Struct Odd 

pub struct Odd<T: ?Sized>(/* private fields */);

Wrapper type for odd integers.

These are frequently used in cryptography, e.g. as a modulus.

Implementations

impl<const LIMBS: usize> Odd<Int<LIMBS>>

pub const fn gcd_unsigned(&self, rhs: &Uint<LIMBS>) -> Odd<Uint<LIMBS>>

Compute the greatest common divisor of self and rhs.

pub const fn gcd_unsigned_vartime(&self, rhs: &Uint<LIMBS>) -> OddUint<LIMBS>

Compute the greatest common divisor of self and rhs.

Executes in variable time w.r.t. all input parameters.

pub const fn xgcd( &self, rhs: &NonZero<Int<LIMBS>>, ) -> XgcdOutput<LIMBS, OddUint<LIMBS>>

Execute the Extended GCD algorithm.

Given (self, rhs), computes (g, x, y) s.t. self * x + rhs * y = g = gcd(self, rhs).

impl<T> Odd<T>

pub fn new(n: T) -> CtOption<Self>

where T: Integer,

Create a new odd integer.

pub fn get(self) -> T

Returns the inner value.

pub const fn get_copy(self) -> T

where T: Copy,

Returns a copy of the inner value for Copy types.

This allows the function to be const fn, since Copy is implicitly !Drop, which avoids problems around const fn destructors.

impl<T: ?Sized> Odd<T>

pub const fn as_ref(&self) -> &T

Provides access to the contents of Odd in a const context.

pub const fn as_nz_ref(&self) -> &NonZero<T>

All odd integers are definitionally non-zero, so we can also obtain a reference to the equivalent NonZero type.

impl<T> Odd<T>

where T: Bounded + ?Sized,

pub const BITS: u32 = T::BITS

Total size of the represented integer in bits.

pub const BYTES: usize = T::BYTES

Total size of the represented integer in bytes.

impl<const LIMBS: usize> Odd<Uint<LIMBS>>

pub const fn from_be_hex(hex: &str) -> Self

Create a new OddUint from the provided big endian hex string.

Panics

• if the hex is malformed or not zero-padded accordingly for the size.
• if the value is even.

pub const fn from_le_hex(hex: &str) -> Self

Create a new Odd<Uint<LIMBS>> from the provided little endian hex string.

Panics

• if the hex is malformed or not zero-padded accordingly for the size.
• if the value is even.

pub const fn as_uint_ref(&self) -> &OddUintRef

Borrow this OddUint as a &OddUintRef.

pub const fn resize<const T: usize>(&self) -> Odd<Uint<T>>

Construct an Odd<Uint<T>> from the unsigned integer value, truncating the upper bits if the value is too large to be represented.

impl<const LIMBS: usize> Odd<Int<LIMBS>>

pub const fn abs_sign(&self) -> (Odd<Uint<LIMBS>>, Choice)

The sign and magnitude of this Odd<Int<{LIMBS}>>.

pub const fn abs(&self) -> Odd<Uint<LIMBS>>

The magnitude of this Odd<Int<{LIMBS}>>.

impl Odd<UintRef>

pub const fn to_uint_resize<const T: usize>(&self) -> Odd<Uint<T>>

Construct an Odd<Uint<T>> from the unsigned integer value, truncating the upper bits if the value is too large to be represented.

impl Odd<BoxedUint>

pub const fn as_uint_ref(&self) -> &OddUintRef

Available on crate feature alloc only.

Borrow this OddBoxedUint as a &OddUintRef.

pub fn random<R: TryRng + ?Sized>(rng: &mut R, bit_length: u32) -> Self

Available on crate features alloc and rand_core only.

Generate a random Odd<Uint<T>>.

impl<const LIMBS: usize> Odd<Uint<LIMBS>>

pub const fn gcd_unsigned(&self, rhs: &Uint<LIMBS>) -> Self

Compute the greatest common divisor of self and rhs.

pub const fn gcd_unsigned_vartime(&self, rhs: &Uint<LIMBS>) -> Self

Compute the greatest common divisor of self and rhs.

Executes in variable time w.r.t. all input parameters.

pub const fn xgcd(&self, rhs: &Self) -> XgcdOutput<LIMBS, OddUint<LIMBS>>

Execute the Extended GCD algorithm.

Given (self, rhs), computes (g, x, y) s.t. self * x + rhs * y = g = gcd(self, rhs).

impl Odd<UintRef>

pub const fn invert_mod_u64(&self) -> u64

Returns the multiplicative inverse of the argument modulo 2^64. The implementation is based on the Hurchalla’s method for computing the multiplicative inverse modulo a power of two.

For better understanding the implementation, the following paper is recommended: J. Hurchalla, “An Improved Integer Multiplicative Inverse (modulo 2^w)”, https://arxiv.org/pdf/2204.limbs4342.pdf

Variable time with respect to the number of words in value, however that number will be fixed for a given integer size.

Trait Implementations

impl<T> AsRef<[Limb]> for Odd<T>

where T: AsRef<[Limb]>,

fn as_ref(&self) -> &[Limb]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: ?Sized> AsRef<NonZero<T>> for Odd<T>

fn as_ref(&self) -> &NonZero<T>

Converts this type into a shared reference of the (usually inferred) input type.

impl AsRef<Odd<UintRef>> for OddBoxedUint

Available on crate feature alloc only.

fn as_ref(&self) -> &OddUintRef

Converts this type into a shared reference of the (usually inferred) input type.

impl<const LIMBS: usize> AsRef<Odd<UintRef>> for OddUint<LIMBS>

fn as_ref(&self) -> &OddUintRef

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: ?Sized> AsRef<T> for Odd<T>

fn as_ref(&self) -> &T

Converts this type into a shared reference of the (usually inferred) input type.

impl<T> Binary for Odd<T>

where T: Binary + ?Sized,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Clone + ?Sized> Clone for Odd<T>

fn clone(&self) -> Odd<T>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T> ConditionallySelectable for Odd<T>

where T: Copy, Self: CtSelect,

Available on crate feature subtle only.

fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self

Select a or b according to choice.

fn conditional_assign(&mut self, other: &Self, choice: Choice)

Conditionally assign other to self, according to choice.

fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice)

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves.

impl<T> ConstOne for Odd<T>

where T: ConstOne + One,

const ONE: Self

The multiplicative identity element of Self, 1.

impl<T> ConstantTimeEq for Odd<T>

where T: ?Sized, Self: CtEq,

Available on crate feature subtle only.

fn ct_eq(&self, other: &Self) -> Choice

Determine if two items are equal.

fn ct_ne(&self, other: &Self) -> Choice

Determine if two items are NOT equal.

impl<T> CtAssign for Odd<T>

where T: CtAssign,

fn ct_assign(&mut self, other: &Self, choice: Choice)

Conditionally assign src to self if choice is Choice::TRUE.

impl<T> CtAssignSlice for Odd<T>

where T: CtAssignSlice,

fn ct_assign_slice(dst: &mut [Self], src: &[Self], choice: Choice)

Conditionally assign src to dst if choice is Choice::TRUE, or leave it unchanged for Choice::FALSE.

impl<T> CtEq for Odd<T>

where T: CtEq + ?Sized,

fn ct_eq(&self, other: &Self) -> Choice

Determine if self is equal to other in constant-time.

fn ct_ne(&self, other: &Rhs) -> Choice

Determine if self is NOT equal to other in constant-time.

impl<T> CtEqSlice for Odd<T>

where T: CtEq,

fn ct_eq_slice(a: &[Self], b: &[Self]) -> Choice

Determine if a is equal to b in constant-time.

fn ct_ne_slice(a: &[Self], b: &[Self]) -> Choice

Determine if a is NOT equal to b in constant-time.

impl<T> CtSelect for Odd<T>

where T: CtSelect,

fn ct_select(&self, other: &Self, choice: Choice) -> Self

Select between self and other based on choice, returning a copy of the value.

fn ct_swap(&mut self, other: &mut Self, choice: Choice)

Conditionally swap self and other if choice is Choice::TRUE.

impl<T: Debug + ?Sized> Debug for Odd<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T> Default for Odd<T>

where T: One,

fn default() -> Self

Returns the “default value” for a type.

impl<T: ?Sized> Deref for Odd<T>

type Target = T

The resulting type after dereferencing.

fn deref(&self) -> &T

Dereferences the value.

impl<'de, T: Deserialize<'de> + Integer + Zero> Deserialize<'de> for Odd<T>

Available on crate feature serde only.

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<T> Display for Odd<T>

where T: Display + ?Sized,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<const LIMBS: usize> From<&Odd<Uint<LIMBS>>> for BoxedUint

Available on crate feature alloc only.

fn from(uint: &Odd<Uint<LIMBS>>) -> BoxedUint

Converts to this type from the input type.

impl<const LIMBS: usize> From<&Odd<Uint<LIMBS>>> for Odd<BoxedUint>

Available on crate feature alloc only.

fn from(uint: &Odd<Uint<LIMBS>>) -> Odd<BoxedUint>

Converts to this type from the input type.

impl<T> From<Odd<T>> for NonZero<T>

fn from(odd: Odd<T>) -> NonZero<T>

Converts to this type from the input type.

impl<const LIMBS: usize> From<Odd<Uint<LIMBS>>> for BoxedUint

Available on crate feature alloc only.

fn from(uint: Odd<Uint<LIMBS>>) -> BoxedUint

Converts to this type from the input type.

impl<const LIMBS: usize> From<Odd<Uint<LIMBS>>> for Odd<BoxedUint>

Available on crate feature alloc only.

fn from(uint: Odd<Uint<LIMBS>>) -> Odd<BoxedUint>

Converts to this type from the input type.

impl Gcd<BoxedUint> for Odd<BoxedUint>

Available on crate feature alloc only.

type Output = Odd<BoxedUint>

Output type.

fn gcd(&self, rhs: &BoxedUint) -> Self::Output

Compute the greatest common divisor of self and rhs.

fn gcd_vartime(&self, rhs: &BoxedUint) -> Self::Output

Compute the greatest common divisor of self and rhs in variable time.

impl<const LIMBS: usize> Gcd<Odd<Int<LIMBS>>> for Uint<LIMBS>

type Output = Odd<Uint<LIMBS>>

Output type.

fn gcd(&self, rhs: &OddInt<LIMBS>) -> Self::Output

Compute the greatest common divisor of self and rhs.

fn gcd_vartime(&self, rhs: &OddInt<LIMBS>) -> Self::Output

Compute the greatest common divisor of self and rhs in variable time.

impl<const LIMBS: usize> Gcd<Odd<Uint<LIMBS>>> for Int<LIMBS>

type Output = Odd<Uint<LIMBS>>

Output type.

fn gcd(&self, rhs: &OddUint<LIMBS>) -> Self::Output

Compute the greatest common divisor of self and rhs.

fn gcd_vartime(&self, rhs: &OddUint<LIMBS>) -> Self::Output

Compute the greatest common divisor of self and rhs in variable time.

impl<const LIMBS: usize> Gcd<Odd<Uint<LIMBS>>> for NonZeroUint<LIMBS>

type Output = Odd<Uint<LIMBS>>

Output type.

fn gcd(&self, rhs: &OddUint<LIMBS>) -> Self::Output

Compute the greatest common divisor of self and rhs.

fn gcd_vartime(&self, rhs: &OddUint<LIMBS>) -> Self::Output

Compute the greatest common divisor of self and rhs in variable time.

impl<const LIMBS: usize> Gcd<Odd<Uint<LIMBS>>> for Uint<LIMBS>

type Output = Odd<Uint<LIMBS>>

Output type.

fn gcd(&self, rhs: &OddUint<LIMBS>) -> Self::Output

Compute the greatest common divisor of self and rhs.

fn gcd_vartime(&self, rhs: &OddUint<LIMBS>) -> Self::Output

Compute the greatest common divisor of self and rhs in variable time.

impl<T: Hash + ?Sized> Hash for Odd<T>

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<T> LowerHex for Odd<T>

where T: LowerHex + ?Sized,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T> Mul for Odd<T>

where T: Mul<T, Output = T>,

Any odd integer multiplied by another odd integer is definitionally odd.

type Output = Odd<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self

Performs the * operation.

impl<T> Octal for Odd<T>

where T: Octal + ?Sized,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T> One for Odd<T>

where T: One,

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> Choice

Determine if this value is equal to 1.

fn set_one(&mut self)

Set self to its multiplicative identity, i.e. Self::one.

fn one_like(_other: &Self) -> Self

Return the value 0 with the same precision as other.

impl<T> One for Odd<T>

where T: One + Mul<T, Output = T>,

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

impl<T: Ord + ?Sized> Ord for Odd<T>

fn cmp(&self, other: &Odd<T>) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl PartialEq<Odd<BoxedUint>> for BoxedUint

Available on crate feature alloc only.

fn eq(&self, other: &OddBoxedUint) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<const LIMBS: usize> PartialEq<Odd<Uint<LIMBS>>> for Uint<LIMBS>

fn eq(&self, other: &Odd<Uint<LIMBS>>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<T: PartialEq + ?Sized> PartialEq for Odd<T>

fn eq(&self, other: &Odd<T>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd<Odd<BoxedUint>> for BoxedUint

Available on crate feature alloc only.

fn partial_cmp(&self, other: &OddBoxedUint) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl<const LIMBS: usize> PartialOrd<Odd<Uint<LIMBS>>> for Uint<LIMBS>

fn partial_cmp(&self, other: &Odd<Uint<LIMBS>>) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl<T: PartialOrd + ?Sized> PartialOrd for Odd<T>

fn partial_cmp(&self, other: &Odd<T>) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl<const LIMBS: usize> Random for Odd<Uint<LIMBS>>

Available on crate feature rand_core only.

fn try_random_from_rng<R: TryRng + ?Sized>( rng: &mut R, ) -> Result<Self, R::Error>

Generate a random Odd<Uint<T>>.

fn random_from_rng<R: Rng + ?Sized>(rng: &mut R) -> Self

Generate a random value.

fn try_random() -> Result<Self, Error>

Available on crate feature getrandom only.

Randomly generate a value of this type using the system’s ambient cryptographically secure random number generator.

fn random() -> Self

Available on crate feature getrandom only.

Randomly generate a value of this type using the system’s ambient cryptographically secure random number generator.

impl<T: Serialize + Zero> Serialize for Odd<T>

Available on crate feature serde only.

fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>

where S: Serializer,

Serialize this value into the given Serde serializer.

impl<T> UpperHex for Odd<T>

where T: UpperHex + ?Sized,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Zeroize> Zeroize for Odd<T>

Available on crate feature zeroize only.

fn zeroize(&mut self)

Zero out this object from memory using Rust intrinsics which ensure the zeroization operation is not “optimized away” by the compiler.

impl<T: Copy + ?Sized> Copy for Odd<T>

impl<T: Eq + ?Sized> Eq for Odd<T>

impl<T: ?Sized> StructuralPartialEq for Odd<T>