Struct Fr

pub struct Fr(/* private fields */);

Implementations

impl Fr

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

pub const fn double(&self) -> Self

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

pub const fn neg(&self) -> Self

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

pub const fn square(&self) -> Self

impl Fr

pub const SIZE: usize = 32usize

pub const NUM_LIMBS: usize = 4usize

pub const fn zero() -> Fr

Returns zero, the additive identity.

pub const fn one() -> Fr

Returns one, the multiplicative identity.

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

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

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

Attempts to convert a <#endian>-endian byte representation of a scalar into a $field, failing if the input is not canonical.

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

Converts an element of $field into a byte representation in <#endian>-endian byte order.

pub fn lexicographically_largest(&self) -> Choice

Returns whether or not this element is strictly lexicographically larger than its negation.

Trait Implementations

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

type Output = Fr

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Fr

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Fr

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add for Fr

type Output = Fr

The resulting type after applying the + operator.

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

Performs the + operation.

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

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

Performs the += operation.

impl AddAssign for Fr

fn add_assign(&mut self, rhs: Fr)

Performs the += operation.

impl Clone for Fr

fn clone(&self) -> Fr

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for Fr

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 Fr

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 Debug for Fr

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

Formats the value using the given formatter.

impl Default for Fr

fn default() -> Fr

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Fr

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

Deserialize this value from the given Serde deserializer.

impl EndianRepr for Fr

const ENDIAN: Endian = crate::serde::endian::Endian::LE

fn to_bytes(&self) -> Vec<u8>

fn from_bytes(bytes: &[u8]) -> CtOption<Self>

impl Field for Fr

const ZERO: Self = _

The zero element of the field, the additive identity.

const ONE: Self = _

The one element of the field, the multiplicative identity.

fn random(rng: impl RngCore) -> Self

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

fn double(&self) -> Self

Doubles this element.

fn square(&self) -> Self

Squares 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 is_zero(&self) -> Choice

Returns true iff this element is zero.

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<'a> From<&'a Fr> for Repr<{ Fr::SIZE }>

fn from(value: &'a Fr) -> Repr<{ Fr::SIZE }>

Converts to this type from the input type.

impl From<Fr> for Repr<{ Fr::SIZE }>

fn from(value: Fr) -> Repr<{ Fr::SIZE }>

Converts to this type from the input type.

impl From<bool> for Fr

fn from(val: bool) -> Fr

Converts to this type from the input type.

impl From<u64> for Fr

fn from(val: u64) -> Fr

Converts to this type from the input type.

impl FromUniformBytes<64> for Fr

fn from_uniform_bytes(bytes: &[u8; 64]) -> Self

Returns a field element that is congruent to the provided little endian unsigned byte representation of an integer.

impl Hash for Fr

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 Legendre for Fr

fn legendre(&self) -> i64

fn ct_quadratic_non_residue(&self) -> Choice

fn ct_quadratic_residue(&self) -> Choice

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

type Output = Fr

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b> Mul<&'b Fr> for &'a G1

type Output = G1

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b> Mul<&'b Fr> for &'a G1Affine

type Output = G1

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b> Mul<&'b Fr> for &'a G2

type Output = G2

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b> Mul<&'b Fr> for &'a G2Affine

type Output = G2

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b> Mul<&'b Fr> for &'a Gt

type Output = Gt

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Fr

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b> Mul<&'b Fr> for G1

type Output = G1

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fr) -> G1

Performs the * operation.

impl<'b> Mul<&'b Fr> for G1Affine

type Output = G1

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fr) -> G1

Performs the * operation.

impl<'b> Mul<&'b Fr> for G2

type Output = G2

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fr) -> G2

Performs the * operation.

impl<'b> Mul<&'b Fr> for G2Affine

type Output = G2

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fr) -> G2

Performs the * operation.

impl<'b> Mul<&'b Fr> for Gt

type Output = Gt

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Fr

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a> Mul<Fr> for &'a G1

type Output = G1

The resulting type after applying the * operator.

fn mul(self, rhs: Fr) -> G1

Performs the * operation.

impl<'a> Mul<Fr> for &'a G1Affine

type Output = G1

The resulting type after applying the * operator.

fn mul(self, rhs: Fr) -> G1

Performs the * operation.

impl<'a> Mul<Fr> for &'a G2

type Output = G2

The resulting type after applying the * operator.

fn mul(self, rhs: Fr) -> G2

Performs the * operation.

impl<'a> Mul<Fr> for &'a G2Affine

type Output = G2

The resulting type after applying the * operator.

fn mul(self, rhs: Fr) -> G2

Performs the * operation.

impl<'a> Mul<Fr> for &'a Gt

type Output = Gt

The resulting type after applying the * operator.

fn mul(self, rhs: Fr) -> Gt

Performs the * operation.

impl Mul<Fr> for G1

type Output = G1

The resulting type after applying the * operator.

fn mul(self, rhs: Fr) -> G1

Performs the * operation.

impl Mul<Fr> for G1Affine

type Output = G1

The resulting type after applying the * operator.

fn mul(self, rhs: Fr) -> G1

Performs the * operation.

impl Mul<Fr> for G2

type Output = G2

The resulting type after applying the * operator.

fn mul(self, rhs: Fr) -> G2

Performs the * operation.

impl Mul<Fr> for G2Affine

type Output = G2

The resulting type after applying the * operator.

fn mul(self, rhs: Fr) -> G2

Performs the * operation.

impl Mul<Fr> for Gt

type Output = Gt

The resulting type after applying the * operator.

fn mul(self, rhs: Fr) -> Gt

Performs the * operation.

impl Mul for Fr

type Output = Fr

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Performs the *= operation.

impl<'b> MulAssign<&'b Fr> for G1

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

Performs the *= operation.

impl<'b> MulAssign<&'b Fr> for G2

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

Performs the *= operation.

impl<'b> MulAssign<&'b Fr> for Gt

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

Performs the *= operation.

impl MulAssign<Fr> for G1

fn mul_assign(&mut self, rhs: Fr)

Performs the *= operation.

impl MulAssign<Fr> for G2

fn mul_assign(&mut self, rhs: Fr)

Performs the *= operation.

impl MulAssign<Fr> for Gt

fn mul_assign(&mut self, rhs: Fr)

Performs the *= operation.

impl MulAssign for Fr

fn mul_assign(&mut self, rhs: Fr)

Performs the *= operation.

impl<'a> Neg for &'a Fr

type Output = Fr

The resulting type after applying the - operator.

fn neg(self) -> Fr

Performs the unary - operation.

impl Neg for Fr

type Output = Fr

The resulting type after applying the - operator.

fn neg(self) -> Fr

Performs the unary - operation.

impl Ord for Fr

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 PartialEq for Fr

fn eq(&self, other: &Fr) -> 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 for Fr

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 PrimeField for Fr

const NUM_BITS: u32 = 255u32

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

const CAPACITY: u32 = 254u32

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 = 32u32

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.

const MODULUS: &'static str = "0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001"

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

type Repr = Repr<impl_field!( bls12381_scalar, Fr, modulus = "73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001", mul_gen = "7", zeta = "ac45a4010001a40200000000ffffffff", from_uniform = [64], endian = "little", )>

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

fn from_u128(v: u128) -> Self

Obtains a field element congruent to the integer v.

fn from_repr(repr: 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_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 PrimeFieldBits for Fr

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<T: Borrow<Fr>> Product<T> for Fr

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

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

impl SerdeObject for Fr

fn from_raw_bytes_unchecked(bytes: &[u8]) -> Self

The purpose of unchecked functions is to read the internal memory representation of a type from bytes as quickly as possible. No sanitization checks are performed to ensure the bytes represent a valid object. As such this function should only be used internally as an extension of machine memory. It should not be used to deserialize externally provided data.

fn from_raw_bytes(bytes: &[u8]) -> Option<Self>

fn to_raw_bytes(&self) -> Vec<u8>

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

The purpose of unchecked functions is to read the internal memory representation of a type from disk as quickly as possible. No sanitization checks are performed to ensure the bytes represent a valid object. This function should only be used internally when some machine state cannot be kept in memory (e.g., between runs) and needs to be reloaded as quickly as possible.

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

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

impl Serialize for Fr

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

Serialize this value into the given Serde serializer.

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

type Output = Fr

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Fr

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Fr

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub for Fr

type Output = Fr

The resulting type after applying the - operator.

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

Performs the - operation.

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

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

Performs the -= operation.

impl SubAssign for Fr

fn sub_assign(&mut self, rhs: Fr)

Performs the -= operation.

impl<T: Borrow<Fr>> Sum<T> for Fr

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

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

impl WithSmallOrderMulGroup<3> for Fr

const ZETA: Self = _

A field element of small multiplicative order $N$.

impl Copy for Fr

impl Eq for Fr

impl StructuralPartialEq for Fr