Struct pasta_curves::Fq

pub struct Fq(_);

This represents an element of $\mathbb{F}_q$ where

q = 0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001

is the base field of the Vesta curve.

Implementations

impl Fq

pub const fn zero() -> Fq

Returns zero, the additive identity.

pub const fn one() -> Fq

Returns one, the multiplicative identity.

pub const fn double(&self) -> Fq

Doubles this field element.

pub const fn from_raw(val: [u64; 4]) -> Self

Converts from an integer represented in little endian into its (congruent) Fq representation.

pub const fn square(&self) -> Fq

Squares this element.

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

Multiplies rhs by self, returning the result.

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

Subtracts rhs from self, returning the result.

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

Adds rhs to self, returning the result.

pub const fn neg(&self) -> Self

Negates self.

Trait Implementations

impl<'a, 'b> Add<&'b Fq> for &'a Fq

type Output = Fq

The resulting type after applying the + operator.

fn add(self, rhs: &'b Fq) -> Fq

Performs the + operation.

impl<'b> Add<&'b Fq> for Fq

type Output = Fq

The resulting type after applying the + operator.

fn add(self, rhs: &'b Fq) -> Fq

Performs the + operation.

impl<'a> Add<Fq> for &'a Fq

type Output = Fq

The resulting type after applying the + operator.

fn add(self, rhs: Fq) -> Fq

Performs the + operation.

impl Add<Fq> for Fq

type Output = Fq

The resulting type after applying the + operator.

fn add(self, rhs: Fq) -> Fq

Performs the + operation.

impl<'b> AddAssign<&'b Fq> for Fq

fn add_assign(&mut self, rhs: &'b Fq)

Performs the += operation.

impl AddAssign<Fq> for Fq

fn add_assign(&mut self, rhs: Fq)

Performs the += operation.

impl Clone for Fq

fn clone(&self) -> Fq

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for Fq

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 ConstantTimeEq for Fq

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

Determine if two items are equal.

impl Debug for Fq

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

Formats the value using the given formatter.

impl Default for Fq

fn default() -> Self

Returns the “default value” for a type.

impl Field for Fq

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

Computes the square root of this element, if it exists.

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

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

fn random(rng: impl RngCore) -> Self

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

fn zero() -> Self

Returns the zero element of the field, the additive identity.

fn one() -> Self

Returns the one element of the field, the multiplicative identity.

fn is_zero(&self) -> bool

Returns true iff this element is zero.

fn double(&self) -> Self

Doubles this element.

fn square(&self) -> Self

Squares this element.

fn pow_vartime<S: AsRef<[u64]>>(&self, exp: S) -> Self

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

#[must_use]

fn cube(&self) -> Self

Cubes this element.

impl FieldExt for Fq

fn from_bytes(bytes: &[u8; 32]) -> CtOption<Fq>

Attempts to convert a little-endian byte representation of a scalar into a Fq, failing if the input is not canonical.

fn to_bytes(&self) -> [u8; 32]

Converts an element of Fq into a byte representation in little-endian byte order.

fn from_bytes_wide(bytes: &[u8; 64]) -> Fq

Converts a 512-bit little endian integer into a Fq by reducing by the modulus.

const MODULUS: &'static str

Modulus of the field written as a string for display purposes

const ROOT_OF_UNITY: Self

Generator of the $2^S$ multiplicative subgroup

const ROOT_OF_UNITY_INV: Self

Inverse of ROOT_OF_UNITY

const T_MINUS1_OVER2: [u64; 4]

The value $(T-1)/2$ such that $2^S \cdot T = p - 1$ with $T$ odd.

const DELTA: Self

Generator of the $t-order$ multiplicative subgroup

const TWO_INV: Self

Inverse of $2$ in the field.

const RESCUE_ALPHA: u64

Ideally the smallest prime $\alpha$ such that gcd($p - 1$, $\alpha$) = $1$

const RESCUE_INVALPHA: [u64; 4]

$RESCUE_INVALPHA \cdot RESCUE_ALPHA = 1 \mod p - 1$ such that (a^RESCUE_ALPHA)^RESCUE_INVALPHA = a.

const ZETA: Self

Element of multiplicative order $3$.

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

Computes:

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

Equivalent to sqrt_ratio(self, one()).

fn ct_is_zero(&self) -> Choice

Returns whether or not this element is zero.

fn from_u64(v: u64) -> Self

Obtains a field element congruent to the integer v.

fn from_u128(v: u128) -> Self

Obtains a field element congruent to the integer v.

fn get_lower_128(&self) -> u128

Gets the lower 128 bits of this field element when expressed canonically.

fn get_lower_32(&self) -> u32

Gets the lower 32 bits of this field element when expressed canonically.

fn pow_by_t_minus1_over2(&self) -> Self

Raise this field element to the power T_MINUS1_OVER2. Field implementations may override this to use an efficient addition chain.

fn rand() -> Self

This computes a random element of the field using system randomness.

fn write<W: Write>(&self, writer: &mut W) -> Result<()>

Writes this element in its normalized, little endian form into a buffer.

fn read<R: Read>(reader: &mut R) -> Result<Self>

Reads a normalized, little endian represented field element from a buffer.

fn pow(&self, by: &[u64; 4]) -> Self

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

fn batch_invert(v: &mut [Self]) -> Self

Performs a batch inversion using Montgomery’s trick, returns the product of every inverse. Zero inputs are ignored.

impl From<bool> for Fq

fn from(bit: bool) -> Fq

Performs the conversion.

impl From<u64> for Fq

fn from(val: u64) -> Fq

Performs the conversion.

impl Group for Fq

type Scalar = Fq

The group is assumed to be of prime order $p$. Scalar is the associated scalar field of size $p$.

fn group_zero() -> Self

Returns the additive identity of the group.

fn group_add(&mut self, rhs: &Self)

Adds rhs to this group element.

fn group_sub(&mut self, rhs: &Self)

Subtracts rhs from this group element.

fn group_scale(&mut self, by: &Self::Scalar)

Scales this group element by a scalar.

impl<'a, 'b> Mul<&'b Fq> for &'a Ep

type Output = Ep

The resulting type after applying the * operator.

fn mul(self, other: &'b Fq) -> Self::Output

Performs the * operation.

impl<'a, 'b> Mul<&'b Fq> for &'a EpAffine

type Output = Ep

The resulting type after applying the * operator.

fn mul(self, other: &'b Fq) -> Self::Output

Performs the * operation.

impl<'b> Mul<&'b Fq> for Ep

type Output = Ep

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fq) -> Ep

Performs the * operation.

impl<'b> Mul<&'b Fq> for EpAffine

type Output = Ep

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fq) -> Ep

Performs the * operation.

impl<'a, 'b> Mul<&'b Fq> for &'a Fq

type Output = Fq

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fq) -> Fq

Performs the * operation.

impl<'b> Mul<&'b Fq> for Fq

type Output = Fq

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fq) -> Fq

Performs the * operation.

impl<'a> Mul<Fq> for &'a Ep

type Output = Ep

The resulting type after applying the * operator.

fn mul(self, rhs: Fq) -> Ep

Performs the * operation.

impl Mul<Fq> for Ep

type Output = Ep

The resulting type after applying the * operator.

fn mul(self, rhs: Fq) -> Ep

Performs the * operation.

impl<'a> Mul<Fq> for &'a EpAffine

type Output = Ep

The resulting type after applying the * operator.

fn mul(self, rhs: Fq) -> Ep

Performs the * operation.

impl Mul<Fq> for EpAffine

type Output = Ep

The resulting type after applying the * operator.

fn mul(self, rhs: Fq) -> Ep

Performs the * operation.

impl<'a> Mul<Fq> for &'a Fq

type Output = Fq

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Fq> for Fq

type Output = Fq

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b> MulAssign<&'b Fq> for Ep

fn mul_assign(&mut self, rhs: &'b Fq)

Performs the *= operation.

impl<'b> MulAssign<&'b Fq> for Fq

fn mul_assign(&mut self, rhs: &'b Fq)

Performs the *= operation.

impl MulAssign<Fq> for Ep

fn mul_assign(&mut self, rhs: Fq)

Performs the *= operation.

impl MulAssign<Fq> for Fq

fn mul_assign(&mut self, rhs: Fq)

Performs the *= operation.

impl<'a> Neg for &'a Fq

type Output = Fq

The resulting type after applying the - operator.

fn neg(self) -> Fq

Performs the unary - operation.

impl Neg for Fq

type Output = Fq

The resulting type after applying the - operator.

fn neg(self) -> Fq

Performs the unary - operation.

impl Ord for Fq

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

#[must_use]

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

Compares and returns the maximum of two values.

#[must_use]

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

Compares and returns the minimum of two values.

#[must_use]

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

Restrict a value to a certain interval.

impl PartialEq<Fq> for Fq

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

This method tests for self and other values to be equal, and is used by ==.

#[must_use]

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

This method tests for !=.

impl PartialOrd<Fq> for Fq

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

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

#[must_use]

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

This method tests less than (for self and other) and is used by the < operator.

#[must_use]

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

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

#[must_use]

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

This method tests greater than (for self and other) and is used by the > operator.

#[must_use]

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

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

impl PrimeField for Fq

type Repr = [u8; 32]

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

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 S: u32

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

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

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

fn is_odd(&self) -> bool

Returns true iff this element is odd.

fn multiplicative_generator() -> Self

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

fn root_of_unity() -> Self

Returns the 2^s root of unity.

fn from_str(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 is_even(&self) -> bool

Returns true iff this element is even.

impl PrimeFieldBits for Fq

type ReprBits = [u64; 4]

The backing store for a bit representation of a prime field element.

fn to_le_bits(&self) -> FieldBits<Self::ReprBits>

Converts an element of the prime field into a little-endian sequence of bits.

fn char_le_bits() -> FieldBits<Self::ReprBits>

Returns the bits of the field characteristic (the modulus) in little-endian order.

impl<'a, 'b> Sub<&'b Fq> for &'a Fq

type Output = Fq

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Fq) -> Fq

Performs the - operation.

impl<'b> Sub<&'b Fq> for Fq

type Output = Fq

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Fq) -> Fq

Performs the - operation.

impl<'a> Sub<Fq> for &'a Fq

type Output = Fq

The resulting type after applying the - operator.

fn sub(self, rhs: Fq) -> Fq

Performs the - operation.

impl Sub<Fq> for Fq

type Output = Fq

The resulting type after applying the - operator.

fn sub(self, rhs: Fq) -> Fq

Performs the - operation.

impl<'b> SubAssign<&'b Fq> for Fq

fn sub_assign(&mut self, rhs: &'b Fq)

Performs the -= operation.

impl SubAssign<Fq> for Fq

fn sub_assign(&mut self, rhs: Fq)

Performs the -= operation.

impl Copy for Fq

impl Eq for Fq

impl StructuralEq for Fq