3164    /// define_utypes_with!(u8);
3165    /// 
3166    /// let mut rand = Random::new();
3167    /// let prime: U256 = rand.random_prime_with_msb_set_using_miller_rabin_biguint(5);
3168    /// println!("Random prime number: {}", prime);
3169    /// ```
3170    /// 
3171    /// # For more examples,
3172    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.random_prime_with_msb_set_using_miller_rabin_biguint)
3173    #[inline]
3174    pub fn random_prime_with_msb_set_using_miller_rabin_biguint<T, const N: usize>(&mut self, repetition: usize) -> BigUInt<T, N>
3175    where T: SmallUInt
3176    {
3177        self.random_primes_with_msb_set_using_miller_rabin_biguint(repetition, 1).pop().unwrap()
3178    }
3179
3180    // pub fn random_prime_with_msb_set_using_miller_rabin_biguint_sequentially<T, const N: usize>(&mut self, repetition: usize) -> BigUInt<T, N>
3181    /// Constucts a new `BigUInt<T, N>`-type object which represents a random
3182    /// prime number of full-size of BigUInt<T, N>.
3183    /// 
3184    /// # Argument
3185    /// The argument `repetition` defines how many times it tests whether the
3186    /// generated random number is prime. Usually, `repetition` is given to be
3187    /// `5` for 99.9% accuracy or `7` for 99.99% accuracy.
3188    /// 
3189    /// # Output
3190    /// The random prime numbers which ranges from
3191    /// BigUInt::halfmax() up to BigUInt::max() inclusively.
3192    /// 
3193    /// # Features
3194    /// - This method does not use concurrency.
3195    /// - This method generates a random number, and then simply sets its MSB
3196    ///   (Most Significant Bit) to be one, and then checks whether or not the
3197    ///   generated random number is prime number, and then it repeats until it
3198    ///   will generate a prime number.
3199    /// - It uses [Miller Rabin algorithm](https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test).
3200    /// - If this test results in composite number, the tested number is surely
3201    ///   a composite number. If this test results in prime number, the
3202    ///   probability that the tested number is not a prime number is 1/4. So,
3203    ///   if the test results in prime number twice, the probability that the
3204    ///   tested number is not a prime number is 1/16 (= 1/4 * 1/4). Therefore,
3205    ///   if you test any number 5 times and they all result in a prime number,
3206    ///   it is 99.9% that the number is a prime number.
3207    /// 
3208    /// # Example 1 for Random
3209    /// ```
3210    /// use cryptocol::random::Random;
3211    /// use cryptocol::define_utypes_with;
3212    /// define_utypes_with!(u8);
3213    /// 
3214    /// let mut rand = Random::new();
3215    /// let prime: U256 = rand.random_prime_with_msb_set_using_miller_rabin_biguint_sequentially(5);
3216    /// println!("Random prime number: {}", prime);
3217    /// ```
3218    /// 
3219    /// # For more examples,
3220    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.random_prime_with_msb_set_using_miller_rabin_biguint_sequentially)
3221    pub fn random_prime_with_msb_set_using_miller_rabin_biguint_sequentially<T, const N: usize>(&mut self, repetition: usize) -> BigUInt<T, N>
3222    where T: SmallUInt
3223    {
3224        let mut res = self.random_odd_with_msb_set_biguint::<T, N>();
3225        while !res.is_prime_using_miller_rabin(repetition)
3226            { res = self.random_odd_with_msb_set_biguint::<T, N>(); }
3227        res
3228    }
3229
3230    // pub fn random_primes_with_msb_set_using_miller_rabin_biguint<T, const N: usize>(&mut self, repetition: usize, how_many: usize) -> Vec<BigUInt<T, N>>
3231    /// Returns a collection of new `BigUInt<T, N>`-type objects which represent
3232    /// random prime numbers of full-size of BigUInt<T, N>.
3233    /// 
3234    /// # Argument
3235    /// - `repetition`: determines how many times it tests whether the
3236    ///   generated random number is prime. Usually, `repetition` is given
3237    ///   to be `5` for 99.9% accuracy or `7` for 99.99% accuracy.
3238    /// - `how_many`: determines how many prime numbers this method returns.
3239    /// 
3240    /// # Output
3241    /// The random prime number which ranges from
3242    /// BigUInt::halfmax() up to BigUInt::max() inclusively.
3243    /// 
3244    /// # Features
3245    /// - This method generates several threads, each of which checks whether or
3246    ///   not the given random number is prime number, and then it repeats until
3247    ///   it will find `how_many` prime numbers.
3248    /// - It uses [Miller Rabin algorithm](https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test).
3249    /// - If this test results in composite number, the tested number is surely
3250    ///   a composite number. If this test results in prime number, the
3251    ///   probability that the tested number is not a prime number is 1/4. So,
3252    ///   if the test results in prime number twice, the probability that the
3253    ///   tested number is not a prime number is 1/16 (= 1/4 * 1/4). Therefore,
3254    ///   if you test any number 5 times and they all result in a prime number,
3255    ///   it is 99.9% that the number is a prime number.
3256    /// - The random prime numbers that may or may not be cryptographically
3257    ///   secure depending on what pseudo-random number generator is used.
3258    pub fn random_primes_with_msb_set_using_miller_rabin_biguint<T, const N: usize>(&mut self, repetition: usize, how_many: usize) -> Vec<BigUInt<T, N>>
3259    where T: SmallUInt
3260    {
3261        let mut v = Vec::new();
3262        let mut number_of_threads = match available_parallelism()
3263        {
3264            Ok(non_zero) => non_zero.get() as usize,
3265            Err(_) => 1_usize,
3266        };
3267
3268        if number_of_threads <= 2
3269        {
3270            for _ in 0..how_many
3271                { v.push(self.random_prime_with_msb_set_using_miller_rabin_biguint_sequentially::<T, N>(repetition)); }
3272            return v;
3273        }
3274        number_of_threads >>= 1;
3275        let mut candidates = VecDeque::new();
3276        for _ in 0..number_of_threads
3277        {
3278            let candidate = self.random_prime_candidate_with_msb_set_biguint::<T, N>();
3279            candidates.push_back((candidate, 0_usize));
3280        }
3281
3282        let prime_like = Mutex::new(candidates);
3283        let vv = Mutex::new(v);
3284        let running = AtomicBool::new(true);
3285        let len = A_LIST.len();
3286        scope(|s| {
3287            for _ in 0..number_of_threads
3288            {
3289                s.spawn(|| {
3290                    let mut rand = Random::new();
3291                    loop
3292                    {
3293                        let mut prime = { prime_like.lock().unwrap().pop_front().unwrap() };
3294                        if !running.load(Ordering::Relaxed)
3295                            { break; }
3296                        if repetition <= len
3297                        {
3298                            if prime.1 < repetition - 1
3299                            {
3300                                if prime.0.test_miller_rabin(&BigUInt::<T, N>::from_uint(A_LIST[prime.1]))
3301                                {
3302                                    prime.1 += 1;
3303                                    { prime_like.lock().unwrap().push_back(prime); }
3304                                }
3305                                else
3306                                {
3307                                    let candidate = rand.random_prime_candidate_with_msb_set_biguint::<T, N>();
3308                                    { prime_like.lock().unwrap().push_back((candidate, 0_usize)); }
3309                                }
3310                            }
3311                            else    // prime.1 >= repetition - 1
3312                            {
3313                                if prime.0.test_miller_rabin(&BigUInt::<T, N>::from_uint(A_LIST[prime.1]))
3314                                {
3315                                    let length;
3316                                    {
3317                                        let mut v = vv.lock().unwrap();
3318                                        v.push(prime.0);
3319                                        length = v.len();
3320                                    }
3321                                    if length >= how_many
3322                                    {
3323                                        running.store(false, Ordering::Relaxed);
3324                                        break;
3325                                    }
3326                                }
3327                                let candidate = rand.random_prime_candidate_with_msb_set_biguint::<T, N>();
3328                                { prime_like.lock().unwrap().push_back((candidate, 0_usize)); }
3329                            }
3330                        }
3331                        else    // if repetition > len
3332                        {
3333                            if prime.1 < len
3334                            {
3335                                if prime.0.test_miller_rabin(&BigUInt::<T, N>::from_uint(A_LIST[prime.1]))
3336                                {
3337                                    prime.1 += 1;
3338                                    { prime_like.lock().unwrap().push_back(prime); }
3339                                }
3340                                else
3341                                {
3342                                    let candidate = rand.random_prime_candidate_with_msb_set_biguint::<T, N>();
3343                                    { prime_like.lock().unwrap().push_back((candidate, 0_usize)); }
3344                                }
3345                            }
3346                            else if prime.1 == len
3347                            {
3348                                prime.1 = A_LIST[len-1] as usize + 2;
3349                                if prime.0.test_miller_rabin(&BigUInt::<T, N>::from_uint(prime.1))
3350                                {
3351                                    prime.1 += 2;
3352                                    { prime_like.lock().unwrap().push_back(prime); }
3353                                }
3354                                else
3355                                {
3356                                    let candidate = rand.random_prime_candidate_with_msb_set_biguint::<T, N>();
3357                                    { prime_like.lock().unwrap().push_back((candidate, 0_usize)); }
3358                                }
3359                            }
3360                            else    // if prime.1 > len
3361                            {
3362                                if prime.0.test_miller_rabin(&BigUInt::<T, N>::from_uint(prime.1))
3363                                {
3364                                    if prime.1 >= A_LIST[len-1] as usize + ((repetition - len) << 1)
3365                                    {
3366                                        let length;
3367                                        {
3368                                            let mut v = vv.lock().unwrap();
3369                                            v.push(prime.0);
3370                                            length = v.len();
3371                                        }
3372                                        if length >= how_many
3373                                        {
3374                                            running.store(false, Ordering::Relaxed);
3375                                            break;
3376                                        }
3377                                        let candidate = rand.random_prime_candidate_with_msb_set_biguint::<T, N>();
3378                                        { prime_like.lock().unwrap().push_back((candidate, 0_usize)); }
3379                                    }
3380                                    else
3381                                    {
3382                                        prime.1 += 2;
3383                                        { prime_like.lock().unwrap().push_back(prime); }
3384                                    }
3385                                }
3386                                else
3387                                {
3388                                    let candidate = rand.random_prime_candidate_with_msb_set_biguint::<T, N>();
3389                                    { prime_like.lock().unwrap().push_back((candidate, 0_usize)); }
3390                                }
3391                            }
3392                        }
3393                    }
3394                });
3395            }
3396        });
3397        vv.into_inner().unwrap()
3398    }
3399
3400    // pub fn random_prime_with_half_length_using_miller_rabin_biguint<T, const N: usize>(&mut self, repetition: usize) -> BigUInt<T, N>
3401    /// Constucts a new `BigUInt<T, N>`-type object which represents a 
3402    /// `N * T::size_in_bits() / 2`-bit random prime number.
3403    /// 
3404    /// # Argument
3405    /// The argument `repetition` defines how many times it tests whether the
3406    /// generated random number is prime. Usually, `repetition` is given to be
3407    /// `5` for 99.9% accuracy or `7` for 99.99% accuracy.
3408    /// 
3409    /// # Output
3410    /// This method returns a random prime number whose length is
3411    /// `N * T::size_in_bits() / 2` bits.
3412    /// 
3413    /// # Features
3414    /// - This method generates a random number of half length, and then simply
3415    ///   sets all the bytes from `N * T::size_in_bits() / 2`-th bit to 
3416    ///   `N * T::size_in_bits() - 1`-th bit to be `zero`, and then checks
3417    ///   whether or not the generated random number is prime number, and then
3418    ///   it repeats until it will generate a prime number. Here, 0-th bit is
3419    ///   LSB (Least Significant Bit) and `N * T::size_in_bits() - 1`-th bit
3420    ///   is MSB (Most Significant Bit).
3421    /// - It uses
3422    ///   [Miller Rabin algorithm](https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test).
3423    /// - If this test results in composite number, the tested number is surely
3424    ///   a composite number. If this test results in prime number, the
3425    ///   probability that the tested number is not a prime number is 1/4. So,
3426    ///   if the test results in prime number twice, the probability that the
3427    ///   tested number is not a prime number is 1/16 (= 1/4 * 1/4). Therefore,
3428    ///   if you test any number 5 times and they all result in a prime number,
3429    ///   it is 99.9% that the number is a prime number.
3430    /// - The random prime numbers that may or may not be cryptographically
3431    ///   secure depending on what pseudo-random number generator is used.
3432    /// 
3433    /// # Cryptographical Security
3434    /// - If you use either `Random_*` or `Any_*`, it is considered to be
3435    ///   cryptographically secure.
3436    /// - If you use `Slapdash_*`, it is considered that it may be
3437    ///   cryptographically insecure.
3438    /// 
3439    /// # Counterpart Methods
3440    /// - If you want to use a normal random number, you are highly recommended
3441    ///   to use the method
3442    ///   [random_biguint()](struct@Random_Generic#method.random_biguint)
3443    ///   rather than this method.
3444    /// - If you want to use a random number less than a certain value, you are
3445    ///   highly recommended to use the method
3446    ///   [random_under_biguint()](struct@Random_Generic#method.random_under_biguint)
3447    ///   rather than this method.
3448    /// - If you want to use a random odd number, you are highly recommended to
3449    ///   use the method
3450    ///   [random_odd_biguint()](struct@Random_Generic#method.random_odd_biguint)
3451    ///   rather than this method.
3452    /// - If you want to use a random odd number less than a certain value,
3453    ///   you are highly recommended to use the method
3454    ///   [ranodm_odd_under_biguint()](struct@Random_Generic#method.ranodm_odd_under_biguint)
3455    ///   rather than this method.
3456    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random
3457    ///   number, you are highly recommended to use the method
3458    ///   [random_with_msb_set_biguint()](struct@Random_Generic#method.random_with_msb_set_biguint)
3459    ///   rather than this method.
3460    /// - If you want to use a `(N * sizeof::<T>() * 8)`-bit long random odd
3461    ///   number, you are highly recommended to use the method
3462    ///   [random_odd_with_msb_set_biguint()](struct@Random_Generic#method.random_odd_with_msb_set_biguint)
3463    ///   rather than this method.
3464    /// - If you want to use a normal random prime number, you are highly
3465    ///   recommended to use the method
3466    ///   [random_prime_using_miller_rabin_biguint()](struct@Random_Generic#method.random_prime_using_miller_rabin_biguint)
3467    ///   rather than this method.
3468    /// 
3469    /// # Example 1 for Random
3470    /// ```
3471    /// use cryptocol::random::Random;
3472    /// use cryptocol::define_utypes_with;
3473    /// define_utypes_with!(u128);
3474    /// 
3475    /// let mut rand = Random::new();
3476    /// let prime: U256 = rand.random_prime_with_half_length_using_miller_rabin_biguint(5);
3477    /// println!("Random prime number: {}", prime);
3478    /// ```
3479    /// 
3480    /// # For more examples,
3481    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.random_prime_with_half_length_using_miller_rabin_biguint)
3482    pub fn random_prime_with_half_length_using_miller_rabin_biguint<T, const N: usize>(&mut self, repetition: usize) -> BigUInt<T, N>
3483    where T: SmallUInt
3484    {
3485        let half = (T::BITS * N as u32) >> 1;
3486        let mut res: BigUInt<T, N> = self.random_with_msb_set_biguint();
3487        res.shift_right_assign(half);
3488        res.set_lsb();
3489        while !res.is_prime_using_miller_rabin(repetition)
3490        {
3491            res = self.random_with_msb_set_biguint();
3492            res.shift_right_assign(half);
3493            res.set_lsb();
3494        }
3495        res
3496    }
3497
3498    // pub fn random_primes_with_half_length_using_miller_rabin_biguint<T, const N: usize>(&mut self, repetition: usize, how_many: usize) -> Vec<BigUInt<T, N>>
3499    /// Returns a collection of new `BigUInt<T, N>`-type objects which represent
3500    /// random prime numbers of half-size of BigUInt<T, N>.
3501    /// 
3502    /// # Argument
3503    /// - `repetition`: determines how many times it tests whether the
3504    ///   generated random number is prime. Usually, `repetition` is given
3505    ///   to be `5` for 99.9% accuracy or `7` for 99.99% accuracy.
3506    /// - `how_many`: determines how many prime numbers this method returns.
3507    /// 
3508    /// # Output
3509    /// The random prime number which ranges from
3510    /// BigUInt::halfmax() up to BigUInt::max() inclusively.
3511    /// 
3512    /// # Features
3513    /// - This method generates several threads, each of which checks whether or
3514    ///   not the given random number is prime number, and then it repeats until
3515    ///   it will find `how_many` prime numbers.
3516    /// - It uses [Miller Rabin algorithm](https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test).
3517    /// - If this test results in composite number, the tested number is surely
3518    ///   a composite number. If this test results in prime number, the
3519    ///   probability that the tested number is not a prime number is 1/4. So,
3520    ///   if the test results in prime number twice, the probability that the
3521    ///   tested number is not a prime number is 1/16 (= 1/4 * 1/4). Therefore,
3522    ///   if you test any number 5 times and they all result in a prime number,
3523    ///   it is 99.9% that the number is a prime number.
3524    /// - The random prime numbers that may or may not be cryptographically
3525    ///   secure depending on what pseudo-random number generator is used.
3526    pub fn random_primes_with_half_length_using_miller_rabin_biguint<T, const N: usize>(&mut self, repetition: usize, how_many: usize) -> Vec<BigUInt<T, N>>
3527    where T: SmallUInt
3528    {
3529        let mut v = Vec::new();
3530        let mut number_of_threads = match available_parallelism()
3531        {
3532            Ok(non_zero) => non_zero.get() as usize,
3533            Err(_) => 1_usize,
3534        };
3535
3536        if number_of_threads <= 2
3537        {
3538            for _ in 0..how_many
3539                { v.push(self.random_prime_with_msb_set_using_miller_rabin_biguint_sequentially::<T, N>(repetition)); }
3540            return v;
3541        }
3542        number_of_threads >>= 1;
3543        let mut candidates = VecDeque::new();
3544        for _ in 0..number_of_threads
3545        {
3546            let candidate = self.random_prime_candidate_with_half_length_biguint::<T, N>();
3547            candidates.push_back((candidate, 0_usize));
3548        }
3549        let prime_like = Mutex::new(candidates);
3550        let vv = Mutex::new(v);
3551        let running = AtomicBool::new(true);
3552        let len = A_LIST.len();
3553        scope(|s| {
3554            for _ in 0..number_of_threads
3555            {
3556                s.spawn(|| {
3557                    let mut rand = Random::new();
3558                    loop
3559                    {
3560                        let mut prime = { prime_like.lock().unwrap().pop_front().unwrap() };
3561                        if !running.load(Ordering::Relaxed)
3562                            { break; }
3563                        if repetition <= len
3564                        {
3565                            if prime.1 < repetition - 1
3566                            {
3567                                if prime.0.test_miller_rabin(&BigUInt::<T, N>::from_uint(A_LIST[prime.1]))
3568                                {
3569                                    prime.1 += 1;
3570                                    { prime_like.lock().unwrap().push_back(prime); }
3571                                }
3572                                else
3573                                {
3574                                    let candidate = rand.random_prime_candidate_with_half_length_biguint::<T, N>();
3575                                    { prime_like.lock().unwrap().push_back((candidate, 0_usize)); }
3576                                }
3577                            }
3578                            else    // prime.1 >= repetition - 1
3579                            {
3580                                if prime.0.test_miller_rabin(&BigUInt::<T, N>::from_uint(A_LIST[prime.1]))
3581                                {
3582                                    let length;
3583                                    {
3584                                        let mut v = vv.lock().unwrap();
3585                                        v.push(prime.0);
3586                                        length = v.len();
3587                                    }
3588                                    if length >= how_many
3589                                    {
3590                                        running.store(false, Ordering::Relaxed);
3591                                        break;
3592                                    }
3593                                }
3594                                let candidate = rand.random_prime_candidate_with_half_length_biguint::<T, N>();
3595                                { prime_like.lock().unwrap().push_back((candidate, 0_usize)); }
3596                            }
3597                        }
3598                        else    // if repetition > len
3599                        {
3600                            if prime.1 < len
3601                            {
3602                                if prime.0.test_miller_rabin(&BigUInt::<T, N>::from_uint(A_LIST[prime.1]))
3603                                {
3604                                    prime.1 += 1;
3605                                    { prime_like.lock().unwrap().push_back(prime); }
3606                                }
3607                                else
3608                                {
3609                                    let candidate = rand.random_prime_candidate_with_half_length_biguint::<T, N>();
3610                                    { prime_like.lock().unwrap().push_back((candidate, 0_usize)); }
3611                                }
3612                            }
3613                            else if prime.1 == len
3614                            {
3615                                prime.1 = A_LIST[len-1] as usize + 2;
3616                                if prime.0.test_miller_rabin(&BigUInt::<T, N>::from_uint(prime.1))
3617                                {
3618                                    prime.1 += 2;
3619                                    { prime_like.lock().unwrap().push_back(prime); }
3620                                }
3621                                else
3622                                {
3623                                    let candidate = rand.random_prime_candidate_with_half_length_biguint::<T, N>();
3624                                    { prime_like.lock().unwrap().push_back((candidate, 0_usize)); }
3625                                }
3626                            }
3627                            else    // if prime.1 > len
3628                            {
3629                                if prime.0.test_miller_rabin(&BigUInt::<T, N>::from_uint(prime.1))
3630                                {
3631                                    if prime.1 >= A_LIST[len-1] as usize + ((repetition - len) << 1)
3632                                    {
3633                                        let length;
3634                                        {
3635                                            let mut v = vv.lock().unwrap();
3636                                            v.push(prime.0);
3637                                            length = v.len();
3638                                        }
3639                                        if length >= how_many
3640                                        {
3641                                            running.store(false, Ordering::Relaxed);
3642                                            break;
3643                                        }
3644                                        let candidate = rand.random_prime_candidate_with_half_length_biguint::<T, N>();
3645                                        { prime_like.lock().unwrap().push_back((candidate, 0_usize)); }
3646                                    }
3647                                    else
3648                                    {
3649                                        prime.1 += 2;
3650                                        { prime_like.lock().unwrap().push_back(prime); }
3651                                    }
3652                                }
3653                                else
3654                                {
3655                                    let candidate = rand.random_prime_candidate_with_half_length_biguint::<T, N>();
3656                                    { prime_like.lock().unwrap().push_back((candidate, 0_usize)); }
3657                                }
3658                            }
3659                        }
3660                    }
3661                });
3662            }
3663        });
3664        vv.into_inner().unwrap()
3665    }
3666
3667    // pub fn random_prime_with_half_length_using_rsa_biguint<T, const N: usize>(&mut self, repetition: usize) -> (BigUInt<T, N>, BigUInt<T, N>)
3668    /// Constucts a new `BigUInt<T, N>`-type object which represents a random
3669    /// prime number.
3670    /// 
3671    /// # Argument
3672    /// The argument `repetition` defines how many times it tests whether the
3673    /// generated random number is prime. Usually, `repetition` is given to be
3674    /// `5` for 99.9% accuracy or `7` for 99.99% accuracy.
3675    /// 
3676    /// # Output
3677    /// The tuple of the two random prime numbers that this method returns is
3678    /// the tuple of the two random prime number each of which ranges
3679    /// from BigUInt::halfmax() up to BigUInt::max() inclusively.
3680    /// 
3681    /// # Features
3682    /// This method uses Millar-Rabin algorithm and then determines whether or
3683    /// not the generated random prime number candidate is really prime with
3684    /// the RSA test. If it fails, this method repeats searching for another
3685    /// ranmdom prime candidate until this method finds the true random prime
3686    /// number, and return it.
3687    /// 
3688    /// # Example
3689    /// ```
3690    /// use cryptocol::random::Random;
3691    /// use cryptocol::define_utypes_with;
3692    /// define_utypes_with!(u64);
3693    /// 
3694    /// let mut prng = Random::new();
3695    /// let (prime1, prime2): (U1024, U1024) = prng.random_prime_with_half_length_using_rsa_biguint(7);
3696    /// let (prime1, prime2): (U512, U512) = (prime1.into_biguint(), prime2.into_biguint());
3697    /// println!("U512 Prime number: {}", prime1);
3698    /// println!("U512 Prime number: {}", prime2);
3699    /// ```
3700    pub fn random_prime_with_half_length_using_rsa_biguint<T, const N: usize>(&mut self, repetition: usize) -> (BigUInt<T, N>, BigUInt<T, N>)
3701    where T: SmallUInt
3702    {
3703        use crate::asymmetric::RSA_Generic;
3704        let length = N * (T::BITS >> 1) as usize;
3705        loop
3706        {
3707            let mut primes: Vec<BigUInt<T, N>> = self.random_primes_with_half_length_using_miller_rabin_biguint(repetition, 2);
3708            let prime_1 = primes.pop().unwrap();
3709            let mut prime_2 = primes.pop().unwrap();
3710            while prime_1 == prime_2
3711                { prime_2 = self.random_prime_with_half_length_using_miller_rabin_biguint(repetition); }
3712            let rsa = RSA_Generic::<N, T>::new_with_primes(prime_1.clone(), prime_2.clone());
3713            let message = rsa.get_modulus().shift_right(length);
3714            let cipher = rsa.encrypt_biguint(&message);
3715            let recover = rsa.decrypt_biguint(&cipher);
3716            if recover == message
3717            {
3718                let cipher = rsa.encrypt_biguint(&prime_1);
3719                let recover = rsa.decrypt_biguint(&cipher);
3720                if prime_1 == recover
3721                {
3722                    let cipher = rsa.encrypt_biguint(&prime_2);
3723                    let recover = rsa.decrypt_biguint(&cipher);
3724                    if prime_2 == recover
3725                        { return (prime_1, prime_2); }
3726                }
3727            }
3728        }
3729    }
3730
3731    // pub fn prepared_random_prime_with_msb_set<T, const N: usize>(&mut self) -> BigUInt<T, N>
3732    /// Constucts a new `BigUInt<T, N>`-type object out of the prepared prime
3733    /// number pool, which represents a prime number of full-size of
3734    /// BigUInt<T, N>.
3735    /// 
3736    /// # Output
3737    /// This method returns a prime number randomly chosen out of the prepared
3738    /// prime number pool consisting of many prime numbers, whose range is from
3739    /// BigUInt::halfmax() up to BigUInt::max() inclusively.
3740    /// 
3741    /// # Features
3742    /// - This method chooses a prime number ramdomly out of the prepared prime
3743    ///   number pool consisting of many prime numbers whose MSB (Most
3744    ///   Significant Bit) is set to be one.
3745    /// - It uses a prime number pool.
3746    /// 
3747    /// # Caution and Cryptographical Security
3748    /// The source code of this method is openly publicised. It means that
3749    /// anyone can have the full familiarity of the prime number pool which
3750    /// this method uses. So, you are NOT encouraged to use this method for
3751    /// serious cryptographical purposes. You can use this method temporarily
3752    /// for testing or debugging purposes because of the slowness of the
3753    /// Millar-Rabin algorithm for big numbers.
3754    /// 
3755    /// # Example 1 for Random
3756    /// ```
3757    /// use cryptocol::random::Random;
3758    /// use cryptocol::define_utypes_with;
3759    /// define_utypes_with!(u64);
3760    /// 
3761    /// let mut rand = Random::new();
3762    /// let biguint: U256 = rand.prepared_random_prime_with_msb_set();
3763    /// println!("Random Number: {}", biguint);
3764    /// ```
3765    /// 
3766    /// # For more examples,
3767    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.prepared_random_prime_with_msb_set)
3768    #[inline]
3769    pub fn prepared_random_prime_with_msb_set<T, const N: usize>(&mut self) -> BigUInt<T, N>
3770    where T: SmallUInt
3771    {
3772        self.get_prepared_prime_number(T::size_in_bytes() as usize * N)
3773    }
3774
3775    // pub fn prepared_random_prime_with_half_length<T, const N: usize>(&mut self) -> BigUInt<T, N>
3776    /// Constucts a new `BigUInt<T, N>`-type object out of the prepared prime
3777    /// number pool, which represents a prime number of half-size of
3778    /// BigUInt<T, N>.
3779    /// 
3780    /// # Output
3781    /// This method returns a prime number randomly chosen out of the prepared
3782    /// prime number pool consisting of many prime numbers, whose length is
3783    /// `N * T::size_in_bits() / 2` bits.
3784    /// 
3785    /// # Features
3786    /// 
3787    /// - This method chooses a prime number ramdomly out of the prepared prime
3788    ///   number pool consisting of many prime numbers whose length is
3789    ///   `N * T::size_in_bits() / 2` bits.
3790    /// - It uses a prime number pool.
3791    /// 
3792    /// # Caution and Cryptographical Security
3793    /// The source code of this method is openly publicised. It means that
3794    /// anyone can have the full familiarity of the prime number pool which
3795    /// this method uses. So, you are NOT encouraged to use this method for
3796    /// serious cryptographical purposes. You can use this method temporarily
3797    /// for testing or debugging purposes because of the slowness of the
3798    /// Millar-Rabin algorithm for big numbers.
3799    /// 
3800    /// # Example 1 for Random
3801    /// ```
3802    /// use cryptocol::random::Random;
3803    /// use cryptocol::define_utypes_with;
3804    /// define_utypes_with!(u32);
3805    /// 
3806    /// let mut rand = Random::new();
3807    /// let biguint: U256 = rand.prepared_random_prime_with_half_length();
3808    /// println!("Random Number: {}", biguint);
3809    /// ```
3810    /// 
3811    /// # For more examples,
3812    /// click [here](./documentation/random_random_biguint/struct.Random_Generic.html#method.prepared_random_prime_with_half_length)
3813    pub fn prepared_random_prime_with_half_length<T, const N: usize>(&mut self) -> BigUInt<T, N>
3814    where T: SmallUInt
3815    {
3816        self.get_prepared_prime_number((T::size_in_bytes() as usize * N) >> 1)
3817    }
3818
3819    fn get_prepared_prime_number<T, const N: usize>(&mut self, length_in_bytes: usize) -> BigUInt<T, N>
3820    where T: SmallUInt
3821    {
3822        let row: usize;
3823        match length_in_bytes
3824        {
3825            512 =>  { row = 0; },   // 4096-bit
3826            256 =>  { row = 1; },   // 2048-bit
3827            128 =>  { row = 2; },   // 1024-bit
3828            64 =>   { row = 3; },   // 512-bit
3829            32 =>   { row = 4; },   // 256-bit
3830            _ =>
3831            {
3832                return
3833                    if length_in_bytes == T::size_in_bytes() as usize * N
3834                        { self.random_prime_with_msb_set_using_miller_rabin_biguint(7) }
3835                    else
3836                        { self.random_prime_with_half_length_using_miller_rabin_biguint(7) }
3837            },
3838        }
3839        let col = self.random_usize() % COLUMN;
3840        BigUInt::<T, N>::from_str_radix(NUM_STR[row][col], 16).unwrap()
3841    }
3842
3843    // pub fn prepared_random_prime_numbers(&mut self) -> &[[&str; COLUMN]; 4]
3844    /// Returns a refenece to the prepared prime number pool, which represents
3845    /// a two-dimensional array prime numbers.
3846    /// 
3847    /// # Output
3848    /// A refenece to the prepared prime number pool, which represents
3849    /// a two-dimensional array prime number strings.
3850    /// 
3851    /// # Features
3852    /// - The zeroth one-dimensional array contains 4096-bit prime number array.
3853    /// - The first one-dimensional array contains 2048-bit prime number array.
3854    /// - The second one-dimensional array contains 1024-bit prime number array.
3855    /// - The third one-dimensional array contains 512-bit prime number array.
3856    /// - The fourth one-dimensional array contains 256-bit prime number array.
3857    #[inline]
3858    pub fn prepared_random_prime_numbers() -> &'static [[&'static str; COLUMN]; ROW]
3859    {
3860        &NUM_STR
3861    }
3862
3863    // pub fn shuffle(&self, slice: &mut [T])
3864    /// Shuffles an array slice.
3865    pub fn shuffle<T>(&mut self, slice: &mut [T])
3866    {
3867        let len = slice.len();
3868        for n in (2..len).rev()
3869        {
3870            let m = self.random_under_uint_(n);
3871            slice.swap(m, n-1);
3872        }
3873    }
3874}
3875
cryptocol/random/random.rs

cryptocol/random/
random.rs
