Struct MontyFieldElement 

pub struct MontyFieldElement<MOD, const LIMBS: usize>
where
    MOD: MontyFieldParams<LIMBS>,
{
    inner: ConstMontyForm<MOD, LIMBS>,
}

Field element type which uses an internal Montgomery form representation.

Fields

inner: ConstMontyForm<MOD, LIMBS>

Implementations

impl<MOD, const LIMBS: usize> MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

pub const ZERO: Self

Zero element (additive identity).

pub const ONE: Self

Multiplicative identity.

pub const LIMBS: usize = LIMBS

Number of limbs used by the internal integer representation.

pub fn from_bytes(repr: &MontyFieldBytes<MOD, LIMBS>) -> CtOption<Self>

where Uint<LIMBS>: ArrayEncoding,

Decode field element from a canonical bytestring representation.

pub fn from_slice(slice: &[u8]) -> Option<Self>

where Uint<LIMBS>: ArrayEncoding,

Decode field element from a canonical byte slice.

Slice is expected to be zero padded to the expected byte size.

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

Decode a field element from hex-encoded bytes.

This is primarily intended for defining constants using hex literals.

Panics

• When hex is malformed
• When input is the wrong length
• If input overflows the modulus

pub const fn from_uint_reduced(uint: &Uint<LIMBS>) -> Self

Convert Uint into MontyFieldElement, first converting it into Montgomery form:

w * R^2 * R^-1 mod p = wR mod p

Reduces the input modulo p.

pub fn from_uint(uint: &Uint<LIMBS>) -> CtOption<Self>

Convert Uint into MontyFieldElement, first converting it into Montgomery form:

w * R^2 * R^-1 mod p = wR mod p

Returns

The CtOption equivalent of None if the input overflows the modulus.

pub const fn from_u32(w: u32) -> Self

Convert a u32 into a MontyFieldElement.

Panics

If the modulus is 32-bits or smaller.

pub const fn from_u64(w: u64) -> Self

Convert a u64 into a MontyFieldElement.

Panics

If the modulus is 64-bits or smaller.

pub const fn from_montgomery(uint: Uint<LIMBS>) -> Self

Create MontyFieldElement from a Uint which is already in Montgomery form.

⚠️ Warning

This value is expected to be in Montgomery form and reduced. Failure to maintain these invariants will lead to miscomputation and potential security issues!

pub const fn from_montgomery_words(words: [Word; LIMBS]) -> Self

Helper function to construct MontyFieldElement from words in Montgomery form.

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

Borrow the inner Uint type which is in Montgomery form.

⚠️ Warning

Make sure you are actually expecting a value in Montgomery form! This is not the correct function for converting out of Montgomery form: that would be MontyFieldElement::to_canonical.

pub const fn to_montgomery_words(&self) -> [Word; LIMBS]

Retrieve the Montgomery form representation as an array of Words.

pub fn to_bytes(self) -> MontyFieldBytes<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>, Uint<LIMBS>: ArrayEncoding,

Returns the bytestring encoding of this field element.

pub fn is_odd(&self) -> Choice

Determine if this field element is odd: self mod 2 == 1.

Returns

If odd, return Choice(1). Otherwise, return Choice(0).

pub fn is_even(&self) -> Choice

Determine if this field element is even: self mod 2 == 0.

Returns

If even, return Choice(1). Otherwise, return Choice(0).

pub fn is_zero(&self) -> Choice

Determine if this field element is zero.

Returns

If zero, return Choice(1). Otherwise, return Choice(0).

pub const fn to_canonical(self) -> Uint<LIMBS>

Translate field element out of the Montgomery domain, returning a Uint in canonical form.

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

Add elements.

pub const fn double(&self) -> Self

Double element (add it to itself).

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

Subtract elements.

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

Multiply elements.

pub const fn neg(&self) -> Self

Negate element.

pub const fn square(&self) -> Self

Compute modular square.

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

Compute field inversion: 1 / self.

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

Compute field inversion: 1 / self in variable-time.

pub const fn const_invert(&self) -> Self

Compute field inversion as a const fn. Panics if self is zero.

This is mainly intended for inverting constants at compile time.

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

Returns self^exp, where exp is a little-endian integer exponent.

This operation is variable time with respect to the exponent exp.

If exp is fixed, this operation is constant time. Note that exp will still be branched upon and should NOT be a secret.

pub const fn sqn_vartime(&self, n: usize) -> Self

Returns self^(2^n) mod p.

This operation is variable time with respect to the exponent n.

If the exponent is fixed, this operation is constant time.

Trait Implementations

impl<MOD, const LIMBS: usize> Add<&MontyFieldElement<MOD, LIMBS>> for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

type Output = MontyFieldElement<MOD, LIMBS>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<MOD, const LIMBS: usize> Add for &MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

type Output = MontyFieldElement<MOD, LIMBS>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<MOD, const LIMBS: usize> Add for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

type Output = MontyFieldElement<MOD, LIMBS>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<MOD, const LIMBS: usize> AddAssign<&MontyFieldElement<MOD, LIMBS>> for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn add_assign(&mut self, other: &MontyFieldElement<MOD, LIMBS>)

Performs the += operation.

impl<MOD, const LIMBS: usize> AddAssign for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn add_assign(&mut self, other: MontyFieldElement<MOD, LIMBS>)

Performs the += operation.

impl<MOD, const LIMBS: usize> Binary for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

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

Formats the value using the given formatter.

impl<MOD, const LIMBS: usize> Clone for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS> + Clone,

fn clone(&self) -> MontyFieldElement<MOD, LIMBS>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<MOD, const LIMBS: usize> ConditionallySelectable for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

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<MOD, const LIMBS: usize> ConstMontyParams<LIMBS> for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

const LIMBS: usize = LIMBS

Number of limbs required to encode the Montgomery form

const PARAMS: FixedMontyParams<LIMBS> = MOD::PARAMS

Montgomery parameters constant.

impl<MOD, const LIMBS: usize> ConstantTimeEq for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

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<MOD, const LIMBS: usize> ConstantTimeGreater for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

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

Determine whether self > other.

impl<MOD, const LIMBS: usize> ConstantTimeLess for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

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

Determine whether self < other.

impl<MOD, const LIMBS: usize> CtEq for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<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<MOD, const LIMBS: usize> CtGt for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

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

Compute whether self > other in constant time.

impl<MOD, const LIMBS: usize> CtLt for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

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

Compute whether self < other in constant time.

impl<MOD, const LIMBS: usize> CtSelect for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

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<MOD, const LIMBS: usize> Debug for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

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

Formats the value using the given formatter.

impl<MOD, const LIMBS: usize> Default for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn default() -> Self

Returns the “default value” for a type.

impl<MOD, const LIMBS: usize> Display for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

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

Formats the value using the given formatter.

impl<MOD, const LIMBS: usize> Field for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>, MontyFieldBytes<MOD, LIMBS>: Copy, Uint<LIMBS>: ArrayEncoding,

const ZERO: Self = Self::ZERO

The zero element of the field, the additive identity.

const ONE: Self = Self::ONE

The one element of the field, the multiplicative identity.

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

Returns an element chosen uniformly at random using a user-provided fallible RNG.

fn is_zero(&self) -> Choice

Returns true iff this element is zero.

fn square(&self) -> Self

Squares this element.

fn double(&self) -> Self

Doubles this element.

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

Computes the multiplicative inverse of this element, failing if the element is zero.

fn sqrt(&self) -> CtOption<Self>

Returns the square root of the field element, if it is quadratic residue.

fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self)

Computes:

fn random<R>(rng: &mut R) -> Self

where R: Rng + ?Sized,

Returns an element chosen uniformly at random using a user-provided infallible RNG.

fn is_zero_vartime(&self) -> bool

Returns true iff this element is zero.

fn cube(&self) -> Self

Cubes this element.

fn sqrt_alt(&self) -> (Choice, Self)

Equivalent to Self::sqrt_ratio(self, one()).

fn pow<S>(&self, exp: S) -> Self

where S: AsRef<[u64]>,

Exponentiates self by exp, where exp is a little-endian order integer exponent.

fn pow_vartime<S>(&self, exp: S) -> Self

where S: AsRef<[u64]>,

Exponentiates self by exp, where exp is a little-endian order integer exponent.

impl<MOD, const LIMBS: usize> From<&MontyFieldElement<MOD, LIMBS>> for MontyFieldBytes<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>, Uint<LIMBS>: ArrayEncoding,

fn from(fe: &MontyFieldElement<MOD, LIMBS>) -> Self

Converts to this type from the input type.

impl<MOD, const LIMBS: usize> From<&MontyFieldElement<MOD, LIMBS>> for Uint<LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn from(fe: &MontyFieldElement<MOD, LIMBS>) -> Uint<LIMBS>

Converts to this type from the input type.

impl<MOD, const LIMBS: usize> From<MontyFieldElement<MOD, LIMBS>> for MontyFieldBytes<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>, Uint<LIMBS>: ArrayEncoding,

fn from(fe: MontyFieldElement<MOD, LIMBS>) -> Self

Converts to this type from the input type.

impl<MOD, const LIMBS: usize> From<MontyFieldElement<MOD, LIMBS>> for Uint<LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn from(fe: MontyFieldElement<MOD, LIMBS>) -> Uint<LIMBS>

Converts to this type from the input type.

impl<MOD, const LIMBS: usize> From<u128> for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn from(n: u128) -> MontyFieldElement<MOD, LIMBS>

Converts to this type from the input type.

impl<MOD, const LIMBS: usize> From<u32> for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn from(n: u32) -> MontyFieldElement<MOD, LIMBS>

Converts to this type from the input type.

impl<MOD, const LIMBS: usize> From<u64> for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn from(n: u64) -> MontyFieldElement<MOD, LIMBS>

Converts to this type from the input type.

impl<MOD, const LIMBS: usize> Generate for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>, MontyFieldBytes<MOD, LIMBS>: Copy, Uint<LIMBS>: ArrayEncoding,

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

Generate random key using the provided TryCryptoRng.

fn generate_from_rng<R>(rng: &mut R) -> Self

where R: CryptoRng + ?Sized,

Generate random key using the provided CryptoRng.

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

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

fn generate() -> Self

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

impl<MOD, const LIMBS: usize> Invert for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>, ConstMontyForm<MOD, LIMBS>: Invert<Output = CtOption<ConstMontyForm<MOD, LIMBS>>>,

type Output = CtOption<MontyFieldElement<MOD, LIMBS>>

Output of the inversion.

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

Computes the inverse.

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

Computes the inverse in variable-time.

impl<MOD, const LIMBS: usize> LowerHex for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

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

Formats the value using the given formatter.

impl<MOD, const LIMBS: usize> Mul<&MontyFieldElement<MOD, LIMBS>> for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

type Output = MontyFieldElement<MOD, LIMBS>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<MOD, const LIMBS: usize> Mul for &MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

type Output = MontyFieldElement<MOD, LIMBS>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<MOD, const LIMBS: usize> Mul for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

type Output = MontyFieldElement<MOD, LIMBS>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<MOD, const LIMBS: usize> MulAssign<&MontyFieldElement<MOD, LIMBS>> for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn mul_assign(&mut self, other: &MontyFieldElement<MOD, LIMBS>)

Performs the *= operation.

impl<MOD, const LIMBS: usize> MulAssign for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn mul_assign(&mut self, other: MontyFieldElement<MOD, LIMBS>)

Performs the *= operation.

impl<MOD, const LIMBS: usize> Neg for &MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

type Output = MontyFieldElement<MOD, LIMBS>

The resulting type after applying the - operator.

fn neg(self) -> MontyFieldElement<MOD, LIMBS>

Performs the unary - operation.

impl<MOD, const LIMBS: usize> Neg for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

type Output = MontyFieldElement<MOD, LIMBS>

The resulting type after applying the - operator.

fn neg(self) -> MontyFieldElement<MOD, LIMBS>

Performs the unary - operation.

impl<MOD, const LIMBS: usize> Ord for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn cmp(&self, other: &Self) -> 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<MOD: MontyFieldParams<LIMBS>, const LIMBS: usize> PartialEq for MontyFieldElement<MOD, LIMBS>

fn eq(&self, rhs: &Self) -> 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<MOD, const LIMBS: usize> PartialOrd for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn partial_cmp(&self, other: &Self) -> 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<MOD, const LIMBS: usize> PrimeField for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>, MontyFieldBytes<MOD, LIMBS>: Copy, Uint<LIMBS>: ArrayEncoding,

const MODULUS: &'static str = MOD::MODULUS_HEX

Modulus of the field written as a string for debugging purposes.

const NUM_BITS: u32

How many bits are needed to represent an element of this field.

const CAPACITY: u32

How many bits of information can be reliably stored in the field element.

const TWO_INV: Self

Inverse of $2$ in the field.

const MULTIPLICATIVE_GENERATOR: Self

A fixed multiplicative generator of modulus - 1 order. This element must also be a quadratic nonresidue.

const S: u32

An integer s satisfying the equation 2^s * t = modulus - 1 with t odd.

const ROOT_OF_UNITY: Self

The 2^s root of unity.

const ROOT_OF_UNITY_INV: Self

Inverse of Self::ROOT_OF_UNITY.

const DELTA: Self

Generator of the t-order multiplicative subgroup.

type Repr = Array<u8, <MOD as MontyFieldParams<LIMBS>>::ByteSize>

The prime field can be converted back and forth into this binary representation.

fn from_repr(bytes: Self::Repr) -> CtOption<Self>

Attempts to convert a byte representation of a field element into an element of this prime field, failing if the input is not canonical (is not smaller than the field’s modulus).

fn to_repr(&self) -> Self::Repr

Converts an element of the prime field into the standard byte representation for this field.

fn is_odd(&self) -> Choice

Returns true iff this element is odd.

fn from_str_vartime(s: &str) -> Option<Self>

Interpret a string of numbers as a (congruent) prime field element. Does not accept unnecessary leading zeroes or a blank string.

fn from_u128(v: u128) -> Self

Obtains a field element congruent to the integer v.

fn from_repr_vartime(repr: Self::Repr) -> Option<Self>

Attempts to convert a byte representation of a field element into an element of this prime field, failing if the input is not canonical (is not smaller than the field’s modulus).

fn is_even(&self) -> Choice

Returns true iff this element is even.

impl<'a, MOD: MontyFieldParams<LIMBS>, const LIMBS: usize> Product<&'a MontyFieldElement<MOD, LIMBS>> for MontyFieldElement<MOD, LIMBS>

fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by multiplying the items.

impl<MOD, const LIMBS: usize> Product for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn product<I: Iterator<Item = Self>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by multiplying the items.

impl<MOD, const LIMBS: usize> Reduce<Array<u8, <MOD as MontyFieldParams<LIMBS>>::ByteSize>> for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>, Uint<LIMBS>: ArrayEncoding<ByteSize = MOD::ByteSize>,

fn reduce(bytes: &MontyFieldBytes<MOD, LIMBS>) -> Self

Reduces self modulo Modulus.

impl<MOD, const LIMBS: usize> Reduce<Uint<LIMBS>> for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn reduce(w: &Uint<LIMBS>) -> Self

Reduces self modulo Modulus.

impl<MOD, const LIMBS: usize> Retrieve for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

type Output = Uint<LIMBS>

The original type.

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

Convert the number back from the optimized representation.

impl<MOD, const LIMBS: usize> Sub<&MontyFieldElement<MOD, LIMBS>> for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

type Output = MontyFieldElement<MOD, LIMBS>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<MOD, const LIMBS: usize> Sub for &MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

type Output = MontyFieldElement<MOD, LIMBS>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<MOD, const LIMBS: usize> Sub for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

type Output = MontyFieldElement<MOD, LIMBS>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<MOD, const LIMBS: usize> SubAssign<&MontyFieldElement<MOD, LIMBS>> for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn sub_assign(&mut self, other: &MontyFieldElement<MOD, LIMBS>)

Performs the -= operation.

impl<MOD, const LIMBS: usize> SubAssign for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn sub_assign(&mut self, other: MontyFieldElement<MOD, LIMBS>)

Performs the -= operation.

impl<'a, MOD, const LIMBS: usize> Sum<&'a MontyFieldElement<MOD, LIMBS>> for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn sum<I: Iterator<Item = &'a MontyFieldElement<MOD, LIMBS>>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<MOD, const LIMBS: usize> Sum for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<MOD, const LIMBS: usize> UpperHex for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS>,

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

Formats the value using the given formatter.

impl<MOD, const LIMBS: usize> Copy for MontyFieldElement<MOD, LIMBS>

where MOD: MontyFieldParams<LIMBS> + Copy,

impl<MOD: MontyFieldParams<LIMBS>, const LIMBS: usize> Eq for MontyFieldElement<MOD, LIMBS>