Struct Fr 

pub struct Fr(pub(crate) [u64; 4]);

This represents an element of $\mathbb{F}_r$ where

r = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001

is the scalar field of the BN254 curve.

Tuple Fields

0: [u64; 4]

Implementations

impl Fr

pub const fn zero() -> Fr

Returns zero, the additive identity.

pub const fn one() -> Fr

Returns one, the multiplicative identity.

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

Returns the multiplicative inverse of the element. If it is zero, the method fails.

pub fn jacobi(&self) -> i64

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

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

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

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

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

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

impl Fr

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

Adds rhs to self, returning the result.

impl Fr

pub const fn double(&self) -> Fr

Doubles this field element.

pub const fn square(&self) -> Fr

Squares this element.

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

Multiplies rhs by self, returning the result.

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

Subtracts rhs from self, returning the result.

pub const fn neg(&self) -> Fr

Negates self.

impl Fr

pub const fn size() -> usize

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 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<'de> Deserialize<'de> for Fr

fn deserialize<D>( deserializer: D, ) -> Result<Fr, <D as Deserializer<'de>>::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

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<[u64; 4]> for Fr

fn from(digits: [u64; 4]) -> Fr

Converts to this type from the input type.

impl From<Fr> for [u64; 4]

fn from(elt: Fr) -> [u64; 4]

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<bool> for Fr

fn from(bit: bool) -> 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 FromUniformBytes<64> for Fr

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

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

impl HasByteRepresentation for Fr

TODO(ryancao): Test these implementations!

const REPR_NUM_BYTES: usize = 32

Number of bytes within the element’s representation.

fn from_bytes_le(bytes: &[u8]) -> Fr

Constructor which creates an instance of the element from a vec of less than or equal to length REPR_NUM_BYTES. If length less than REPR_NUM_BYTES, pads the most significant bits with 0s until it is of equal length to REPR_NUM_BYTES.

fn to_bytes_le(&self) -> Vec<u8>

Function which creates an equivalent representation of the element in a byte array of length REPR_NUM_BYTES.

fn to_u64s_le(&self) -> Vec<u64>

Similar to to_bytes_le but returns chunks of u64s.

fn from_u64s_le(words: Vec<u64>) -> Fr

where Fr: Sized,

Similar to from_bytes_le but takes chunks of u64s.

fn vec_from_bytes_le(bytes: &[u8]) -> Vec<Fr>

where Fr: Sized,

Creates a Vec of elements from an arbitrary string of bytes.

impl Hash for Fr

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 Legendre for Fr

fn legendre(&self) -> i64

fn ct_quadratic_non_residue(&self) -> Choice

fn ct_quadratic_residue(&self) -> Choice

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<'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<'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 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 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: &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 NUM_BITS: u32 = 254

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

const CAPACITY: u32 = 253

How many bits of information can be reliably stored in the field element.

const MODULUS: &'static str = MODULUS_STR

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

const MULTIPLICATIVE_GENERATOR: Fr = GENERATOR

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

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 TWO_INV: Fr = TWO_INV

Inverse of $2$ in the field.

const DELTA: Fr = DELTA

Generator of the t-order multiplicative subgroup.

const S: u32 = S

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(repr: <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

Available on crate feature bits only.

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<T> Product<T> for Fr

where T: Borrow<Fr>,

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

where I: Iterator<Item = T>,

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

impl SerdeObject for Fr

fn from_raw_bytes_unchecked(bytes: &[u8]) -> Fr

The purpose of unchecked functions is to read the internal memory representation of a type from bytes as quickly as possible. No sanitization checks are performed to ensure the bytes represent a valid object. As such this function should only be used internally as an extension of machine memory. It should not be used to deserialize externally provided data.

fn from_raw_bytes(bytes: &[u8]) -> Option<Fr>

fn to_raw_bytes(&self) -> Vec<u8>

fn read_raw_unchecked<R>(reader: &mut R) -> Fr

where R: Read,

The purpose of unchecked functions is to read the internal memory representation of a type from disk as quickly as possible. No sanitization checks are performed to ensure the bytes represent a valid object. This function should only be used internally when some machine state cannot be kept in memory (e.g., between runs) and needs to be reloaded as quickly as possible.

fn read_raw<R>(reader: &mut R) -> Result<Fr, Error>

where R: Read,

fn write_raw<W>(&self, writer: &mut W) -> Result<(), Error>

where W: Write,

impl Serialize for Fr

fn serialize<S>( &self, serializer: S, ) -> Result<<S as Serializer>::Ok, <S as Serializer>::Error>

where S: Serializer,

Serialize this value into the given Serde serializer.

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) -> Fr

where I: Iterator<Item = T>,

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

impl WithSmallOrderMulGroup<3> for Fr

const ZETA: Fr = ZETA

A field element of small multiplicative order $N$.

impl Zeroizable for Fr

fn zeroize(&mut self)

impl Field for Fr

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

Returns the multiplicative inverse of the element. If it is zero, the method fails.

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 double(&self) -> Fr

Doubles this element.

fn square(&self) -> Fr

Squares this element.

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

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

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

Computes:

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 Copy for Fr

impl Eq for Fr

impl StructuralPartialEq for Fr