Struct FixedMontyForm 

pub struct FixedMontyForm<const LIMBS: usize> { /* private fields */ }

An integer in Montgomery form represented using LIMBS limbs. The odd modulus is set at runtime.

Implementations

impl<const LIMBS: usize> FixedMontyForm<LIMBS>

pub const fn add(&self, rhs: &Self) -> Self

Adds rhs.

pub const fn double(&self) -> Self

Double self.

impl<const LIMBS: usize> FixedMontyForm<LIMBS>

pub const fn inv(&self) -> CtOption<Self>

👎Deprecated since 0.7.0: please use invert instead

Computes self^-1 representing the multiplicative inverse of self. i.e. self * self^-1 = 1.

If the number was invertible, the second element of the tuple is the truthy value, otherwise it is the falsy value (in which case the first element’s value is unspecified).

pub const fn invert(&self) -> CtOption<Self>

Computes self^-1 representing the multiplicative inverse of self. i.e. self * self^-1 = 1.

If the number was invertible, the second element of the tuple is the truthy value, otherwise it is the falsy value (in which case the first element’s value is unspecified).

pub const fn inv_vartime(&self) -> CtOption<Self>

👎Deprecated since 0.7.0: please use invert_vartime instead

Computes self^-1 representing the multiplicative inverse of self. i.e. self * self^-1 = 1.

If the number was invertible, the second element of the tuple is the truthy value, otherwise it is the falsy value (in which case the first element’s value is unspecified).

This version is variable-time with respect to the value of self, but constant-time with respect to self’s params.

pub const fn invert_vartime(&self) -> CtOption<Self>

Computes self^-1 representing the multiplicative inverse of self. i.e. self * self^-1 = 1.

If the number was invertible, the second element of the tuple is the truthy value, otherwise it is the falsy value (in which case the first element’s value is unspecified).

This version is variable-time with respect to the value of self, but constant-time with respect to self’s params.

impl<const LIMBS: usize> FixedMontyForm<LIMBS>

pub const fn lincomb_vartime(products: &[(&Self, &Self)]) -> Self

Calculate the sum of products of pairs (a, b) in products.

This method is variable time only with the value of the modulus. For a modulus with leading zeros, this method is more efficient than a naive sum of products.

This method will panic if products is empty. All terms must be associated with equivalent MontyParams.

Panics

• if products is empty.

impl<const LIMBS: usize> FixedMontyForm<LIMBS>

pub const fn jacobi_symbol(&self) -> JacobiSymbol

Compute the Jacobi symbol (self|modulus).

For a prime modulus, this corresponds to the Legendre symbol and indicates whether self is quadratic residue.

pub const fn jacobi_symbol_vartime(&self) -> JacobiSymbol

Compute the Jacobi symbol (self|modulus).

For a prime modulus, this corresponds to the Legendre symbol and indicates whether self is quadratic residue.

This method is variable-time with respect to the value of self.

impl<const LIMBS: usize> FixedMontyForm<LIMBS>

pub const fn mul(&self, rhs: &Self) -> Self

Multiplies by rhs.

pub const fn square(&self) -> Self

Computes the (reduced) square.

pub const fn square_repeat_vartime(&self, n: u32) -> Self

Computes the reduced product self^2n.

This method is variable time in n only.

impl<const LIMBS: usize> FixedMontyForm<LIMBS>

pub const fn neg(&self) -> Self

Negates the number.

impl<const LIMBS: usize> FixedMontyForm<LIMBS>

pub const fn pow<const RHS_LIMBS: usize>( &self, exponent: &Uint<RHS_LIMBS>, ) -> Self

Raises to the exponent power.

pub const fn pow_bounded_exp<const RHS_LIMBS: usize>( &self, exponent: &Uint<RHS_LIMBS>, exponent_bits: u32, ) -> Self

Raises to the exponent power, with exponent_bits representing the number of (least significant) bits to take into account for the exponent.

NOTE: exponent_bits may be leaked in the time pattern.

pub const fn pow_vartime<const RHS_LIMBS: usize>( &self, exponent: &Uint<RHS_LIMBS>, ) -> Self

Raises to the exponent power.

This method is variable time in exponent.

pub fn pow_amm(&self, exponent: &Uint<LIMBS>) -> Self

Raises to the exponent power using Almost Montgomery Multiplication (AMM).

pub fn pow_amm_bounded_exp( &self, exponent: &Uint<LIMBS>, exponent_bits: u32, ) -> Self

Raises to the exponent power using Almost Montgomery Multiplication (AMM) with exponent_bits representing the number of (least significant) bits to take into account for the exponent.

NOTE: exponent_bits may be leaked in the time pattern.

impl<const LIMBS: usize> FixedMontyForm<LIMBS>

pub const fn sub(&self, rhs: &Self) -> Self

Subtracts rhs.

impl<const LIMBS: usize> FixedMontyForm<LIMBS>

pub const fn new( integer: &Uint<LIMBS>, params: &FixedMontyParams<LIMBS>, ) -> Self

Instantiates a new MontyForm that represents this integer mod MOD.

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

Retrieves the integer currently encoded in this MontyForm, guaranteed to be reduced.

pub const fn zero(params: &FixedMontyParams<LIMBS>) -> Self

Instantiates a new MontyForm that represents zero.

pub const fn one(params: &FixedMontyParams<LIMBS>) -> Self

Instantiates a new MontyForm that represents 1.

pub const fn params(&self) -> &FixedMontyParams<LIMBS>

Returns the parameter struct used to initialize this object.

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

Access the MontyForm value in Montgomery form.

pub fn as_montgomery_mut(&mut self) -> &mut Uint<LIMBS>

Mutably access the MontyForm value in Montgomery form.

pub const fn from_montgomery( integer: Uint<LIMBS>, params: &FixedMontyParams<LIMBS>, ) -> Self

Create a MontyForm from a value in Montgomery form.

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

Extract the value from the MontyForm in Montgomery form.

pub const fn div_by_2(&self) -> Self

Performs division by 2, that is returns x such that x + x = self.

Trait Implementations

impl<const LIMBS: usize> Add<&FixedMontyForm<LIMBS>> for &FixedMontyForm<LIMBS>

type Output = FixedMontyForm<LIMBS>

The resulting type after applying the + operator.

fn add(self, rhs: &FixedMontyForm<LIMBS>) -> FixedMontyForm<LIMBS>

Performs the + operation.

impl<const LIMBS: usize> Add<&FixedMontyForm<LIMBS>> for FixedMontyForm<LIMBS>

type Output = FixedMontyForm<LIMBS>

The resulting type after applying the + operator.

fn add(self, rhs: &FixedMontyForm<LIMBS>) -> FixedMontyForm<LIMBS>

Performs the + operation.

impl<const LIMBS: usize> Add<FixedMontyForm<LIMBS>> for &FixedMontyForm<LIMBS>

type Output = FixedMontyForm<LIMBS>

The resulting type after applying the + operator.

fn add(self, rhs: FixedMontyForm<LIMBS>) -> FixedMontyForm<LIMBS>

Performs the + operation.

impl<const LIMBS: usize> Add for FixedMontyForm<LIMBS>

type Output = FixedMontyForm<LIMBS>

The resulting type after applying the + operator.

fn add(self, rhs: FixedMontyForm<LIMBS>) -> FixedMontyForm<LIMBS>

Performs the + operation.

impl<const LIMBS: usize> AddAssign<&FixedMontyForm<LIMBS>> for FixedMontyForm<LIMBS>

fn add_assign(&mut self, rhs: &FixedMontyForm<LIMBS>)

Performs the += operation.

impl<const LIMBS: usize> AddAssign for FixedMontyForm<LIMBS>

fn add_assign(&mut self, rhs: FixedMontyForm<LIMBS>)

Performs the += operation.

impl<const LIMBS: usize> Clone for FixedMontyForm<LIMBS>

fn clone(&self) -> FixedMontyForm<LIMBS>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const LIMBS: usize> ConditionallySelectable for FixedMontyForm<LIMBS>

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<const LIMBS: usize> ConstantTimeEq for FixedMontyForm<LIMBS>

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<const LIMBS: usize> CtAssign for FixedMontyForm<LIMBS>

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

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

impl<const LIMBS: usize> CtAssignSlice for FixedMontyForm<LIMBS>

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<const LIMBS: usize> CtEq for FixedMontyForm<LIMBS>

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<const LIMBS: usize> CtEqSlice for FixedMontyForm<LIMBS>

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<const LIMBS: usize> Debug for FixedMontyForm<LIMBS>

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

Formats the value using the given formatter.

impl<const LIMBS: usize, P: ConstMontyParams<LIMBS>> From<&ConstMontyForm<P, LIMBS>> for FixedMontyForm<LIMBS>

fn from(const_monty_form: &ConstMontyForm<P, LIMBS>) -> Self

Converts to this type from the input type.

impl<const LIMBS: usize> From<&FixedMontyForm<LIMBS>> for BoxedMontyForm

Available on crate feature alloc only.

fn from(input: &FixedMontyForm<LIMBS>) -> Self

Converts to this type from the input type.

impl<const LIMBS: usize> From<FixedMontyForm<LIMBS>> for BoxedMontyForm

Available on crate feature alloc only.

fn from(input: FixedMontyForm<LIMBS>) -> Self

Converts to this type from the input type.

impl<const LIMBS: usize> Invert for FixedMontyForm<LIMBS>

type Output = CtOption<FixedMontyForm<LIMBS>>

Output of the inversion.

fn invert(&self) -> Self::Output

Computes the inverse.

fn invert_vartime(&self) -> Self::Output

Computes the inverse in variable-time.

impl<const LIMBS: usize> MontyForm for FixedMontyForm<LIMBS>

type Integer = Uint<LIMBS>

The original integer type.

type Params = MontyParams<Uint<LIMBS>>

The precomputed data needed for this representation.

type Multiplier<'a> = FixedMontyMultiplier<'a, LIMBS>

Prepared Montgomery multiplier for tight loops.

fn new_params_vartime(modulus: Odd<Self::Integer>) -> Self::Params

Create the precomputed data for Montgomery representation of integers modulo modulus, variable time in modulus.

fn new(value: Self::Integer, params: &Self::Params) -> Self

Convert the value into the representation using precomputed data.

fn zero(params: &Self::Params) -> Self

Returns zero in this representation.

fn one(params: &Self::Params) -> Self

Returns one in this representation.

fn params(&self) -> &Self::Params

Returns the parameter struct used to initialize this object.

fn as_montgomery(&self) -> &Self::Integer

Access the value in Montgomery form.

fn into_montgomery(self) -> Self::Integer

Move the Montgomery form result out of self and return it.

fn copy_montgomery_from(&mut self, other: &Self)

Copy the Montgomery representation from other into self. NOTE: the parameters remain unchanged.

fn double(&self) -> Self

Performs doubling, returning self + self.

fn div_by_2(&self) -> Self

Performs division by 2, that is returns x such that x + x = self.

fn lincomb_vartime(products: &[(&Self, &Self)]) -> Self

Calculate the sum of products of pairs (a, b) in products.

fn div_by_2_assign(&mut self)

Performs division by 2 inplace, that is finds x such that x + x = self and writes it into self.

impl<const LIMBS: usize> Mul<&FixedMontyForm<LIMBS>> for &FixedMontyForm<LIMBS>

type Output = FixedMontyForm<LIMBS>

The resulting type after applying the * operator.

fn mul(self, rhs: &FixedMontyForm<LIMBS>) -> FixedMontyForm<LIMBS>

Performs the * operation.

impl<const LIMBS: usize> Mul<&FixedMontyForm<LIMBS>> for FixedMontyForm<LIMBS>

type Output = FixedMontyForm<LIMBS>

The resulting type after applying the * operator.

fn mul(self, rhs: &FixedMontyForm<LIMBS>) -> FixedMontyForm<LIMBS>

Performs the * operation.

impl<const LIMBS: usize> Mul<FixedMontyForm<LIMBS>> for &FixedMontyForm<LIMBS>

type Output = FixedMontyForm<LIMBS>

The resulting type after applying the * operator.

fn mul(self, rhs: FixedMontyForm<LIMBS>) -> FixedMontyForm<LIMBS>

Performs the * operation.

impl<const LIMBS: usize> Mul for FixedMontyForm<LIMBS>

type Output = FixedMontyForm<LIMBS>

The resulting type after applying the * operator.

fn mul(self, rhs: FixedMontyForm<LIMBS>) -> FixedMontyForm<LIMBS>

Performs the * operation.

impl<const LIMBS: usize> MulAssign<&FixedMontyForm<LIMBS>> for FixedMontyForm<LIMBS>

fn mul_assign(&mut self, rhs: &FixedMontyForm<LIMBS>)

Performs the *= operation.

impl<const LIMBS: usize> MulAssign for FixedMontyForm<LIMBS>

fn mul_assign(&mut self, rhs: FixedMontyForm<LIMBS>)

Performs the *= operation.

impl<const LIMBS: usize, const RHS_LIMBS: usize> MultiExponentiateBoundedExp<Uint<RHS_LIMBS>, [(FixedMontyForm<LIMBS>, Uint<RHS_LIMBS>)]> for FixedMontyForm<LIMBS>

Available on crate feature alloc only.

fn multi_exponentiate_bounded_exp( bases_and_exponents: &[(Self, Uint<RHS_LIMBS>)], exponent_bits: u32, ) -> Self

Calculates x1 ^ k1 * ... * xn ^ kn.

impl<const N: usize, const LIMBS: usize, const RHS_LIMBS: usize> MultiExponentiateBoundedExp<Uint<RHS_LIMBS>, [(FixedMontyForm<LIMBS>, Uint<RHS_LIMBS>); N]> for FixedMontyForm<LIMBS>

fn multi_exponentiate_bounded_exp( bases_and_exponents: &[(Self, Uint<RHS_LIMBS>); N], exponent_bits: u32, ) -> Self

Calculates x1 ^ k1 * ... * xn ^ kn.

impl<const LIMBS: usize> Neg for &FixedMontyForm<LIMBS>

type Output = FixedMontyForm<LIMBS>

The resulting type after applying the - operator.

fn neg(self) -> FixedMontyForm<LIMBS>

Performs the unary - operation.

impl<const LIMBS: usize> Neg for FixedMontyForm<LIMBS>

type Output = FixedMontyForm<LIMBS>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<const LIMBS: usize> PartialEq for FixedMontyForm<LIMBS>

fn eq(&self, other: &FixedMontyForm<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<const LIMBS: usize, const RHS_LIMBS: usize> PowBoundedExp<Uint<RHS_LIMBS>> for FixedMontyForm<LIMBS>

fn pow_bounded_exp( &self, exponent: &Uint<RHS_LIMBS>, exponent_bits: u32, ) -> Self

Raises to the exponent power, with exponent_bits representing the number of (least significant) bits to take into account for the exponent.

impl<const LIMBS: usize> Retrieve for FixedMontyForm<LIMBS>

type Output = Uint<LIMBS>

The original type.

fn retrieve(&self) -> Self::Output

Convert the number back from the optimized representation.

impl<const LIMBS: usize> Square for FixedMontyForm<LIMBS>

fn square(&self) -> Self

Computes the same as self * self, but may be more efficient.

impl<const LIMBS: usize> SquareAssign for FixedMontyForm<LIMBS>

fn square_assign(&mut self)

Computes the same as self * self, but may be more efficient. Writes the result in self.

impl<const LIMBS: usize> Sub<&FixedMontyForm<LIMBS>> for &FixedMontyForm<LIMBS>

type Output = FixedMontyForm<LIMBS>

The resulting type after applying the - operator.

fn sub(self, rhs: &FixedMontyForm<LIMBS>) -> FixedMontyForm<LIMBS>

Performs the - operation.

impl<const LIMBS: usize> Sub<&FixedMontyForm<LIMBS>> for FixedMontyForm<LIMBS>

type Output = FixedMontyForm<LIMBS>

The resulting type after applying the - operator.

fn sub(self, rhs: &FixedMontyForm<LIMBS>) -> FixedMontyForm<LIMBS>

Performs the - operation.

impl<const LIMBS: usize> Sub<FixedMontyForm<LIMBS>> for &FixedMontyForm<LIMBS>

type Output = FixedMontyForm<LIMBS>

The resulting type after applying the - operator.

fn sub(self, rhs: FixedMontyForm<LIMBS>) -> FixedMontyForm<LIMBS>

Performs the - operation.

impl<const LIMBS: usize> Sub for FixedMontyForm<LIMBS>

type Output = FixedMontyForm<LIMBS>

The resulting type after applying the - operator.

fn sub(self, rhs: FixedMontyForm<LIMBS>) -> FixedMontyForm<LIMBS>

Performs the - operation.

impl<const LIMBS: usize> SubAssign<&FixedMontyForm<LIMBS>> for FixedMontyForm<LIMBS>

fn sub_assign(&mut self, rhs: &FixedMontyForm<LIMBS>)

Performs the -= operation.

impl<const LIMBS: usize> SubAssign for FixedMontyForm<LIMBS>

fn sub_assign(&mut self, rhs: FixedMontyForm<LIMBS>)

Performs the -= operation.

impl<const LIMBS: usize> Zeroize for FixedMontyForm<LIMBS>

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<const LIMBS: usize> Copy for FixedMontyForm<LIMBS>

impl<const LIMBS: usize> CtSelectUsingCtAssign for FixedMontyForm<LIMBS>

impl<const LIMBS: usize> Eq for FixedMontyForm<LIMBS>

impl<const LIMBS: usize> StructuralPartialEq for FixedMontyForm<LIMBS>