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 = 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: 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 = 32u32

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

impl Eq for Scalar