Struct Bn254

pub struct Bn254 { /* private fields */ }

The BN254 curve scalar field prime, defined as F_P where P = 21888242871839275222246405745257275088548364400416034343698204186575808495617.

Implementations

impl Bn254

pub fn from_biguint(value: BigUint) -> Option<Self>

Trait Implementations

impl Add for Bn254

type Output = Bn254

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self

Performs the + operation.

impl<T: Into<Self>> AddAssign<T> for Bn254

fn add_assign(&mut self, rhs: T)

Performs the += operation.

impl Clone for Bn254

fn clone(&self) -> Bn254

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Bn254

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

Formats the value using the given formatter.

impl Default for Bn254

fn default() -> Bn254

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Bn254

fn deserialize<D: Deserializer<'de>>(d: D) -> Result<Self, D::Error>

Deserializes from raw bytes, which correspond to the Montgomery representation of the field element. Performs a check that the deserialized field element corresponds to a value less than the field modulus, and returns an error otherwise.

impl Display for Bn254

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

Formats the value using the given formatter.

impl Distribution<Bn254> for StandardUniform

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Bn254

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> Iter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> Map<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Map sampled values to type S

impl Div for Bn254

type Output = Bn254

The resulting type after applying the / operator.

fn div(self, rhs: Bn254) -> Self

Performs the / operation.

impl DivAssign for Bn254

fn div_assign(&mut self, rhs: Bn254)

Performs the /= operation.

impl<const WIDTH: usize> ExternalLayer<Bn254, WIDTH, BN254_S_BOX_DEGREE> for ExternalLayerConstants<Bn254, WIDTH>

fn permute_state_initial(&self, state: &mut [Bn254; WIDTH])

Perform the initial external layers of the Poseidon2 permutation on the given state.

fn permute_state_terminal(&self, state: &mut [Bn254; WIDTH])

Perform the terminal external layers of the Poseidon2 permutation on the given state.

impl<const WIDTH: usize> ExternalLayerConstructor<Bn254, WIDTH> for ExternalLayerConstants<Bn254, WIDTH>

fn new_from_constants(external_constants: Self) -> Self

A constructor which internally will convert the supplied constants into the appropriate form for the implementation.

impl Field for Bn254

const GENERATOR: Self

The Montgomery form of the BN254 field element 5 which generates the multiplicative group.

Can check this in SageMath by running:

    BN254_prime = 21888242871839275222246405745257275088548364400416034343698204186575808495617
    BN254_field = GF(BN254_prime)
    BN254_field(5).multiplicative_order()

Equal to 9866131518759821339448375666750386964092448917385927261134611188594627313638

fn order() -> BigUint

r = 21888242871839275222246405745257275088548364400416034343698204186575808495617

type Packing = Bn254

fn is_zero(&self) -> bool

Check if the given field element is equal to the unique additive identity (ZERO).

fn try_inverse(&self) -> Option<Self>

The multiplicative inverse of this field element, if it exists.

fn is_one(&self) -> bool

Check if the given field element is equal to the unique multiplicative identity (ONE).

fn inverse(&self) -> Self

The multiplicative inverse of this field element.

fn add_slices(slice_1: &mut [Self], slice_2: &[Self])

Add two slices of field elements together, returning the result in the first slice.

fn bits() -> usize

The number of bits required to define an element of this field.

impl Hash for Bn254

fn hash<H: Hasher>(&self, state: &mut H)

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 InjectiveMonomial<5> for Bn254

Degree of the smallest permutation polynomial for BN254.

As p - 1 is divisible by 2 and 3 the smallest choice for a degree D satisfying gcd(p - 1, D) = 1 is 5.

fn injective_exp_n(&self) -> Self

Compute x -> x^n for a given n > 1 such that this map is injective.

impl Mul for Bn254

type Output = Bn254

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self

Performs the * operation.

impl<T: Into<Self>> MulAssign<T> for Bn254

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl Neg for Bn254

type Output = Bn254

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Ord for Bn254

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,

Restrict a value to a certain interval.

impl PartialEq for Bn254

fn eq(&self, other: &Bn254) -> 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 Bn254

fn partial_cmp(&self, other: &Self) -> 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 PrimeCharacteristicRing for Bn254

const ONE: Self

The Montgomery form of the BN254 field element 1.

Equal to 2^256 mod P = 6350874878119819312338956282401532410528162663560392320966563075034087161851

const TWO: Self

The Montgomery form of the BN254 field element 2.

Equal to 2^257 mod P = 12701749756239638624677912564803064821056325327120784641933126150068174323702

const NEG_ONE: Self

The Montgomery form of the BN254 field element -1.

Equal to -2^256 mod P = 15537367993719455909907449462855742678020201736855642022731641111541721333766

const ZERO: Self

The additive identity of the ring.

type PrimeSubfield = Bn254

The field ℤ/p where the characteristic of this ring is p.

fn from_prime_subfield(f: Self::PrimeSubfield) -> Self

Embed an element of the prime field ℤ/p into the ring R.

fn halve(&self) -> Self

The elementary function halve(a) = a/2.

fn from_bool(b: bool) -> Self

Return Self::ONE if b is true and Self::ZERO if b is false.

fn from_u8(int: u8) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u16(int: u16) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u32(int: u32) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u64(int: u64) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u128(int: u128) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_usize(int: usize) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i8(int: i8) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i16(int: i16) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i32(int: i32) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i64(int: i64) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i128(int: i128) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_isize(int: isize) -> Self

Given an integer r, return the sum of r copies of ONE:

fn double(&self) -> Self

The elementary function double(a) = 2*a.

fn square(&self) -> Self

The elementary function square(a) = a^2.

fn cube(&self) -> Self

The elementary function cube(a) = a^3.

fn xor(&self, y: &Self) -> Self

Computes the arithmetic generalization of boolean xor.

fn xor3(&self, y: &Self, z: &Self) -> Self

Computes the arithmetic generalization of a triple xor.

fn andn(&self, y: &Self) -> Self

Computes the arithmetic generalization of andnot.

fn bool_check(&self) -> Self

The vanishing polynomial for boolean values: x * (x - 1).

fn exp_u64(&self, power: u64) -> Self

Exponentiation by a u64 power.

fn exp_const_u64<const POWER: u64>(&self) -> Self

Exponentiation by a small constant power.

fn exp_power_of_2(&self, power_log: usize) -> Self

The elementary function exp_power_of_2(a, power_log) = a^{2^power_log}.

fn mul_2exp_u64(&self, exp: u64) -> Self

The elementary function mul_2exp_u64(a, exp) = a * 2^{exp}.

fn div_2exp_u64(&self, exp: u64) -> Self

Divide by a given power of two. div_2exp_u64(a, exp) = a/2^exp

fn powers(&self) -> Powers<Self>

Construct an iterator which returns powers of self: self^0, self^1, self^2, ....

fn shifted_powers(&self, start: Self) -> Powers<Self>

Construct an iterator which returns powers of self shifted by start: start, start*self^1, start*self^2, ....

fn dot_product<const N: usize>(u: &[Self; N], v: &[Self; N]) -> Self

Compute the dot product of two vectors.

fn sum_array<const N: usize>(input: &[Self]) -> Self

Compute the sum of a slice of elements whose length is a compile time constant.

fn zero_vec(len: usize) -> Vec<Self>

Allocates a vector of zero elements of length len. Many operating systems zero pages before assigning them to a userspace process. In that case, our process should not need to write zeros, which would be redundant. However, the compiler may not always recognize this.

impl PrimeField for Bn254

fn as_canonical_biguint(&self) -> BigUint

Return the representative of value in canonical form which lies in the range 0 <= x < self.order().

impl Product for Bn254

fn product<I: Iterator<Item = Self>>(iter: I) -> Self

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

impl QuotientMap<i128> for Bn254

fn from_int(int: i128) -> Self

Due to the size of the BN254 prime, the input value is always canonical.

fn from_canonical_checked(int: i128) -> Option<Self>

Due to the size of the BN254 prime, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: i128) -> Self

Due to the size of the BN254 prime, the input value is always canonical.

impl QuotientMap<i16> for Bn254

fn from_int(int: i16) -> Self

Convert a given i16 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

fn from_canonical_checked(int: i16) -> Option<Self>

Convert a given i16 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: i16) -> Self

Convert a given i16 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

impl QuotientMap<i32> for Bn254

fn from_int(int: i32) -> Self

Convert a given i32 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

fn from_canonical_checked(int: i32) -> Option<Self>

Convert a given i32 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: i32) -> Self

Convert a given i32 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

impl QuotientMap<i64> for Bn254

fn from_int(int: i64) -> Self

Convert a given i64 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

fn from_canonical_checked(int: i64) -> Option<Self>

Convert a given i64 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: i64) -> Self

Convert a given i64 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

impl QuotientMap<i8> for Bn254

fn from_int(int: i8) -> Self

Convert a given i8 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

fn from_canonical_checked(int: i8) -> Option<Self>

Convert a given i8 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: i8) -> Self

Convert a given i8 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

impl QuotientMap<u128> for Bn254

fn from_int(int: u128) -> Self

Due to the size of the BN254 prime, the input value is always canonical.

fn from_canonical_checked(int: u128) -> Option<Self>

Due to the size of the BN254 prime, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: u128) -> Self

Due to the size of the BN254 prime, the input value is always canonical.

impl QuotientMap<u16> for Bn254

fn from_int(int: u16) -> Self

Convert a given u16 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

fn from_canonical_checked(int: u16) -> Option<Self>

Convert a given u16 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: u16) -> Self

Convert a given u16 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

impl QuotientMap<u32> for Bn254

fn from_int(int: u32) -> Self

Convert a given u32 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

fn from_canonical_checked(int: u32) -> Option<Self>

Convert a given u32 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: u32) -> Self

Convert a given u32 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

impl QuotientMap<u64> for Bn254

fn from_int(int: u64) -> Self

Convert a given u64 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

fn from_canonical_checked(int: u64) -> Option<Self>

Convert a given u64 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: u64) -> Self

Convert a given u64 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

impl QuotientMap<u8> for Bn254

fn from_int(int: u8) -> Self

Convert a given u8 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

fn from_canonical_checked(int: u8) -> Option<Self>

Convert a given u8 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: u8) -> Self

Convert a given u8 integer into an element of the Bn254 field.

Due to the integer type, the input value is always canonical.

impl RawDataSerializable for Bn254

const NUM_BYTES: usize = 32usize

The number of bytes which this field element occupies in memory. Must be equal to the length of self.into_bytes().

fn into_bytes(self) -> [u8; 32]

Convert a field element into a collection of bytes.

fn into_u32_stream( input: impl IntoIterator<Item = Self>, ) -> impl IntoIterator<Item = u32>

Convert an iterator of field elements into an iterator of u32s.

fn into_u64_stream( input: impl IntoIterator<Item = Self>, ) -> impl IntoIterator<Item = u64>

Convert an iterator of field elements into an iterator of u64s.

fn into_parallel_byte_streams<const N: usize>( input: impl IntoIterator<Item = [Self; N]>, ) -> impl IntoIterator<Item = [u8; N]>

Convert an iterator of field element arrays into an iterator of byte arrays.

fn into_parallel_u32_streams<const N: usize>( input: impl IntoIterator<Item = [Self; N]>, ) -> impl IntoIterator<Item = [u32; N]>

Convert an iterator of field element arrays into an iterator of u32 arrays.

fn into_parallel_u64_streams<const N: usize>( input: impl IntoIterator<Item = [Self; N]>, ) -> impl IntoIterator<Item = [u64; N]>

Convert an iterator of field element arrays into an iterator of u64 arrays.

fn into_byte_stream( input: impl IntoIterator<Item = Self>, ) -> impl IntoIterator<Item = u8>

Convert an iterator of field elements into an iterator of bytes.

impl Serialize for Bn254

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

Serializes to raw bytes, which correspond to the Montgomery representation of the field element.

impl Sub for Bn254

type Output = Bn254

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self

Performs the - operation.

impl<T: Into<Self>> SubAssign<T> for Bn254

fn sub_assign(&mut self, rhs: T)

Performs the -= operation.

impl Sum for Bn254

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

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

impl TwoAdicField for Bn254

const TWO_ADICITY: usize = 28usize

The number of factors of two in this field’s multiplicative group.

fn two_adic_generator(bits: usize) -> Self

Returns a generator of the multiplicative group of order 2^bits. Assumes bits <= TWO_ADICITY, otherwise the result is undefined.

impl Copy for Bn254

impl Eq for Bn254

impl Packable for Bn254

impl StructuralPartialEq for Bn254