Type Alias Base

pub type Base = Fq;

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

Aliased Type

struct Base(/* private fields */);

Implementations

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 sqrt(&self) -> CtOption<Scalar>

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

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) -> CtOption<Scalar>

Computes the multiplicative inverse of this element, 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<'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 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 Clone for Scalar

fn clone(&self) -> Scalar

Returns a copy 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 Display for Scalar

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

Formats the value using the given formatter.

impl Field for Scalar

fn random(rng: impl RngCore) -> Scalar

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

fn zero() -> Scalar

Returns the zero element of the field, the additive identity.

fn one() -> Scalar

Returns the one element of the field, the multiplicative identity.

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(&self) -> CtOption<Scalar>

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 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> for Scalar

fn from(val: u64) -> Scalar

Converts to this type from the input type.

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<'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<'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<'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<'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 Mul<G1Affine> for Scalar

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: G1Affine) -> 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 Mul<G2Affine> for Scalar

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: G2Affine) -> 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 Neg for Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Scalar

Performs the unary - operation.

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 PrimeField for Scalar

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 S: u32 = 32u32

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

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 multiplicative_generator() -> Scalar

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

fn root_of_unity() -> Scalar

Returns the 2^s root of unity.

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 Scalar

type ReprBits = [u64; 4]

The backing store for a bit representation of a prime field element.

fn to_le_bits(&self) -> BitArray<<Scalar as PrimeFieldBits>::ReprBits>

Converts an element of the prime field into a little-endian sequence of bits.

fn char_le_bits() -> BitArray<<Scalar as PrimeFieldBits>::ReprBits>

Returns the bits of the field characteristic (the modulus) in little-endian order.

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 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 Eq for Scalar