//! BigNum implementation
//!
//! Large numbers are important for a cryptographic library. OpenSSL implementation
//! of BigNum uses dynamically assigned memory to store an array of bit chunks. This
//! allows numbers of any size to be compared and mathematical functions performed.
//!
//! OpenSSL wiki describes the [`BIGNUM`] data structure.
//!
//! # Examples
//!
//! ```
//! use openssl::bn::BigNum;
//! use openssl::error::ErrorStack;
//!
//! fn bignums() -> Result< (), ErrorStack > {
//! let a = BigNum::new()?; // a = 0
//! let b = BigNum::from_dec_str("1234567890123456789012345")?;
//! let c = &a * &b;
//! assert_eq!(a,c);
//! Ok(())
//! }
//! # fn main() {
//! # bignums();
//! # }
//!
//! [`BIGNUM`]: https://wiki.openssl.org/index.php/Manual:Bn_internal(3)
use ffi;
use foreign_types::{ForeignType, ForeignTypeRef};
use libc::c_int;
use std::cmp::Ordering;
use std::ffi::CString;
use std::{fmt, ptr};
use std::ops::{Add, Div, Mul, Neg, Rem, Shl, Shr, Sub, Deref};
use {cvt, cvt_p, cvt_n};
use asn1::Asn1Integer;
use error::ErrorStack;
use string::OpensslString;
#[cfg(ossl10x)]
use ffi::{get_rfc2409_prime_768 as BN_get_rfc2409_prime_768,
get_rfc2409_prime_1024 as BN_get_rfc2409_prime_1024,
get_rfc3526_prime_1536 as BN_get_rfc3526_prime_1536,
get_rfc3526_prime_2048 as BN_get_rfc3526_prime_2048,
get_rfc3526_prime_3072 as BN_get_rfc3526_prime_3072,
get_rfc3526_prime_4096 as BN_get_rfc3526_prime_4096,
get_rfc3526_prime_6144 as BN_get_rfc3526_prime_6144,
get_rfc3526_prime_8192 as BN_get_rfc3526_prime_8192};
#[cfg(ossl110)]
use ffi::{BN_get_rfc2409_prime_768, BN_get_rfc2409_prime_1024, BN_get_rfc3526_prime_1536,
BN_get_rfc3526_prime_2048, BN_get_rfc3526_prime_3072, BN_get_rfc3526_prime_4096,
BN_get_rfc3526_prime_6144, BN_get_rfc3526_prime_8192};
/// Options for the most significant bits of a randomly generated `BigNum`.
pub struct MsbOption(c_int);
/// The most significant bit of the number may be 0.
pub const MSB_MAYBE_ZERO: MsbOption = MsbOption(-1);
/// The most significant bit of the number must be 1.
pub const MSB_ONE: MsbOption = MsbOption(0);
/// The most significant two bits of the number must be 1.
///
/// The number of bits in the product of two such numbers will always be exactly twice the number
/// of bits in the original numbers.
pub const TWO_MSB_ONE: MsbOption = MsbOption(1);
foreign_type_and_impl_send_sync! {
type CType = ffi::BN_CTX;
fn drop = ffi::BN_CTX_free;
/// Temporary storage for BigNums on the secure heap
///
/// BigNum values are stored dynamically and therefore can be expensive
/// to allocate. BigNumContext and the OpenSSL [`BN_CTX`] structure are used
/// internally when passing BigNum values between subroutines.
///
/// [`BN_CTX`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_CTX_new.html
pub struct BigNumContext;
/// Reference to [`BigNumContext`]
///
/// [`BigNumContext`]: struct.BigNumContext.html
pub struct BigNumContextRef;
}
impl BigNumContext {
/// Returns a new `BigNumContext`.
///
/// See OpenSSL documentation at [`BN_CTX_new`].
///
/// [`BN_CTX_new`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_CTX_new.html
pub fn new() -> Result<BigNumContext, ErrorStack> {
unsafe {
ffi::init();
cvt_p(ffi::BN_CTX_new()).map(BigNumContext)
}
}
}
foreign_type_and_impl_send_sync! {
type CType = ffi::BIGNUM;
fn drop = ffi::BN_free;
/// Dynamically sized large number impelementation
///
/// Perform large number mathematics. Create a new BigNum
/// with [`new`]. Perform stanard mathematics on large numbers using
/// methods from [`Dref<Target = BigNumRef>`]
///
/// OpenSSL documenation at [`BN_new`].
///
/// [`new`]: struct.BigNum.html#method.new
/// [`Dref<Target = BigNumRef>`]: struct.BigNum.html#deref-methods
/// [`BN_new`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_new.html
///
/// # Examples
/// ```
/// use openssl::bn::BigNum;
/// # use openssl::error::ErrorStack;
/// # fn bignums() -> Result< (), ErrorStack > {
/// let little_big = BigNum::from_u32(std::u32::MAX)?;
/// assert_eq!(*&little_big.num_bytes(), 4);
/// # Ok(())
/// # }
/// # fn main () { bignums(); }
/// ```
pub struct BigNum;
/// Reference to a [`BigNum`]
///
/// [`BigNum`]: struct.BigNum.html
pub struct BigNumRef;
}
impl BigNumRef {
/// Erases the memory used by this `BigNum`, resetting its value to 0.
///
/// This can be used to destroy sensitive data such as keys when they are no longer needed.
///
/// OpenSSL documentation at [`BN_clear`]
///
/// [`BN_clear`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_clear.html
pub fn clear(&mut self) {
unsafe { ffi::BN_clear(self.as_ptr()) }
}
/// Adds a `u32` to `self`.
///
/// OpenSSL documentation at [`BN_add_word`]
///
/// [`BN_add_word`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_add_word.html
pub fn add_word(&mut self, w: u32) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_add_word(self.as_ptr(), w as ffi::BN_ULONG)).map(|_| ()) }
}
/// Subtracts a `u32` from `self`.
///
/// OpenSSL documentation at [`BN_sub_word`]
///
/// [`BN_sub_word`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_sub_word.html
pub fn sub_word(&mut self, w: u32) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_sub_word(self.as_ptr(), w as ffi::BN_ULONG)).map(|_| ()) }
}
/// Multiplies a `u32` by `self`.
///
/// OpenSSL documentation at [`BN_mul_word`]
///
/// [`BN_mul_word`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_mul_word.html
pub fn mul_word(&mut self, w: u32) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_mul_word(self.as_ptr(), w as ffi::BN_ULONG)).map(|_| ()) }
}
/// Divides `self` by a `u32`, returning the remainder.
///
/// OpenSSL documentation at [`BN_div_word`]
///
/// [`BN_div_word`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_div_word.html
pub fn div_word(&mut self, w: u32) -> Result<u64, ErrorStack> {
unsafe {
let r = ffi::BN_div_word(self.as_ptr(), w.into());
if r == ffi::BN_ULONG::max_value() {
Err(ErrorStack::get())
} else {
Ok(r.into())
}
}
}
/// Returns the result of `self` modulo `w`.
///
/// OpenSSL documentation at [`BN_mod_word`]
///
/// [`BN_mod_word`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_mod_word.html
pub fn mod_word(&self, w: u32) -> Result<u64, ErrorStack> {
unsafe {
let r = ffi::BN_mod_word(self.as_ptr(), w.into());
if r == ffi::BN_ULONG::max_value() {
Err(ErrorStack::get())
} else {
Ok(r.into())
}
}
}
/// Places a cryptographically-secure pseudo-random nonnegative
/// number less than `self` in `rnd`.
///
/// OpenSSL documentation at [`BN_rand_range`]
///
/// [`BN_rand_range`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_rand_range.html
pub fn rand_range(&self, rnd: &mut BigNumRef) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_rand_range(rnd.as_ptr(), self.as_ptr())).map(|_| ()) }
}
/// The cryptographically weak counterpart to `rand_in_range`.
///
/// OpenSSL documentation at [`BN_pseudo_rand_range`]
///
/// [`BN_pseudo_rand_range`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_pseudo_rand_range.html
pub fn pseudo_rand_range(&self, rnd: &mut BigNumRef) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_pseudo_rand_range(rnd.as_ptr(), self.as_ptr())).map(|_| ()) }
}
/// Sets bit `n`. Equivalent to `self |= (1 << n)`.
///
/// When setting a bit outside of `self`, it is expanded.
///
/// OpenSSL documentation at [`BN_set_bit`]
///
/// [`BN_set_bit`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_set_bit.html
pub fn set_bit(&mut self, n: i32) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_set_bit(self.as_ptr(), n.into())).map(|_| ()) }
}
/// Clears bit `n`, setting it to 0. Equivalent to `self &= ~(1 << n)`.
///
/// When clearing a bit outside of `self`, an error is returned.
///
/// OpenSSL documentation at [`BN_clear_bit`]
///
/// [`BN_clear_bit`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_clear_bit.html
pub fn clear_bit(&mut self, n: i32) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_clear_bit(self.as_ptr(), n.into())).map(|_| ()) }
}
/// Returns `true` if the `n`th bit of `self` is set to 1, `false` otherwise.
///
/// OpenSSL documentation at [`BN_is_bit_set`]
///
/// [`BN_is_bit_set`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_is_bit_set.html
pub fn is_bit_set(&self, n: i32) -> bool {
unsafe { ffi::BN_is_bit_set(self.as_ptr(), n.into()) == 1 }
}
/// Truncates `self` to the lowest `n` bits.
///
/// An error occurs if `self` is already shorter than `n` bits.
///
/// OpenSSL documentation at [`BN_mask_bits`]
///
/// [`BN_mask_bits`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_mask_bits.html
pub fn mask_bits(&mut self, n: i32) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_mask_bits(self.as_ptr(), n.into())).map(|_| ()) }
}
/// Places `a << 1` in `self`. Equivalent to `self * 2`.
///
/// OpenSSL documentation at [`BN_lshift1`]
///
/// [`BN_lshift1`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_lshift1.html
pub fn lshift1(&mut self, a: &BigNumRef) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_lshift1(self.as_ptr(), a.as_ptr())).map(|_| ()) }
}
/// Places `a >> 1` in `self`. Equivalent to `self / 2`.
///
/// OpenSSL documentation at [`BN_rshift1`]
///
/// [`BN_rshift1`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_rshift1.html
pub fn rshift1(&mut self, a: &BigNumRef) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_rshift1(self.as_ptr(), a.as_ptr())).map(|_| ()) }
}
/// Places `a + b` in `self`. [`core::ops::Add`] is also implemented for `BigNumRef`.
///
/// OpenSSL documentation at [`BN_add`]
///
/// [`core::ops::Add`]: struct.BigNumRef.html#method.add
/// [`BN_add`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_add.html
pub fn checked_add(&mut self, a: &BigNumRef, b: &BigNumRef) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_add(self.as_ptr(), a.as_ptr(), b.as_ptr())).map(|_| ()) }
}
/// Places `a - b` in `self`. [`core::ops::Sub`] is also implemented for `BigNumRef`.
///
/// OpenSSL documentation at [`BN_sub`]
///
/// [`core::ops::Sub`]: struct.BigNumRef.html#method.sub
/// [`BN_sub`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_sub.html
pub fn checked_sub(&mut self, a: &BigNumRef, b: &BigNumRef) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_sub(self.as_ptr(), a.as_ptr(), b.as_ptr())).map(|_| ()) }
}
/// Places `a << n` in `self`. Equivalent to `a * 2 ^ n`.
///
/// OpenSSL documentation at [`BN_lshift`]
///
/// [`BN_lshift`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_lshift.html
pub fn lshift(&mut self, a: &BigNumRef, n: i32) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_lshift(self.as_ptr(), a.as_ptr(), n.into())).map(|_| ()) }
}
/// Places `a >> n` in `self`. Equivalent to `a / 2 ^ n`.
///
/// OpenSSL documentation at [`BN_rshift`]
///
/// [`BN_rshift`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_rshift.html
pub fn rshift(&mut self, a: &BigNumRef, n: i32) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_rshift(self.as_ptr(), a.as_ptr(), n.into())).map(|_| ()) }
}
/// Creates a new BigNum with the same value.
///
/// OpenSSL documentation at [`BN_dup`]
///
/// [`BN_dup`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_dup.html
pub fn to_owned(&self) -> Result<BigNum, ErrorStack> {
unsafe { cvt_p(ffi::BN_dup(self.as_ptr())).map(|b| BigNum::from_ptr(b)) }
}
/// Sets the sign of `self`. Pass true to set `self` to a negative. False sets
/// `self` positive.
pub fn set_negative(&mut self, negative: bool) {
unsafe { ffi::BN_set_negative(self.as_ptr(), negative as c_int) }
}
/// Compare the absolute values of `self` and `oth`.
///
/// OpenSSL documentation at [`BN_ucmp`]
///
/// [`BN_ucmp`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_ucmp.html
///
/// # Examples
///
/// ```
/// # use openssl::bn::BigNum;
/// # use std::cmp::Ordering;
/// let s = -BigNum::from_u32(8).unwrap();
/// let o = BigNum::from_u32(8).unwrap();
///
/// assert_eq!(s.ucmp(&o), Ordering::Equal);
/// ```
pub fn ucmp(&self, oth: &BigNumRef) -> Ordering {
unsafe { ffi::BN_ucmp(self.as_ptr(), oth.as_ptr()).cmp(&0) }
}
/// Returns `true` if `self` is negative.
pub fn is_negative(&self) -> bool {
self._is_negative()
}
#[cfg(ossl10x)]
fn _is_negative(&self) -> bool {
unsafe { (*self.as_ptr()).neg == 1 }
}
#[cfg(ossl110)]
fn _is_negative(&self) -> bool {
unsafe { ffi::BN_is_negative(self.as_ptr()) == 1 }
}
/// Returns the number of significant bits in `self`.
///
/// OpenSSL documentation at [`BN_num_bits`]
///
/// [`BN_num_bits`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_num_bits.html
pub fn num_bits(&self) -> i32 {
unsafe { ffi::BN_num_bits(self.as_ptr()) as i32 }
}
/// Returns the size of `self` in bytes. Implemented natively.
pub fn num_bytes(&self) -> i32 {
(self.num_bits() + 7) / 8
}
/// Generates a cryptographically strong pseudo-random `BigNum`, placing it in `self`.
///
/// # Parameters
///
/// * `bits`: Length of the number in bits.
/// * `msb`: The desired properties of the most significant bit. See [`constants`].
/// * `odd`: If `true`, the generated number will be odd.
///
/// # Examples
///
/// ```
/// use openssl::bn::{BigNum,MSB_MAYBE_ZERO};
/// use openssl::error::ErrorStack;
///
/// fn generate_random() -> Result< BigNum, ErrorStack > {
/// let mut big = BigNum::new()?;
///
/// // Generates a 128-bit odd random number
/// big.rand(128, MSB_MAYBE_ZERO, true);
/// Ok((big))
/// }
/// ```
///
/// OpenSSL documentation at [`BN_rand`]
///
/// [`constants`]: index.html#constants
/// [`BN_rand`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_rand.html
pub fn rand(&mut self, bits: i32, msb: MsbOption, odd: bool) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_rand(
self.as_ptr(),
bits.into(),
msb.0,
odd as c_int,
)).map(|_| ())
}
}
/// The cryptographically weak counterpart to `rand`. Not suitable for key generation.
///
/// OpenSSL documentation at [`BN_psuedo_rand`]
///
/// [`BN_psuedo_rand`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_pseudo_rand.html
pub fn pseudo_rand(&mut self, bits: i32, msb: MsbOption, odd: bool) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_pseudo_rand(
self.as_ptr(),
bits.into(),
msb.0,
odd as c_int,
)).map(|_| ())
}
}
/// Generates a prime number, placing it in `self`.
///
/// # Parameters
///
/// * `bits`: The length of the prime in bits (lower bound).
/// * `safe`: If true, returns a "safe" prime `p` so that `(p-1)/2` is also prime.
/// * `add`/`rem`: If `add` is set to `Some(add)`, `p % add == rem` will hold, where `p` is the
/// generated prime and `rem` is `1` if not specified (`None`).
///
/// # Examples
///
/// ```
/// use openssl::bn::BigNum;
/// use openssl::error::ErrorStack;
///
/// fn generate_weak_prime() -> Result< BigNum, ErrorStack > {
/// let mut big = BigNum::new()?;
///
/// // Generates a 128-bit simple prime number
/// big.generate_prime(128, false, None, None);
/// Ok((big))
/// }
/// ```
///
/// OpenSSL documentation at [`BN_generate_prime_ex`]
///
/// [`BN_generate_prime_ex`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_generate_prime_ex.html
pub fn generate_prime(
&mut self,
bits: i32,
safe: bool,
add: Option<&BigNumRef>,
rem: Option<&BigNumRef>,
) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_generate_prime_ex(
self.as_ptr(),
bits as c_int,
safe as c_int,
add.map(|n| n.as_ptr()).unwrap_or(ptr::null_mut()),
rem.map(|n| n.as_ptr()).unwrap_or(ptr::null_mut()),
ptr::null_mut(),
)).map(|_| ())
}
}
/// Places the result of `a * b` in `self`.
/// [`core::ops::Mul`] is also implemented for `BigNumRef`.
///
/// OpenSSL documentation at [`BN_mul`]
///
/// [`core::ops::Mul`]: struct.BigNumRef.html#method.mul
/// [`BN_mul`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_mul.html
pub fn checked_mul(
&mut self,
a: &BigNumRef,
b: &BigNumRef,
ctx: &mut BigNumContextRef,
) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_mul(
self.as_ptr(),
a.as_ptr(),
b.as_ptr(),
ctx.as_ptr(),
)).map(|_| ())
}
}
/// Places the result of `a / b` in `self`. The remainder is discarded.
/// [`core::ops::Div`] is also implemented for `BigNumRef`.
///
/// OpenSSL documentation at [`BN_div`]
///
/// [`core::ops::Div`]: struct.BigNumRef.html#method.div
/// [`BN_div`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_div.html
pub fn checked_div(
&mut self,
a: &BigNumRef,
b: &BigNumRef,
ctx: &mut BigNumContextRef,
) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_div(
self.as_ptr(),
ptr::null_mut(),
a.as_ptr(),
b.as_ptr(),
ctx.as_ptr(),
)).map(|_| ())
}
}
/// Places the result of `a % b` in `self`.
///
/// OpenSSL documentation at [`BN_div`]
///
/// [`BN_div`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_div.html
pub fn checked_rem(
&mut self,
a: &BigNumRef,
b: &BigNumRef,
ctx: &mut BigNumContextRef,
) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_div(
ptr::null_mut(),
self.as_ptr(),
a.as_ptr(),
b.as_ptr(),
ctx.as_ptr(),
)).map(|_| ())
}
}
/// Places the result of `a / b` in `self` and `a % b` in `rem`.
///
/// OpenSSL documentation at [`BN_div`]
///
/// [`BN_div`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_div.html
pub fn div_rem(
&mut self,
rem: &mut BigNumRef,
a: &BigNumRef,
b: &BigNumRef,
ctx: &mut BigNumContextRef,
) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_div(
self.as_ptr(),
rem.as_ptr(),
a.as_ptr(),
b.as_ptr(),
ctx.as_ptr(),
)).map(|_| ())
}
}
/// Places the result of `a²` in `self`.
///
/// OpenSSL documentation at [`BN_sqr`]
///
/// [`BN_sqr`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_sqr.html
pub fn sqr(&mut self, a: &BigNumRef, ctx: &mut BigNumContextRef) -> Result<(), ErrorStack> {
unsafe { cvt(ffi::BN_sqr(self.as_ptr(), a.as_ptr(), ctx.as_ptr())).map(|_| ()) }
}
/// Places the result of `a mod m` in `self`. As opposed to `div_rem`
/// the result is non-negative.
///
/// OpenSSL documentation at [`BN_nnmod`]
///
/// [`BN_nnmod`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_nnmod.html
pub fn nnmod(
&mut self,
a: &BigNumRef,
m: &BigNumRef,
ctx: &mut BigNumContextRef,
) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_nnmod(
self.as_ptr(),
a.as_ptr(),
m.as_ptr(),
ctx.as_ptr(),
)).map(|_| ())
}
}
/// Places the result of `(a + b) mod m` in `self`.
///
/// OpenSSL documentation at [`BN_mod_add`]
///
/// [`BN_mod_add`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_mod_add.html
pub fn mod_add(
&mut self,
a: &BigNumRef,
b: &BigNumRef,
m: &BigNumRef,
ctx: &mut BigNumContextRef,
) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_mod_add(
self.as_ptr(),
a.as_ptr(),
b.as_ptr(),
m.as_ptr(),
ctx.as_ptr(),
)).map(|_| ())
}
}
/// Places the result of `(a - b) mod m` in `self`.
///
/// OpenSSL documentation at [`BN_mod_sub`]
///
/// [`BN_mod_sub`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_mod_sub.html
pub fn mod_sub(
&mut self,
a: &BigNumRef,
b: &BigNumRef,
m: &BigNumRef,
ctx: &mut BigNumContextRef,
) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_mod_sub(
self.as_ptr(),
a.as_ptr(),
b.as_ptr(),
m.as_ptr(),
ctx.as_ptr(),
)).map(|_| ())
}
}
/// Places the result of `(a * b) mod m` in `self`.
///
/// OpenSSL documentation at [`BN_mod_mul`]
///
/// [`BN_mod_mul`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_mod_mul.html
pub fn mod_mul(
&mut self,
a: &BigNumRef,
b: &BigNumRef,
m: &BigNumRef,
ctx: &mut BigNumContextRef,
) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_mod_mul(
self.as_ptr(),
a.as_ptr(),
b.as_ptr(),
m.as_ptr(),
ctx.as_ptr(),
)).map(|_| ())
}
}
/// Places the result of `a² mod m` in `self`.
///
/// OpenSSL documentation at [`BN_mod_sqr`]
///
/// [`BN_mod_sqr`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_mod_sqr.html
pub fn mod_sqr(
&mut self,
a: &BigNumRef,
m: &BigNumRef,
ctx: &mut BigNumContextRef,
) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_mod_sqr(
self.as_ptr(),
a.as_ptr(),
m.as_ptr(),
ctx.as_ptr(),
)).map(|_| ())
}
}
/// Places the result of `a^p` in `self`.
///
/// OpenSSL documentation at [`BN_exp`]
///
/// [`BN_exp`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_exp.html
pub fn exp(
&mut self,
a: &BigNumRef,
p: &BigNumRef,
ctx: &mut BigNumContextRef,
) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_exp(
self.as_ptr(),
a.as_ptr(),
p.as_ptr(),
ctx.as_ptr(),
)).map(|_| ())
}
}
/// Places the result of `a^p mod m` in `self`.
///
/// OpenSSL documentation at [`BN_mod_exp`]
///
/// [`BN_mod_exp`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_mod_exp.html
pub fn mod_exp(
&mut self,
a: &BigNumRef,
p: &BigNumRef,
m: &BigNumRef,
ctx: &mut BigNumContextRef,
) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_mod_exp(
self.as_ptr(),
a.as_ptr(),
p.as_ptr(),
m.as_ptr(),
ctx.as_ptr(),
)).map(|_| ())
}
}
/// Places the inverse of `a` modulo `n` in `self`.
pub fn mod_inverse(
&mut self,
a: &BigNumRef,
n: &BigNumRef,
ctx: &mut BigNumContextRef,
) -> Result<(), ErrorStack> {
unsafe {
cvt_p(ffi::BN_mod_inverse(
self.as_ptr(),
a.as_ptr(),
n.as_ptr(),
ctx.as_ptr(),
)).map(|_| ())
}
}
/// Places the greatest common denominator of `a` and `b` in `self`.
///
/// OpenSSL documentation at [`BN_gcd`]
///
/// [`BN_gcd`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_gcd.html
pub fn gcd(
&mut self,
a: &BigNumRef,
b: &BigNumRef,
ctx: &mut BigNumContextRef,
) -> Result<(), ErrorStack> {
unsafe {
cvt(ffi::BN_gcd(
self.as_ptr(),
a.as_ptr(),
b.as_ptr(),
ctx.as_ptr(),
)).map(|_| ())
}
}
/// Checks whether `self` is prime.
///
/// Performs a Miller-Rabin probabilistic primality test with `checks` iterations.
///
/// OpenSSL documentation at [`BN_is_prime_ex`]
///
/// [`BN_is_prime_ex`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_is_prime_ex.html
///
/// # Return Value
///
/// Returns `true` if `self` is prime with an error probability of less than `0.25 ^ checks`.
pub fn is_prime(&self, checks: i32, ctx: &mut BigNumContextRef) -> Result<bool, ErrorStack> {
unsafe {
cvt_n(ffi::BN_is_prime_ex(
self.as_ptr(),
checks.into(),
ctx.as_ptr(),
ptr::null_mut(),
)).map(|r| r != 0)
}
}
/// Checks whether `self` is prime with optional trial division.
///
/// If `do_trial_division` is `true`, first performs trial division by a number of small primes.
/// Then, like `is_prime`, performs a Miller-Rabin probabilistic primality test with `checks`
/// iterations.
///
/// OpenSSL documentation at [`BN_is_prime_fasttest_ex`]
///
/// [`BN_is_prime_fasttest_ex`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_is_prime_fasttest_ex.html
///
/// # Return Value
///
/// Returns `true` if `self` is prime with an error probability of less than `0.25 ^ checks`.
pub fn is_prime_fasttest(
&self,
checks: i32,
ctx: &mut BigNumContextRef,
do_trial_division: bool,
) -> Result<bool, ErrorStack> {
unsafe {
cvt_n(ffi::BN_is_prime_fasttest_ex(
self.as_ptr(),
checks.into(),
ctx.as_ptr(),
do_trial_division as c_int,
ptr::null_mut(),
)).map(|r| r != 0)
}
}
/// Returns a big-endian byte vector representation of the absolute value of `self`.
///
/// `self` can be recreated by using `from_slice`.
///
/// ```
/// # use openssl::bn::BigNum;
/// let s = -BigNum::from_u32(4543).unwrap();
/// let r = BigNum::from_u32(4543).unwrap();
///
/// let s_vec = s.to_vec();
/// assert_eq!(BigNum::from_slice(&s_vec).unwrap(), r);
/// ```
pub fn to_vec(&self) -> Vec<u8> {
let size = self.num_bytes() as usize;
let mut v = Vec::with_capacity(size);
unsafe {
ffi::BN_bn2bin(self.as_ptr(), v.as_mut_ptr());
v.set_len(size);
}
v
}
/// Returns a decimal string representation of `self`.
///
/// ```
/// # use openssl::bn::BigNum;
/// let s = -BigNum::from_u32(12345).unwrap();
///
/// assert_eq!(&**s.to_dec_str().unwrap(), "-12345");
/// ```
pub fn to_dec_str(&self) -> Result<OpensslString, ErrorStack> {
unsafe {
let buf = cvt_p(ffi::BN_bn2dec(self.as_ptr()))?;
Ok(OpensslString::from_ptr(buf))
}
}
/// Returns a hexadecimal string representation of `self`.
///
/// ```
/// # use openssl::bn::BigNum;
/// let s = -BigNum::from_u32(0x99ff).unwrap();
///
/// assert_eq!(&**s.to_hex_str().unwrap(), "-99FF");
/// ```
pub fn to_hex_str(&self) -> Result<OpensslString, ErrorStack> {
unsafe {
let buf = cvt_p(ffi::BN_bn2hex(self.as_ptr()))?;
Ok(OpensslString::from_ptr(buf))
}
}
/// Returns an `Asn1Integer` containing the value of `self`.
pub fn to_asn1_integer(&self) -> Result<Asn1Integer, ErrorStack> {
unsafe {
cvt_p(ffi::BN_to_ASN1_INTEGER(self.as_ptr(), ptr::null_mut()))
.map(|p| Asn1Integer::from_ptr(p))
}
}
}
impl BigNum {
/// Creates a new `BigNum` with the value 0.
pub fn new() -> Result<BigNum, ErrorStack> {
unsafe {
ffi::init();
let v = cvt_p(ffi::BN_new())?;
Ok(BigNum::from_ptr(v))
}
}
/// Creates a new `BigNum` with the given value.
///
/// OpenSSL documentation at [`BN_set_word`]
///
/// [`BN_set_word`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_set_word.html
pub fn from_u32(n: u32) -> Result<BigNum, ErrorStack> {
BigNum::new().and_then(|v| unsafe {
cvt(ffi::BN_set_word(v.as_ptr(), n as ffi::BN_ULONG)).map(|_| v)
})
}
/// Creates a `BigNum` from a decimal string.
///
/// OpenSSL documentation at [`BN_dec2bn`]
///
/// [`BN_dec2bn`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_dec2bn.html
pub fn from_dec_str(s: &str) -> Result<BigNum, ErrorStack> {
unsafe {
ffi::init();
let c_str = CString::new(s.as_bytes()).unwrap();
let mut bn = ptr::null_mut();
cvt(ffi::BN_dec2bn(&mut bn, c_str.as_ptr() as *const _))?;
Ok(BigNum::from_ptr(bn))
}
}
/// Creates a `BigNum` from a hexadecimal string.
///
/// OpenSSL documentation at [`BN_hex2bn`]
///
/// [`BN_hex2bn`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_hex2bn.html
pub fn from_hex_str(s: &str) -> Result<BigNum, ErrorStack> {
unsafe {
ffi::init();
let c_str = CString::new(s.as_bytes()).unwrap();
let mut bn = ptr::null_mut();
cvt(ffi::BN_hex2bn(&mut bn, c_str.as_ptr() as *const _))?;
Ok(BigNum::from_ptr(bn))
}
}
/// Returns a constant used in IKE as defined in [`RFC 2409`]. This prime number is in
/// the order of magnitude of `2 ^ 768`. This number is used during calculated key
/// exchanges such as Diffie-Hellman. This number is labeled Oakley group id 1.
///
/// OpenSSL documentation at [`BN_get_rfc2409_prime_768`]
///
/// [`RFC 2409`]: https://tools.ietf.org/html/rfc2409#page-21
/// [`BN_get_rfc2409_prime_768`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_get_rfc2409_prime_768.html
pub fn get_rfc2409_prime_768() -> Result<BigNum, ErrorStack> {
unsafe {
ffi::init();
cvt_p(BN_get_rfc2409_prime_768(ptr::null_mut())).map(BigNum)
}
}
/// Returns a constant used in IKE as defined in [`RFC 2409`]. This prime number is in
/// the order of magnitude of `2 ^ 1024`. This number is used during calculated key
/// exchanges such as Diffie-Hellman. This number is labeled Oakly group 2.
///
/// OpenSSL documentation at [`BN_get_rfc2409_prime_1024`]
///
/// [`RFC 2409`]: https://tools.ietf.org/html/rfc2409#page-21
/// [`BN_get_rfc2409_prime_1024`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_get_rfc2409_prime_1024.html
pub fn get_rfc2409_prime_1024() -> Result<BigNum, ErrorStack> {
unsafe {
ffi::init();
cvt_p(BN_get_rfc2409_prime_1024(ptr::null_mut())).map(BigNum)
}
}
/// Returns a constant used in IKE as defined in [`RFC 3526`]. The prime is in the order
/// of magnitude of `2 ^ 1536`. This number is used during calculated key
/// exchanges such as Diffie-Hellman. This number is labeled MODP group 5.
///
/// OpenSSL documentation at [`BN_get_rfc3526_prime_1536`]
///
/// [`RFC 3526`]: https://tools.ietf.org/html/rfc3526#page-3
/// [`BN_get_rfc3526_prime_1536`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_get_rfc3526_prime_1536.html
pub fn get_rfc3526_prime_1536() -> Result<BigNum, ErrorStack> {
unsafe {
ffi::init();
cvt_p(BN_get_rfc3526_prime_1536(ptr::null_mut())).map(BigNum)
}
}
/// Returns a constant used in IKE as defined in [`RFC 3526`]. The prime is in the order
/// of magnitude of `2 ^ 2048`. This number is used during calculated key
/// exchanges such as Diffie-Hellman. This number is labeled MODP group 14.
///
/// OpenSSL documentation at [`BN_get_rfc3526_prime_2048`]
///
/// [`RFC 3526`]: https://tools.ietf.org/html/rfc3526#page-3
/// [`BN_get_rfc3526_prime_2048`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_get_rfc3526_prime_2048.html
pub fn get_rfc3526_prime_2048() -> Result<BigNum, ErrorStack> {
unsafe {
ffi::init();
cvt_p(BN_get_rfc3526_prime_2048(ptr::null_mut())).map(BigNum)
}
}
/// Returns a constant used in IKE as defined in [`RFC 3526`]. The prime is in the order
/// of magnitude of `2 ^ 3072`. This number is used during calculated key
/// exchanges such as Diffie-Hellman. This number is labeled MODP group 15.
///
/// OpenSSL documentation at [`BN_get_rfc3526_prime_3072`]
///
/// [`RFC 3526`]: https://tools.ietf.org/html/rfc3526#page-4
/// [`BN_get_rfc3526_prime_3072`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_get_rfc3526_prime_3072.html
pub fn get_rfc3526_prime_3072() -> Result<BigNum, ErrorStack> {
unsafe {
ffi::init();
cvt_p(BN_get_rfc3526_prime_3072(ptr::null_mut())).map(BigNum)
}
}
/// Returns a constant used in IKE as defined in [`RFC 3526`]. The prime is in the order
/// of magnitude of `2 ^ 4096`. This number is used during calculated key
/// exchanges such as Diffie-Hellman. This number is labeled MODP group 16.
///
/// OpenSSL documentation at [`BN_get_rfc3526_prime_4096`]
///
/// [`RFC 3526`]: https://tools.ietf.org/html/rfc3526#page-4
/// [`BN_get_rfc3526_prime_4096`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_get_rfc3526_prime_4096.html
pub fn get_rfc3526_prime_4096() -> Result<BigNum, ErrorStack> {
unsafe {
ffi::init();
cvt_p(BN_get_rfc3526_prime_4096(ptr::null_mut())).map(BigNum)
}
}
/// Returns a constant used in IKE as defined in [`RFC 3526`]. The prime is in the order
/// of magnitude of `2 ^ 6144`. This number is used during calculated key
/// exchanges such as Diffie-Hellman. This number is labeled MODP group 17.
///
/// OpenSSL documentation at [`BN_get_rfc3526_prime_6144`]
///
/// [`RFC 3526`]: https://tools.ietf.org/html/rfc3526#page-6
/// [`BN_get_rfc3526_prime_6144`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_get_rfc3526_prime_6144.html
pub fn get_rfc3526_prime_6144() -> Result<BigNum, ErrorStack> {
unsafe {
ffi::init();
cvt_p(BN_get_rfc3526_prime_6144(ptr::null_mut())).map(BigNum)
}
}
/// Returns a constant used in IKE as defined in [`RFC 3526`]. The prime is in the order
/// of magnitude of `2 ^ 8192`. This number is used during calculated key
/// exchanges such as Diffie-Hellman. This number is labeled MODP group 18.
///
/// OpenSSL documentation at [`BN_get_rfc3526_prime_8192`]
///
/// [`RFC 3526`]: https://tools.ietf.org/html/rfc3526#page-6
/// [`BN_get_rfc3526_prime_8192`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_get_rfc3526_prime_8192.html
pub fn get_rfc3526_prime_8192() -> Result<BigNum, ErrorStack> {
unsafe {
ffi::init();
cvt_p(BN_get_rfc3526_prime_8192(ptr::null_mut())).map(BigNum)
}
}
/// Creates a new `BigNum` from an unsigned, big-endian encoded number of arbitrary length.
///
/// OpenSSL documentation at [`BN_bin2bn`]
///
/// [`BN_bin2bn`]: https://www.openssl.org/docs/man1.1.0/crypto/BN_bin2bn.html
///
/// ```
/// # use openssl::bn::BigNum;
/// let bignum = BigNum::from_slice(&[0x12, 0x00, 0x34]).unwrap();
///
/// assert_eq!(bignum, BigNum::from_u32(0x120034).unwrap());
/// ```
pub fn from_slice(n: &[u8]) -> Result<BigNum, ErrorStack> {
unsafe {
ffi::init();
assert!(n.len() <= c_int::max_value() as usize);
cvt_p(ffi::BN_bin2bn(
n.as_ptr(),
n.len() as c_int,
ptr::null_mut(),
)).map(|p| BigNum::from_ptr(p))
}
}
}
impl fmt::Debug for BigNumRef {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
match self.to_dec_str() {
Ok(s) => f.write_str(&s),
Err(e) => Err(e.into()),
}
}
}
impl fmt::Debug for BigNum {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
match self.to_dec_str() {
Ok(s) => f.write_str(&s),
Err(e) => Err(e.into()),
}
}
}
impl fmt::Display for BigNumRef {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
match self.to_dec_str() {
Ok(s) => f.write_str(&s),
Err(e) => Err(e.into()),
}
}
}
impl fmt::Display for BigNum {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
match self.to_dec_str() {
Ok(s) => f.write_str(&s),
Err(e) => Err(e.into()),
}
}
}
impl PartialEq<BigNumRef> for BigNumRef {
fn eq(&self, oth: &BigNumRef) -> bool {
self.cmp(oth) == Ordering::Equal
}
}
impl PartialEq<BigNum> for BigNumRef {
fn eq(&self, oth: &BigNum) -> bool {
self.eq(oth.deref())
}
}
impl Eq for BigNumRef {}
impl PartialEq for BigNum {
fn eq(&self, oth: &BigNum) -> bool {
self.deref().eq(oth)
}
}
impl PartialEq<BigNumRef> for BigNum {
fn eq(&self, oth: &BigNumRef) -> bool {
self.deref().eq(oth)
}
}
impl Eq for BigNum {}
impl PartialOrd<BigNumRef> for BigNumRef {
fn partial_cmp(&self, oth: &BigNumRef) -> Option<Ordering> {
Some(self.cmp(oth))
}
}
impl PartialOrd<BigNum> for BigNumRef {
fn partial_cmp(&self, oth: &BigNum) -> Option<Ordering> {
Some(self.cmp(oth.deref()))
}
}
impl Ord for BigNumRef {
fn cmp(&self, oth: &BigNumRef) -> Ordering {
unsafe { ffi::BN_cmp(self.as_ptr(), oth.as_ptr()).cmp(&0) }
}
}
impl PartialOrd for BigNum {
fn partial_cmp(&self, oth: &BigNum) -> Option<Ordering> {
self.deref().partial_cmp(oth.deref())
}
}
impl PartialOrd<BigNumRef> for BigNum {
fn partial_cmp(&self, oth: &BigNumRef) -> Option<Ordering> {
self.deref().partial_cmp(oth)
}
}
impl Ord for BigNum {
fn cmp(&self, oth: &BigNum) -> Ordering {
self.deref().cmp(oth.deref())
}
}
macro_rules! delegate {
($t:ident, $m:ident) => {
impl<'a, 'b> $t<&'b BigNum> for &'a BigNumRef {
type Output = BigNum;
fn $m(self, oth: &BigNum) -> BigNum {
$t::$m(self, oth.deref())
}
}
impl<'a, 'b> $t<&'b BigNumRef> for &'a BigNum {
type Output = BigNum;
fn $m(self, oth: &BigNumRef) -> BigNum {
$t::$m(self.deref(), oth)
}
}
impl<'a, 'b> $t<&'b BigNum> for &'a BigNum {
type Output = BigNum;
fn $m(self, oth: &BigNum) -> BigNum {
$t::$m(self.deref(), oth.deref())
}
}
}
}
impl<'a, 'b> Add<&'b BigNumRef> for &'a BigNumRef {
type Output = BigNum;
fn add(self, oth: &BigNumRef) -> BigNum {
let mut r = BigNum::new().unwrap();
r.checked_add(self, oth).unwrap();
r
}
}
delegate!(Add, add);
impl<'a, 'b> Sub<&'b BigNumRef> for &'a BigNumRef {
type Output = BigNum;
fn sub(self, oth: &BigNumRef) -> BigNum {
let mut r = BigNum::new().unwrap();
r.checked_sub(self, oth).unwrap();
r
}
}
delegate!(Sub, sub);
impl<'a, 'b> Mul<&'b BigNumRef> for &'a BigNumRef {
type Output = BigNum;
fn mul(self, oth: &BigNumRef) -> BigNum {
let mut ctx = BigNumContext::new().unwrap();
let mut r = BigNum::new().unwrap();
r.checked_mul(self, oth, &mut ctx).unwrap();
r
}
}
delegate!(Mul, mul);
impl<'a, 'b> Div<&'b BigNumRef> for &'a BigNumRef {
type Output = BigNum;
fn div(self, oth: &'b BigNumRef) -> BigNum {
let mut ctx = BigNumContext::new().unwrap();
let mut r = BigNum::new().unwrap();
r.checked_div(self, oth, &mut ctx).unwrap();
r
}
}
delegate!(Div, div);
impl<'a, 'b> Rem<&'b BigNumRef> for &'a BigNumRef {
type Output = BigNum;
fn rem(self, oth: &'b BigNumRef) -> BigNum {
let mut ctx = BigNumContext::new().unwrap();
let mut r = BigNum::new().unwrap();
r.checked_rem(self, oth, &mut ctx).unwrap();
r
}
}
delegate!(Rem, rem);
impl<'a> Shl<i32> for &'a BigNumRef {
type Output = BigNum;
fn shl(self, n: i32) -> BigNum {
let mut r = BigNum::new().unwrap();
r.lshift(self, n).unwrap();
r
}
}
impl<'a> Shl<i32> for &'a BigNum {
type Output = BigNum;
fn shl(self, n: i32) -> BigNum {
self.deref().shl(n)
}
}
impl<'a> Shr<i32> for &'a BigNumRef {
type Output = BigNum;
fn shr(self, n: i32) -> BigNum {
let mut r = BigNum::new().unwrap();
r.rshift(self, n).unwrap();
r
}
}
impl<'a> Shr<i32> for &'a BigNum {
type Output = BigNum;
fn shr(self, n: i32) -> BigNum {
self.deref().shr(n)
}
}
impl<'a> Neg for &'a BigNumRef {
type Output = BigNum;
fn neg(self) -> BigNum {
self.to_owned().unwrap().neg()
}
}
impl<'a> Neg for &'a BigNum {
type Output = BigNum;
fn neg(self) -> BigNum {
self.deref().neg()
}
}
impl Neg for BigNum {
type Output = BigNum;
fn neg(mut self) -> BigNum {
let negative = self.is_negative();
self.set_negative(!negative);
self
}
}
#[cfg(test)]
mod tests {
use bn::{BigNumContext, BigNum};
#[test]
fn test_to_from_slice() {
let v0 = BigNum::from_u32(10203004).unwrap();
let vec = v0.to_vec();
let v1 = BigNum::from_slice(&vec).unwrap();
assert!(v0 == v1);
}
#[test]
fn test_negation() {
let a = BigNum::from_u32(909829283).unwrap();
assert!(!a.is_negative());
assert!((-a).is_negative());
}
#[test]
fn test_shift() {
let a = BigNum::from_u32(909829283).unwrap();
use std::ops::{Shl, Shr};
assert!(a == a.shl(1).shr(1));
}
#[test]
fn test_rand_range() {
let range = BigNum::from_u32(909829283).unwrap();
let mut result = BigNum::from_dec_str(&range.to_dec_str().unwrap()).unwrap();
range.rand_range(&mut result).unwrap();
assert!(result >= BigNum::from_u32(0).unwrap() && result < range);
}
#[test]
fn test_pseudo_rand_range() {
let range = BigNum::from_u32(909829283).unwrap();
let mut result = BigNum::from_dec_str(&range.to_dec_str().unwrap()).unwrap();
range.pseudo_rand_range(&mut result).unwrap();
assert!(result >= BigNum::from_u32(0).unwrap() && result < range);
}
#[test]
fn test_prime_numbers() {
let a = BigNum::from_u32(19029017).unwrap();
let mut p = BigNum::new().unwrap();
p.generate_prime(128, true, None, Some(&a)).unwrap();
let mut ctx = BigNumContext::new().unwrap();
assert!(p.is_prime(100, &mut ctx).unwrap());
assert!(p.is_prime_fasttest(100, &mut ctx, true).unwrap());
}
}