Struct BlsScalar 

pub struct BlsScalar(pub [u64; 4]);

Represents an element of the scalar field $\mathbb{F}_q$ of the BLS12-381 elliptic curve construction.

Tuple Fields

0: [u64; 4]

Implementations

impl Scalar

pub fn is_zero(&self) -> Choice

Checks in ct_time whether a Scalar is equal to zero.

pub fn is_one(&self) -> Choice

Checks in ct_time whether a Scalar is equal to one.

pub const fn internal_repr(&self) -> &[u64; 4]

Returns the internal representation of the Scalar.

pub fn to_bits(&self) -> [u8; 256]

Returns the bit representation of the given Scalar as an array of 256 bits represented as u8.

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

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

pub fn reduce(&self) -> Scalar

Reduces the scalar and returns it multiplied by the montgomery radix.

pub fn pow_of_2(by: u64) -> Scalar

Computes 2^X where X is a u64 without the need to generate an array in the stack as pow & pow_vartime require.

pub fn hash_to_scalar(input: &[u8]) -> Scalar

Creates a Scalar from arbitrary bytes by hashing the input with BLAKE2b into a 512-bits number, and then converting the number into its Scalar representation by reducing it by the modulo.

By treating the output of the BLAKE2b hash as a random oracle, this implementation follows the first conversion of https://hackmd.io/zV6qe1_oSU-kYU6Tt7pO7Q with concrete numbers:

p = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
p = 52435875175126190479447740508185965837690552500527637822603658699938581184513

s = 2^512
s = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096

r = 255699135089535202043525422716183576215815630510683217819334674386498370757523

m = 3294906474794265442129797520630710739278575682199800681788903916070560242797

pub fn divn(&mut self, n: u32)

SHR impl

impl Scalar

pub const fn zero() -> Scalar

Returns zero, the additive identity.

pub const fn one() -> Scalar

Returns one, the multiplicative identity.

pub const fn double(&self) -> Scalar

Doubles this field element.

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

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

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

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

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

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

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

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

pub const fn square(&self) -> Scalar

Squares this element.

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

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

pub fn pow_vartime(&self, by: &[u64; 4]) -> Scalar

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

This operation is variable time with respect to the exponent. If the exponent is fixed, this operation is effectively constant time.

pub fn invert(&self) -> Option<Scalar>

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

pub fn invert_ct(&self) -> CtOption<Scalar>

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

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

Multiplies rhs by self, returning the result.

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

Subtracts rhs from self, returning the result.

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

Adds rhs to self, returning the result.

pub const fn neg(&self) -> Scalar

Negates self.

Trait Implementations

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

type Output = Scalar

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Scalar

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Scalar

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add for Scalar

type Output = Scalar

The resulting type after applying the + operator.

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

Performs the + operation.

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

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

Performs the += operation.

impl AddAssign for Scalar

fn add_assign(&mut self, rhs: Scalar)

Performs the += operation.

impl Archive for Scalar

where [u64; 4]: Archive,

type Archived = ArchivedScalar

The archived representation of this type.

type Resolver = ScalarResolver

The resolver for this type. It must contain all the additional information from serializing needed to make the archived type from the normal type.

unsafe fn resolve( &self, pos: usize, resolver: <Scalar as Archive>::Resolver, out: *mut <Scalar as Archive>::Archived, )

Creates the archived version of this value at the given position and writes it to the given output.

impl AsRef<Scalar> for SecretKey

fn as_ref(&self) -> &Scalar

Converts this type into a shared reference of the (usually inferred) input type.

impl<'a, 'b> BitAnd<&'b Scalar> for &'a Scalar

type Output = Scalar

The resulting type after applying the & operator.

fn bitand(self, rhs: &'b Scalar) -> Scalar

Performs the & operation.

impl BitAnd for Scalar

type Output = Scalar

The resulting type after applying the & operator.

fn bitand(self, rhs: Scalar) -> Scalar

Performs the & operation.

impl<'a, 'b> BitXor<&'b Scalar> for &'a Scalar

type Output = Scalar

The resulting type after applying the ^ operator.

fn bitxor(self, rhs: &'b Scalar) -> Scalar

Performs the ^ operation.

impl BitXor for Scalar

type Output = Scalar

The resulting type after applying the ^ operator.

fn bitxor(self, rhs: Scalar) -> Scalar

Performs the ^ operation.

impl Clone for Scalar

fn clone(&self) -> Scalar

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for Scalar

fn conditional_select(a: &Scalar, b: &Scalar, choice: Choice) -> Scalar

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 Scalar

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

Determine if two items are equal.

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

Determine if two items are NOT equal.

impl Debug for Scalar

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

Formats the value using the given formatter.

impl Default for Scalar

fn default() -> Scalar

Returns the “default value” for a type.

impl<__D> Deserialize<Scalar, __D> for <Scalar as Archive>::Archived

where __D: Fallible + ?Sized, [u64; 4]: Archive, <[u64; 4] as Archive>::Archived: Deserialize<[u64; 4], __D>,

fn deserialize( &self, deserializer: &mut __D, ) -> Result<Scalar, <__D as Fallible>::Error>

Deserializes using the given deserializer

impl Display for Scalar

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

Formats the value using the given formatter.

impl Field for Scalar

const ZERO: Scalar

The zero element of the field, the additive identity.

const ONE: Scalar

The one element of the field, the multiplicative identity.

fn random(rng: impl RngCore) -> Scalar

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

fn square(&self) -> Scalar

Squares this element.

fn double(&self) -> Scalar

Doubles this element.

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

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

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

Computes:

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

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

fn is_zero_vartime(&self) -> bool

Returns true iff this element is zero.

fn is_zero(&self) -> Choice

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 Scalar> for [u8; 32]

fn from(value: &'a Scalar) -> [u8; 32]

Converts to this type from the input type.

impl From<&Scalar> for SecretKey

fn from(s: &Scalar) -> SecretKey

Converts to this type from the input type.

impl From<Scalar> for [u8; 32]

fn from(value: Scalar) -> [u8; 32]

Converts to this type from the input type.

impl From<Scalar> for SecretKey

fn from(s: Scalar) -> SecretKey

Converts to this type from the input type.

impl From<Fr> for Scalar

fn from(scalar: Fr) -> Scalar

Converts to this type from the input type.

impl From<u64> for Scalar

fn from(val: u64) -> Scalar

Converts to this type from the input type.

impl Hash for Scalar

fn hash<H>(&self, state: &mut H)

where H: Hasher,

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<'a, 'b> Mul<&'b Scalar> for &'a Scalar

type Output = Scalar

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Scalar

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: &'b G1Affine) -> <&'a Scalar as Mul<&'b G1Affine>>::Output

Performs the * operation.

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

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: &'b G1Affine) -> G1Projective

Performs the * operation.

impl<'a, 'b> Mul<&'b G1Projective> for &'a Scalar

type Output = G1Projective

The resulting type after applying the * operator.

fn mul( self, rhs: &'b G1Projective, ) -> <&'a Scalar as Mul<&'b G1Projective>>::Output

Performs the * operation.

impl<'b> Mul<&'b G1Projective> for Scalar

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: &'b G1Projective) -> G1Projective

Performs the * operation.

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

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: &'b G2Affine) -> <&'a Scalar as Mul<&'b G2Affine>>::Output

Performs the * operation.

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

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: &'b G2Affine) -> G2Projective

Performs the * operation.

impl<'a, 'b> Mul<&'b G2Projective> for &'a Scalar

type Output = G2Projective

The resulting type after applying the * operator.

fn mul( self, rhs: &'b G2Projective, ) -> <&'a Scalar as Mul<&'b G2Projective>>::Output

Performs the * operation.

impl<'b> Mul<&'b G2Projective> for Scalar

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: &'b G2Projective) -> G2Projective

Performs the * operation.

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

type Output = Scalar

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: G1Affine) -> G1Projective

Performs the * operation.

impl Mul<G1Affine> for Scalar

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: G1Affine) -> G1Projective

Performs the * operation.

impl<'a> Mul<G1Projective> for &'a Scalar

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: G1Projective) -> G1Projective

Performs the * operation.

impl Mul<G1Projective> for Scalar

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: G1Projective) -> G1Projective

Performs the * operation.

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

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: G2Affine) -> G2Projective

Performs the * operation.

impl Mul<G2Affine> for Scalar

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: G2Affine) -> G2Projective

Performs the * operation.

impl<'a> Mul<G2Projective> for &'a Scalar

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: G2Projective) -> G2Projective

Performs the * operation.

impl Mul<G2Projective> for Scalar

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: G2Projective) -> G2Projective

Performs the * operation.

impl Mul for Scalar

type Output = Scalar

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Performs the *= operation.

impl MulAssign for Scalar

fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation.

impl<'a> Neg for &'a Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Scalar

Performs the unary - operation.

impl Neg for Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Scalar

Performs the unary - operation.

impl Ord for Scalar

fn cmp(&self, other: &Scalar) -> 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 Scalar

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

fn partial_cmp(&self, other: &Scalar) -> 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 Scalar

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

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

const NUM_BITS: u32 = MODULUS_BITS

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: Scalar = TWO_INV

Inverse of $2$ in the field.

const MULTIPLICATIVE_GENERATOR: Scalar = GENERATOR

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

const S: u32 = TWO_ADACITY

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

const ROOT_OF_UNITY: Scalar = ROOT_OF_UNITY

The 2^s root of unity.

const ROOT_OF_UNITY_INV: Scalar = ROOT_OF_UNITY_INV

Inverse of Self::ROOT_OF_UNITY.

const DELTA: Scalar = DELTA

Generator of the t-order multiplicative subgroup.

type Repr = [u8; 32]

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

fn from_repr(r: <Scalar as PrimeField>::Repr) -> CtOption<Scalar>

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) -> <Scalar as PrimeField>::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 Scalar

where T: Borrow<Scalar>,

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

where I: Iterator<Item = T>,

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

impl Serializable<32> for Scalar

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

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

fn from_bytes( buf: &[u8; 32], ) -> Result<Scalar, <Scalar as Serializable<32>>::Error>

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

type Error = Error

The type returned in the event of a conversion error.

const SIZE: usize = N

The size of

impl<__S> Serialize<__S> for Scalar

where __S: Fallible + ?Sized, [u64; 4]: Serialize<__S>,

fn serialize( &self, serializer: &mut __S, ) -> Result<<Scalar as Archive>::Resolver, <__S as Fallible>::Error>

Writes the dependencies for the object and returns a resolver that can create the archived type.

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

type Output = Scalar

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Scalar

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Scalar

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub for Scalar

type Output = Scalar

The resulting type after applying the - operator.

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

Performs the - operation.

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

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

Performs the -= operation.

impl SubAssign for Scalar

fn sub_assign(&mut self, rhs: Scalar)

Performs the -= operation.

impl<T> Sum<T> for Scalar

where T: Borrow<Scalar>,

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

where I: Iterator<Item = T>,

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

impl Copy for Scalar

impl DefaultIsZeroes for Scalar

Available on crate feature zeroize only.

impl Eq for Scalar