Struct Fp256

pub struct Fp256<P: Fp256Parameters>(pub BigInteger256, _);

Tuple Fields

0: BigInteger256

Trait Implementations

impl<P: Fp256Parameters> Add<&&Fp256<P>> for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the + operator.

fn add(self, other: &&Self) -> Self

Performs the + operation.

impl<'a, P: Fp256Parameters> Add<&'a Fp256<P>> for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the + operator.

fn add(self, other: &Self) -> Self

Performs the + operation.

impl<'a, P: Fp256Parameters> Add<&'a mut Fp256<P>> for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the + operator.

fn add(self, other: &'a mut Self) -> Self

Performs the + operation.

impl<P: Fp256Parameters> Add for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<P: Fp256Parameters> AddAssign<&&Fp256<P>> for Fp256<P>

fn add_assign(&mut self, other: &&Self)

Performs the += operation.

impl<'a, P: Fp256Parameters> AddAssign<&'a Fp256<P>> for Fp256<P>

fn add_assign(&mut self, other: &Self)

Performs the += operation.

impl<'a, P: Fp256Parameters> AddAssign<&'a mut Fp256<P>> for Fp256<P>

fn add_assign(&mut self, other: &'a mut Self)

Performs the += operation.

impl<P: Fp256Parameters> AddAssign for Fp256<P>

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<P: Fp256Parameters> CanonicalDeserialize for Fp256<P>

fn deserialize_with_mode<R: Read>( reader: R, _compress: Compress, _validate: Validate, ) -> Result<Self, SerializationError>

fn deserialize_compressed<R>(reader: R) -> Result<Self, SerializationError>

where R: Read,

fn deserialize_compressed_unchecked<R>( reader: R, ) -> Result<Self, SerializationError>

where R: Read,

fn deserialize_uncompressed<R>(reader: R) -> Result<Self, SerializationError>

where R: Read,

fn deserialize_uncompressed_unchecked<R>( reader: R, ) -> Result<Self, SerializationError>

where R: Read,

impl<P: Fp256Parameters> CanonicalDeserializeWithFlags for Fp256<P>

fn deserialize_with_flags<R: Read, F: Flags>( reader: R, ) -> Result<(Self, F), SerializationError>

Reads Self and Flags from reader. Returns empty flags by default.

impl<P: Fp256Parameters> CanonicalSerialize for Fp256<P>

fn serialize_with_mode<W: Write>( &self, writer: W, _compress: Compress, ) -> Result<(), SerializationError>

fn serialized_size(&self, _compress: Compress) -> usize

fn serialize_compressed<W>(&self, writer: W) -> Result<(), SerializationError>

where W: Write,

fn compressed_size(&self) -> usize

fn serialize_uncompressed<W>(&self, writer: W) -> Result<(), SerializationError>

where W: Write,

fn uncompressed_size(&self) -> usize

impl<P: Fp256Parameters> CanonicalSerializeWithFlags for Fp256<P>

fn serialize_with_flags<W: Write, F: Flags>( &self, writer: W, flags: F, ) -> Result<(), SerializationError>

Serializes self and flags into writer.

fn serialized_size_with_flags<F: Flags>(&self) -> usize

Serializes self and flags into writer.

impl<P: Clone + Fp256Parameters> Clone for Fp256<P>

fn clone(&self) -> Fp256<P>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<P: Fp256Parameters> Debug for Fp256<P>

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

Formats the value using the given formatter.

impl<P: Default + Fp256Parameters> Default for Fp256<P>

fn default() -> Fp256<P>

Returns the “default value” for a type.

impl<'de, P: Fp256Parameters> Deserialize<'de> for Fp256<P>

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

Deserialize this value from the given Serde deserializer.

impl<P: Fp256Parameters> Display for Fp256<P>

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

Formats the value using the given formatter.

impl<P: Fp256Parameters> Distribution<Fp256<P>> for Standard

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Fp256<P>

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

fn sample_iter<R>(self, rng: R) -> DistIter<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) -> DistMap<Self, F, T, S>

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

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<P: Fp256Parameters> Div<&&Fp256<P>> for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the / operator.

fn div(self, other: &&Self) -> Self

Performs the / operation.

impl<'a, P: Fp256Parameters> Div<&'a Fp256<P>> for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the / operator.

fn div(self, other: &Self) -> Self

Performs the / operation.

impl<'a, P: Fp256Parameters> Div<&'a mut Fp256<P>> for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the / operator.

fn div(self, other: &'a mut Self) -> Self

Performs the / operation.

impl<P: Fp256Parameters> Div for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the / operator.

fn div(self, other: Self) -> Self

Performs the / operation.

impl<P: Fp256Parameters> DivAssign<&&Fp256<P>> for Fp256<P>

fn div_assign(&mut self, other: &&Self)

Performs the /= operation.

impl<'a, P: Fp256Parameters> DivAssign<&'a Fp256<P>> for Fp256<P>

fn div_assign(&mut self, other: &Self)

Performs the /= operation.

impl<'a, P: Fp256Parameters> DivAssign<&'a mut Fp256<P>> for Fp256<P>

fn div_assign(&mut self, other: &'a mut Self)

Performs the /= operation.

impl<P: Fp256Parameters> DivAssign for Fp256<P>

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<P: Fp256Parameters> FftField for Fp256<P>

type FftParameters = P

fn two_adic_root_of_unity() -> Self

Returns the 2^s root of unity.

fn large_subgroup_root_of_unity() -> Option<Self>

Returns the 2^s * small_subgroup_base^small_subgroup_base_adicity root of unity if a small subgroup is defined.

fn multiplicative_generator() -> Self

Returns the multiplicative generator of char() - 1 order.

fn get_root_of_unity(n: usize) -> Option<Self>

Returns the root of unity of order n, if one exists. If no small multiplicative subgroup is defined, this is the 2-adic root of unity of order n (for n a power of 2). If a small multiplicative subgroup is defined, this is the root of unity of order n for the larger subgroup generated by FftParams::LARGE_SUBGROUP_ROOT_OF_UNITY (for n = 2^i * FftParams::SMALL_SUBGROUP_BASE^j for some i, j).

fn k_adicity(k: usize, n: usize) -> u32

Calculates the k-adicity of n, i.e., the number of trailing 0s in a base-k representation.

impl<P: Fp256Parameters> Field for Fp256<P>

fn half() -> Self

Returns the constant 2^{-1}.

type BasePrimeField = Fp256<P>

fn from_random_bytes_with_flags<F: Flags>(bytes: &[u8]) -> Option<(Self, F)>

Returns a field element with an extra sign bit used for group parsing if the set of bytes forms a valid field element, otherwise returns None. This function is primarily intended for sampling random field elements from a hash-function or RNG output.

fn from_base_prime_field(other: Self::BasePrimeField) -> Self

Constructs an element of Self from an element of the base prime field.

fn sum_of_products<'a>( a: impl Iterator<Item = &'a Self> + Clone, b: impl Iterator<Item = &'a Self> + Clone, ) -> Self

fn double(&self) -> Self

Returns self + self.

fn double_in_place(&mut self)

Doubles self in place.

fn characteristic<'a>() -> &'a [u64]

Returns the characteristic of the field.

fn square(&self) -> Self

Returns self * self.

fn square_in_place(&mut self) -> &mut Self

Squares self in place.

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

Computes the multiplicative inverse of self if self is nonzero.

fn inverse_in_place(&mut self) -> Option<&mut Self>

Sets self to self’s inverse if it exists. Otherwise it is a no-op.

fn frobenius_map(&mut self, _: usize)

Exponentiates this element by a power of the base prime modulus via the Frobenius automorphism.

fn pow<S: AsRef<[u64]>>(&self, exp: S) -> Self

Exponentiates this element by a number represented with u64 limbs, least significant limb first.

fn from_random_bytes(bytes: &[u8]) -> Option<Self>

Returns a field element if the set of bytes forms a valid field element, otherwise returns None. This function is primarily intended for sampling random field elements from a hash-function or RNG output.

impl<P: Fp256Parameters> From<u128> for Fp256<P>

fn from(other: u128) -> Self

Attempts to convert an integer into a field element. Panics if the provided integer is invalid (e.g. larger than the field modulus).

impl<P: Fp256Parameters> From<u16> for Fp256<P>

fn from(other: u16) -> Self

Attempts to convert an integer into a field element. Panics if the provided integer is invalid (e.g. larger than the field modulus).

impl<P: Fp256Parameters> From<u32> for Fp256<P>

fn from(other: u32) -> Self

Attempts to convert an integer into a field element. Panics if the provided integer is invalid (e.g. larger than the field modulus).

impl<P: Fp256Parameters> From<u64> for Fp256<P>

fn from(other: u64) -> Self

Attempts to convert an integer into a field element. Panics if the provided integer is invalid (e.g. larger than the field modulus).

impl<P: Fp256Parameters> From<u8> for Fp256<P>

fn from(other: u8) -> Self

Attempts to convert an integer into a field element. Panics if the provided integer is invalid (e.g. larger than the field modulus).

impl<P: Fp256Parameters> FromBytes for Fp256<P>

fn read_le<R: Read>(reader: R) -> IoResult<Self>

Reads Self from reader as little-endian bytes.

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

where Self: Sized,

Returns Self from a byte array in little-endian order.

impl<P: Fp256Parameters> FromStr for Fp256<P>

fn from_str(s: &str) -> Result<Self, Self::Err>

Interpret a string of numbers as a (congruent) prime field element. Does not accept unnecessary leading zeroes or a blank string.

type Err = FieldError

The associated error which can be returned from parsing.

impl<P: Hash + Fp256Parameters> Hash for Fp256<P>

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<P: Fp256Parameters> Into<BigInteger256> for Fp256<P>

fn into(self) -> BigInteger256

Converts this type into the (usually inferred) input type.

impl<P: Fp256Parameters> Mul<&&Fp256<P>> for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the * operator.

fn mul(self, other: &&Self) -> Self

Performs the * operation.

impl<'a, P: Fp256Parameters> Mul<&'a Fp256<P>> for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the * operator.

fn mul(self, other: &Self) -> Self

Performs the * operation.

impl<'a, P: Fp256Parameters> Mul<&'a mut Fp256<P>> for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the * operator.

fn mul(self, other: &'a mut Self) -> Self

Performs the * operation.

impl<P: Fp256Parameters> Mul for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<P: Fp256Parameters> MulAssign<&&Fp256<P>> for Fp256<P>

fn mul_assign(&mut self, other: &&Self)

Performs the *= operation.

impl<'a, P: Fp256Parameters> MulAssign<&'a Fp256<P>> for Fp256<P>

fn mul_assign(&mut self, other: &Self)

Performs the *= operation.

impl<'a, P: Fp256Parameters> MulAssign<&'a mut Fp256<P>> for Fp256<P>

fn mul_assign(&mut self, other: &'a mut Self)

Performs the *= operation.

impl<P: Fp256Parameters> MulAssign for Fp256<P>

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<P: Fp256Parameters> Neg for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<P: Fp256Parameters> One for Fp256<P>

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

impl<P: Fp256Parameters> Ord for Fp256<P>

Fp elements are ordered lexicographically.

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<P: PartialEq + Fp256Parameters> PartialEq for Fp256<P>

fn eq(&self, other: &Fp256<P>) -> 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<P: Fp256Parameters> PartialOrd for Fp256<P>

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<P: Fp256Parameters + PoseidonDefaultParameters> PoseidonDefaultField for Fp256<P>

fn default_poseidon_parameters<const RATE: usize>() -> Result<PoseidonParameters<Self, RATE, 1>>

where Self: PrimeField,

Obtain the default Poseidon parameters for this rate and for this prime field, with a specific optimization goal.

impl<P: Fp256Parameters> PrimeField for Fp256<P>

type BigInteger = BigInteger256

type Parameters = P

fn from_bigint(r: BigInteger) -> Option<Self>

Constructs a PrimeField element given a human-readable Self::BigInteger.

fn to_bigint(&self) -> BigInteger

Returns a human-readable Self::BigInteger in the range 0..(Self::MODULUS - 1).

fn decompose( &self, q1: &[u64; 4], q2: &[u64; 4], b1: Self, b2: Self, r128: Self, half_r: &[u64; 8], ) -> (Self, Self, bool, bool)

Returns the decomposition of the scalar.

const SIZE_IN_BITS: usize = _

Returns the field size in bits.

const SIZE_IN_DATA_BITS: usize = _

Returns the field capacity for data bits.

fn size_in_bits() -> usize

Returns the field size in bits.

fn size_in_data_bits() -> usize

Returns the capacity size for data bits.

fn modulus() -> Self::BigInteger

Returns the modulus.

fn modulus_minus_one_div_two() -> Self::BigInteger

Returns the modulus minus one divided by two.

fn trace() -> Self::BigInteger

Returns the trace.

fn trace_minus_one_div_two() -> Self::BigInteger

Returns the trace minus one divided by two.

fn from_bytes_be_mod_order(bytes: &[u8]) -> Self

Reads bytes in big-endian, and converts them to a field element. If the bytes are larger than the modulus, it will reduce them.

fn from_bytes_le_mod_order(bytes: &[u8]) -> Self

Reads bytes in little-endian, and converts them to a field element. If the bytes are larger than the modulus, it will reduce them.

impl<'a, P: Fp256Parameters> Product<&'a Fp256<P>> for Fp256<P>

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

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

impl<P: Fp256Parameters> Product for Fp256<P>

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

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

impl<P: Fp256Parameters> Serialize for Fp256<P>

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

Serialize this value into the given Serde serializer.

impl<P: Fp256Parameters> SquareRootField for Fp256<P>

fn legendre(&self) -> LegendreSymbol

Returns the Legendre symbol.

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

Returns the square root of self, if it exists.

fn sqrt_in_place(&mut self) -> Option<&mut Self>

Sets self to be the square root of self, if it exists.

impl<P: Fp256Parameters> Sub<&&Fp256<P>> for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the - operator.

fn sub(self, other: &&Self) -> Self

Performs the - operation.

impl<'a, P: Fp256Parameters> Sub<&'a Fp256<P>> for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the - operator.

fn sub(self, other: &Self) -> Self

Performs the - operation.

impl<'a, P: Fp256Parameters> Sub<&'a mut Fp256<P>> for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the - operator.

fn sub(self, other: &'a mut Self) -> Self

Performs the - operation.

impl<P: Fp256Parameters> Sub for Fp256<P>

type Output = Fp256<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<P: Fp256Parameters> SubAssign<&&Fp256<P>> for Fp256<P>

fn sub_assign(&mut self, other: &&Self)

Performs the -= operation.

impl<'a, P: Fp256Parameters> SubAssign<&'a Fp256<P>> for Fp256<P>

fn sub_assign(&mut self, other: &Self)

Performs the -= operation.

impl<'a, P: Fp256Parameters> SubAssign<&'a mut Fp256<P>> for Fp256<P>

fn sub_assign(&mut self, other: &'a mut Self)

Performs the -= operation.

impl<P: Fp256Parameters> SubAssign for Fp256<P>

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<'a, P: Fp256Parameters> Sum<&'a Fp256<P>> for Fp256<P>

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

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

impl<P: Fp256Parameters> Sum for Fp256<P>

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

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

impl<P: Fp256Parameters> ToBits for Fp256<P>

fn write_bits_le(&self, vec: &mut Vec<bool>)

Writes self into the given vector as a boolean array in little-endian order.

fn write_bits_be(&self, vec: &mut Vec<bool>)

Writes self into the given vector as a boolean array in big-endian order.

fn num_bits() -> Option<usize>

An optional indication of how many bits an object can be represented with.

fn to_bits_le(&self) -> Vec<bool>

Returns self as a boolean array in little-endian order.

fn to_bits_be(&self) -> Vec<bool>

Returns self as a boolean array in big-endian order.

impl<P: Fp256Parameters> ToBytes for Fp256<P>

fn write_le<W: Write>(&self, writer: W) -> IoResult<()>

Writes self into writer as little-endian bytes.

fn to_bytes_le(&self) -> Result<Vec<u8>, Error>

where Self: Sized,

Returns self as a byte array in little-endian order.

impl<P: Fp256Parameters> Valid for Fp256<P>

fn check(&self) -> Result<(), SerializationError>

fn batch_check<'a>( _batch: impl Iterator<Item = &'a Self> + Send, ) -> Result<(), SerializationError>

where Self: 'a,

impl<P: Fp256Parameters> Zero for Fp256<P>

fn zero() -> Self

fn is_zero(&self) -> bool

impl<P: Fp256Parameters> Zeroize for Fp256<P>

fn zeroize(&mut self)

Zero out this object from memory using Rust intrinsics which ensure the zeroization operation is not “optimized away” by the compiler.

impl<P: Copy + Fp256Parameters> Copy for Fp256<P>

impl<P: Eq + Fp256Parameters> Eq for Fp256<P>

impl<P: Fp256Parameters> StructuralPartialEq for Fp256<P>