Struct Fq

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

Represents an element of the base field $\mathbb{F}_p$ of the BLS12-381 elliptic curve construction. The internal representation of this type is six 64-bit unsigned integers in little-endian order. Fp values are always in Montgomery form; i.e., Scalar(a) = aR mod p, with R = 2^384.

Implementations

impl Fp

pub const fn zero() -> Fp

Returns zero, the additive identity.

pub const fn one() -> Fp

Returns one, the multiplicative identity.

pub fn from_bytes(bytes: &[u8; 48]) -> CtOption<Fp>

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

pub fn from_bytes_be(bytes: &[u8; 48]) -> CtOption<Fp>

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

pub fn to_bytes_be(self) -> [u8; 48]

Converts an element of Fp into a byte representation in big-endian byte order.

pub fn to_bytes(self) -> [u8; 48]

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

pub fn random(rng: impl RngCore) -> Fp

Generates a new uniformly-distributed random element using the given randomness.

pub fn lexicographically_largest(&self) -> Choice

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

pub const fn from_raw_unchecked(v: [u64; 6]) -> Fp

Constructs an element of Fp without checking that it is canonical.

pub fn pow_vartime(&self, by: &[u64; 6]) -> Self

Although this is labeled “vartime”, it is only variable time with respect to the exponent. It is also not exposed in the public API.

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

Performs the square root of an element in constant time.

NOTE: We use Shank’s method, as p = 3 (mod 4). This means we only need to exponentiate by (p+1)/4. This only works for elements that are actually quadratic residue, so we check that we got the correct result at the end.

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

Computes the multiplicative inverse of this field element, returning None in the case that this element is zero.

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

Performs constant time addition of two elements.

pub const fn neg(&self) -> Fp

Performs constant time negation of an element.

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

Performs constant time subtraction of two elements.

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

Performs constant time multiplication of two elements.

pub const fn square(&self) -> Self

Squares this element.

Trait Implementations

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

type Output = Fp

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Fp

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Fp

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add for Fp

type Output = Fp

The resulting type after applying the + operator.

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

Performs the + operation.

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

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

Performs the += operation.

impl AddAssign for Fp

fn add_assign(&mut self, rhs: Fp)

Performs the += operation.

impl Clone for Fp

fn clone(&self) -> Fp

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for Fp

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 Fp

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 Fp

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

Formats the value using the given formatter.

impl Default for Fp

fn default() -> Self

Returns the “default value” for a type.

impl Field for Fp

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 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_ratio(num: &Self, div: &Self) -> (Choice, Self)

Computes:

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

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

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 From<[u64; 6]> for Fp

fn from(digits: [u64; 6]) -> Self

Converts to this type from the input type.

impl From<Fp> for Fp12

fn from(f: Fp) -> Fp12

Converts to this type from the input type.

impl From<Fp> for Fp2

fn from(f: Fp) -> Fp2

Converts to this type from the input type.

impl From<Fp> for Fp6

fn from(f: Fp) -> Fp6

Converts to this type from the input type.

impl From<bool> for Fp

fn from(bit: bool) -> Fp

Converts to this type from the input type.

impl From<u64> for Fp

fn from(value: u64) -> Self

Converts to this type from the input type.

impl FromUniformBytes<64> for Fp

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

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

impl Hash for Fp

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 HashToField for Fp

type InputLength = UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, B0>

The length of the data used to produce an individual field element.

fn from_okm(okm: &GenericArray<u8, U64>) -> Fp

Interprets the given output keying material as a big endian integer, and reduces it into a field element.

fn hash_to_field<X: ExpandMessage>( message: &[u8], dst: &[u8], output: &mut [Self], )

Hashes a byte string of arbitrary length into one or more elements of Self, using ExpandMessage variant X.

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

type Output = Fp

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Fp

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Fp

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul for Fp

type Output = Fp

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Performs the *= operation.

impl MulAssign for Fp

fn mul_assign(&mut self, rhs: Fp)

Performs the *= operation.

impl<'a> Neg for &'a Fp

type Output = Fp

The resulting type after applying the - operator.

fn neg(self) -> Fp

Performs the unary - operation.

impl Neg for Fp

type Output = Fp

The resulting type after applying the - operator.

fn neg(self) -> Fp

Performs the unary - operation.

impl Ord for Fp

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 Fp

fn eq(&self, other: &Fp) -> 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 Fp

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 Fp

const MODULUS: &'static str = "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"

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

const NUM_BITS: u32 = 381u32

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

const CAPACITY: u32 = 380u32

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

const TWO_INV: Self = TWO_INV

Inverse of $2$ in the field.

const MULTIPLICATIVE_GENERATOR: Self = GENERATOR

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

const S: u32 = 1u32

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

const ROOT_OF_UNITY: Self = ROOT_OF_UNITY

The 2^s root of unity.

const ROOT_OF_UNITY_INV: Self = ROOT_OF_UNITY_INV

Inverse of Self::ROOT_OF_UNITY.

const DELTA: Self = DELTA

Generator of the t-order multiplicative subgroup.

type Repr = ReprFp

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

fn from_repr(r: 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<T> Product<T> for Fp

where T: Borrow<Fp>,

fn product<I>(iter: I) -> Self

where I: Iterator<Item = T>,

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

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

type Output = Fp

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Fp

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Fp

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub for Fp

type Output = Fp

The resulting type after applying the - operator.

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

Performs the - operation.

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

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

Performs the -= operation.

impl SubAssign for Fp

fn sub_assign(&mut self, rhs: Fp)

Performs the -= operation.

impl<T> Sum<T> for Fp

where T: Borrow<Fp>,

fn sum<I>(iter: I) -> Self

where I: Iterator<Item = T>,

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

impl WithSmallOrderMulGroup<3> for Fp

const ZETA: Self = ZETA

A field element of small multiplicative order $N$.

impl Copy for Fp

impl Eq for Fp

impl StructuralPartialEq for Fp