Struct JubjubScalar 

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

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

Implementations

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]) -> Fr

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<Fr>

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

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

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

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

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<Fr>

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

pub const fn mul_ref(&self, rhs: &Fr) -> Fr

Multiplies this element by another element

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

pub const fn sub_ref(&self, rhs: &Fr) -> Fr

Subtracts another element from this element.

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

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

Adds this element to another element.

pub const fn neg(&self) -> Fr

Negates this element.

Trait Implementations

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<'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 duplicate of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for Fr

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

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: &Fr) -> 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<(), Error>

Formats the value using the given formatter.

impl Default for Fr

fn default() -> Fr

Returns the “default value” for a type.

impl Display for Fr

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

Formats the value using the given formatter.

impl Field for Fr

const ZERO: Fr

The zero element of the field, the additive identity.

const ONE: Fr

The one element of the field, the multiplicative identity.

fn random(rng: impl RngCore) -> Fr

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

fn square(&self) -> Fr

Squares this element.

fn double(&self) -> Fr

Doubles this element.

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

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

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

Computes:

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

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> for Fr

fn from(val: u64) -> Fr

Converts to this type from the input type.

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 &JubjubAffine

type Output = JubjubExtended

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = JubjubExtended

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = JubjubSubgroup

The resulting type after applying the * operator.

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

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 JubjubAffine

type Output = JubjubExtended

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = JubjubExtended

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = JubjubSubgroup

The resulting type after applying the * operator.

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

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 JubjubAffine

type Output = JubjubExtended

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = JubjubExtended

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = JubjubSubgroup

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Fr> for JubjubAffine

type Output = JubjubExtended

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Fr> for JubjubExtended

type Output = JubjubExtended

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Fr> for JubjubSubgroup

type Output = JubjubSubgroup

The resulting type after applying the * operator.

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

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 Fr

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

Performs the *= operation.

impl<'b> MulAssign<&'b Fr> for JubjubExtended

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

Performs the *= operation.

impl<'b> MulAssign<&'b Fr> for JubjubSubgroup

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

Performs the *= operation.

impl MulAssign<Fr> for JubjubExtended

fn mul_assign(&mut self, rhs: Fr)

Performs the *= operation.

impl MulAssign<Fr> for JubjubSubgroup

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 Neg for &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: &Fr) -> 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 Fr

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

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 Fr

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

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: Fr = TWO_INV

Inverse of $2$ in the field.

const MULTIPLICATIVE_GENERATOR: Fr = GENERATOR

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

const S: u32 = S

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

const ROOT_OF_UNITY: Fr = ROOT_OF_UNITY

The 2^s root of unity.

const ROOT_OF_UNITY_INV: Fr = ROOT_OF_UNITY_INV

Inverse of [Self::ROOT_OF_UNITY].

const DELTA: Fr = 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: <Fr as PrimeField>::Repr) -> CtOption<Fr>

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) -> <Fr 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 PrimeFieldBits for Fr

type ReprBits = [u64; 4]

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

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

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

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

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

impl<'a> Product<&'a Fr> for Fr

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

where I: Iterator<Item = &'a Fr>,

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

impl Product for Fr

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

where I: Iterator<Item = Fr>,

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

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<'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<'a> Sum<&'a Fr> for Fr

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

where I: Iterator<Item = &'a Fr>,

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

impl Sum for Fr

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

where I: Iterator<Item = Fr>,

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

impl Copy for Fr

impl Eq for Fr