Struct dusk_jubjub::Fr

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

Represents an element of the scalar field $\mathbb{F}_r$ of the Jubjub elliptic curve construction.

Implementations

impl Fr

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

Creates a Fr 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 = 0x0e7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7
p = 6554484396890773809930967563523245729705921265872317281365359162392183254199

l = 2

s^l = (2^256)^2 = 2^512
s = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096

r' = 2045593080716281616348203381729468609728209645786990242449482205581148743408809

m' = 2244478849891746936202736009816130624903096691796347063256129649283183245105

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

SHR impl: shifts bits n times, equivalent to division by 2^n.

pub fn reduce(&self) -> Self

Reduces bit representation of numbers, such that they can be evaluated in terms of the least significant bit.

pub fn is_even(&self) -> bool

Evaluate if a Scalar, from Fr is even or not.

pub fn mod_2_pow_k(&self, k: u8) -> u8

Compute the result from Scalar (mod 2^k).

Panics

If the given k is > 32 (5 bits) as the value gets greater than the limb.

pub fn mods_2_pow_k(&self, w: u8) -> i8

Compute the result from Scalar (mods k).

Panics

If the given k > 32 (5 bits) || k == 0 as the value gets greater than the limb.

pub fn compute_windowed_naf(&self, width: u8) -> [i8; 256]

Computes the windowed-non-adjacent form for a given an element in the JubJub Scalar field.

The wnaf of a scalar is its breakdown: scalar = sum_i{wnaf[i]*2^i} where for all i: -2^{w-1} < wnaf[i] < 2^{w-1} and wnaf[i] * wnaf[i+1] = 0

impl Fr

pub const fn zero() -> Fr

Returns zero, the additive identity.

pub const fn one() -> Fr

Returns one, the multiplicative identity.

pub const fn double(&self) -> Fr

Doubles this field element.

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

Attempts to convert a little-endian byte representation of a field element into an element of Fr, failing if the input is not canonical (is not smaller than r).

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

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

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

Converts a 512-bit little endian integer into an element of Fr by reducing modulo r.

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

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

pub const fn square(&self) -> Fr

Squares this element.

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

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

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

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

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

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) -> CtOption<Self>

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

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

Multiplies this element by another element

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

Subtracts another element from this element.

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

Adds this element to another element.

pub const fn neg(&self) -> Self

Negates this element.

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() -> Self

Returns the “default value” for a type.

impl Display for Fr

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

Formats the value using the given formatter.

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 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<'a> From<&'a Fr> for [u8; 32]

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

Converts to this type from the input type.

impl From<Fr> for [u8; 32]

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

Converts to this type from the input type.

impl From<Fr> for BlsScalar

fn from(scalar: Fr) -> BlsScalar

Converts to this type from the input type.

impl From<i8> for Fr

fn from(val: i8) -> 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 Index<usize> for Fr

type Output = u64

The returned type after indexing.

fn index(&self, _index: usize) -> &u64

Performs the indexing (container[index]) operation.

impl IndexMut<usize> for Fr

fn index_mut(&mut self, _index: usize) -> &mut u64

Performs the mutable indexing (container[index]) operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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 SubgroupPoint

type Output = SubgroupPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

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 SubgroupPoint

type Output = SubgroupPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

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 SubgroupPoint

type Output = SubgroupPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Fr> for AffineNielsPoint

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Fr> for AffinePoint

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Fr> for ExtendedNielsPoint

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Fr> for ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Fr> for SubgroupPoint

type Output = SubgroupPoint

The resulting type after applying the * operator.

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

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 ExtendedPoint

fn mul_assign(&mut self, rhs: &'b 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 SubgroupPoint

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

Performs the *= operation.

impl MulAssign<Fr> for ExtendedPoint

fn mul_assign(&mut self, rhs: Fr)

Performs the *= operation.

impl MulAssign<Fr> for SubgroupPoint

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 + PartialOrd,

Restrict a value to a certain interval.

impl PartialEq for Fr

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

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

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

This method 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: &Fr) -> Option<Ordering>

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

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

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

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

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

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

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

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 Fr

type Repr = [u8; 32]

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.

const MODULUS: &'static str = "0x0e7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7"

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

const NUM_BITS: u32 = 252u32

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

const CAPACITY: u32 = 251u32

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.

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 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> Product<T> for Fr

where T: Borrow<Fr>,

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

where I: Iterator<Item = T>,

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl Serializable<32> for Fr

fn from_bytes(bytes: &[u8; 32]) -> Result<Self, Self::Error>

Attempts to convert a little-endian byte representation of a field element into an element of Fr, failing if the input is not canonical (is not smaller than r).

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

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

type Error = Error

The type returned in the event of a conversion error.

const SIZE: usize = N

The size of

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> Sum<T> for Fr

where T: Borrow<Fr>,

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

where I: Iterator<Item = T>,

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl Copy for Fr

impl Eq for Fr