Struct ark_ff::fields::models::Fp448

pub struct Fp448<P>(pub BigInteger448, _);

Represents an element of the prime field F_p, where p == P::MODULUS. This type can represent elements in any field of size at most 448 bits.

Implementations

impl<P> Fp448<P>

pub const fn new(element: BigInteger448) -> Self

Trait Implementations

impl<'a, P: Fp448Parameters> Add<&'a Fp448<P>> for Fp448<P>

type Output = Self

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, P: Fp448Parameters> Add<&'a mut Fp448<P>> for Fp448<P>

type Output = Self

The resulting type after applying the + operator.

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

Performs the + operation.

impl<P: Fp448Parameters> Add<Fp448<P>> for Fp448<P>

type Output = Self

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, P: Fp448Parameters> AddAssign<&'a Fp448<P>> for Fp448<P>

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

Performs the += operation.

impl<'a, P: Fp448Parameters> AddAssign<&'a mut Fp448<P>> for Fp448<P>

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

Performs the += operation.

impl<P: Fp448Parameters> AddAssign<Fp448<P>> for Fp448<P>

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<P: Fp448Parameters> CanonicalDeserialize for Fp448<P>

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

Reads Self from reader.

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

Reads Self from reader without compression.

fn deserialize_unchecked<R>(reader: R) -> Result<Self, SerializationError> where
    R: Read, 

Reads self from reader without compression, and without performing validity checks. Should be used only when the input is trusted.

impl<P: Fp448Parameters> CanonicalDeserializeWithFlags for Fp448<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: Fp448Parameters> CanonicalSerialize for Fp448<P>

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

Serializes self into writer. It is left up to a particular type for how it strikes the serialization efficiency vs compression tradeoff. For standard types (e.g. bool, lengths, etc.) typically an uncompressed form is used, whereas for algebraic types compressed forms are used.

fn serialized_size(&self) -> usize

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

Serializes self into writer without compression.

fn serialize_unchecked<W>(&self, writer: W) -> Result<(), SerializationError> where
    W: Write, 

Serializes self into writer without compression, and without performing validity checks. Should be used only when there is no danger of adversarial manipulation of the output.

fn uncompressed_size(&self) -> usize

impl<P: Fp448Parameters> CanonicalSerializeWithFlags for Fp448<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 for Fp448<P>

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<P> Debug for Fp448<P>

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

Formats the value using the given formatter.

impl<P> Default for Fp448<P>

fn default() -> Self

Returns the “default value” for a type.

impl<P: Fp448Parameters> Display for Fp448<P>

Outputs a string containing the value of self, chunked up into 64-bit limbs.

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

Formats the value using the given formatter.

impl<'a, P: Fp448Parameters> Div<&'a Fp448<P>> for Fp448<P>

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

Returns self * other.inverse() if other.inverse() is Some, and panics otherwise.

type Output = Self

The resulting type after applying the / operator.

impl<'a, P: Fp448Parameters> Div<&'a mut Fp448<P>> for Fp448<P>

type Output = Self

The resulting type after applying the / operator.

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

Performs the / operation.

impl<P: Fp448Parameters> Div<Fp448<P>> for Fp448<P>

type Output = Self

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, P: Fp448Parameters> DivAssign<&'a Fp448<P>> for Fp448<P>

Computes self *= other.inverse() if other.inverse() is Some, and panics otherwise.

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

Performs the /= operation.

impl<'a, P: Fp448Parameters> DivAssign<&'a mut Fp448<P>> for Fp448<P>

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

Performs the /= operation.

impl<P: Fp448Parameters> DivAssign<Fp448<P>> for Fp448<P>

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<P: Fp448Parameters> FftField for Fp448<P>

type FftParams = 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).

impl<P: Fp448Parameters> Field for Fp448<P>

fn frobenius_map(&mut self, _: usize)

The Frobenius map has no effect in a prime field.

type BasePrimeField = Self

fn extension_degree() -> u64

Returns the extension degree of this field with respect to Self::BasePrimeField.

fn from_base_prime_field_elems(elems: &[Self::BasePrimeField]) -> Option<Self>

Convert a slice of base prime field elements into a field element. If the slice length != Self::extension_degree(), must return None.

fn double(&self) -> Self

Returns self + self.

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

Doubles self in place.

fn characteristic() -> &'static [u64]

Returns the characteristic of the field, in little-endian representation.

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 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>

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.

#[must_use]

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

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

fn pow_with_table<S: AsRef<[u64]>>(powers_of_2: &[Self], exp: S) -> Option<Self>

Exponentiates a field element f by a number represented with u64 limbs, using a precomputed table containing as many powers of 2 of f as the 1 + the floor of log2 of the exponent exp, starting from the 1st power. That is, powers_of_2 should equal &[p, p^2, p^4, ..., p^(2^n)] when exp has at most n bits.

impl<P: Fp448Parameters> From<BigInteger448> for Fp448<P>

fn from(int: BigInteger448) -> Self

Converts Self::BigInteger into Self

Panics

This method panics if int is larger than P::MODULUS.

impl<P: Fp448Parameters> From<BigUint> for Fp448<P>

fn from(val: BigUint) -> Fp448<P>

Performs the conversion.

impl<P: Fp448Parameters> From<bool> for Fp448<P>

fn from(other: bool) -> Self

Performs the conversion.

impl<P: Fp448Parameters> From<i128> for Fp448<P>

fn from(other: i128) -> Self

Performs the conversion.

impl<P: Fp448Parameters> From<i16> for Fp448<P>

fn from(other: i16) -> Self

Performs the conversion.

impl<P: Fp448Parameters> From<i32> for Fp448<P>

fn from(other: i32) -> Self

Performs the conversion.

impl<P: Fp448Parameters> From<i64> for Fp448<P>

fn from(other: i64) -> Self

Performs the conversion.

impl<P: Fp448Parameters> From<i8> for Fp448<P>

fn from(other: i8) -> Self

Performs the conversion.

impl<P: Fp448Parameters> From<u128> for Fp448<P>

fn from(other: u128) -> Self

Performs the conversion.

impl<P: Fp448Parameters> From<u16> for Fp448<P>

fn from(other: u16) -> Self

Performs the conversion.

impl<P: Fp448Parameters> From<u32> for Fp448<P>

fn from(other: u32) -> Self

Performs the conversion.

impl<P: Fp448Parameters> From<u64> for Fp448<P>

fn from(other: u64) -> Self

Performs the conversion.

impl<P: Fp448Parameters> From<u8> for Fp448<P>

fn from(other: u8) -> Self

Performs the conversion.

impl<P: Fp448Parameters> FromBytes for Fp448<P>

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

Reads Self from reader.

impl<P: Fp448Parameters> FromStr for Fp448<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 = ()

The associated error which can be returned from parsing.

impl<P> Hash for Fp448<P>

fn hash<__HP>(&self, __state: &mut __HP) where
    __HP: Hasher, 

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H) where
    H: Hasher, 

Feeds a slice of this type into the given Hasher.

impl<P: Fp448Parameters> Into<BigInteger448> for Fp448<P>

fn into(self) -> BigInteger448

Performs the conversion.

impl<P: Fp448Parameters> Into<BigUint> for Fp448<P>

fn into(self) -> BigUint

Performs the conversion.

impl<'a, P: Fp448Parameters> Mul<&'a Fp448<P>> for Fp448<P>

type Output = Self

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, P: Fp448Parameters> Mul<&'a mut Fp448<P>> for Fp448<P>

type Output = Self

The resulting type after applying the * operator.

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

Performs the * operation.

impl<P: Fp448Parameters> Mul<Fp448<P>> for Fp448<P>

type Output = Self

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, P: Fp448Parameters> MulAssign<&'a Fp448<P>> for Fp448<P>

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

Performs the *= operation.

impl<'a, P: Fp448Parameters> MulAssign<&'a mut Fp448<P>> for Fp448<P>

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

Performs the *= operation.

impl<P: Fp448Parameters> MulAssign<Fp448<P>> for Fp448<P>

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<P: Fp448Parameters> Neg for Fp448<P>

type Output = Self

The resulting type after applying the - operator.

#[must_use]

fn neg(self) -> Self

Performs the unary - operation.

impl<P: Fp448Parameters> One for Fp448<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: Fp448Parameters> Ord for Fp448<P>

Note that this implementation of Ord compares field elements viewing them as integers in the range 0, 1, …, P::MODULUS - 1. However, other implementations of PrimeField might choose a different ordering, and as such, users should use this Ord for applications where any ordering suffices (like in a BTreeMap), and not in applications where a particular ordering is required.

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

#[must_use]

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

Compares and returns the maximum of two values.

#[must_use]

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

Compares and returns the minimum of two values.

#[must_use]

fn clamp(self, min: Self, max: Self) -> Self

Restrict a value to a certain interval.

impl<P> PartialEq<Fp448<P>> for Fp448<P>

fn eq(&self, other: &Self) -> bool

This method tests for self and other values to be equal, and is used by ==.

#[must_use]

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<P: Fp448Parameters> PartialOrd<Fp448<P>> for Fp448<P>

Note that this implementation of PartialOrd compares field elements viewing them as integers in the range 0, 1, …, P::MODULUS - 1. However, other implementations of PrimeField might choose a different ordering, and as such, users should use this PartialOrd for applications where any ordering suffices (like in a BTreeMap), and not in applications where a particular ordering is required.

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

#[must_use]

fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

#[must_use]

fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

#[must_use]

fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

#[must_use]

fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl<P: Fp448Parameters> PrimeField for Fp448<P>

type Params = P

type BigInt = BigInteger448

fn from_repr(r: BigInteger448) -> Option<Self>

Returns a prime field element from its underlying representation.

fn into_repr(&self) -> BigInteger448

Returns the underlying representation of the prime field element.

fn from_be_bytes_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_le_bytes_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.

fn qnr_to_t() -> Self

Return the QNR^t, for t defined by 2^s * t = MODULUS - 1, and t coprime to 2.

fn size_in_bits() -> usize

Returns the field size in bits.

fn trace() -> Self::BigInt

Returns the trace.

fn trace_minus_one_div_two() -> Self::BigInt

Returns the trace minus one divided by two.

fn modulus_minus_one_div_two() -> Self::BigInt

Returns the modulus minus one divided by two.

impl<'a, P: Fp448Parameters> Product<&'a Fp448<P>> for Fp448<P>

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

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<P: Fp448Parameters> Product<Fp448<P>> for Fp448<P>

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

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<P: Fp448Parameters> SquareRootField for Fp448<P>

fn legendre(&self) -> LegendreSymbol

Returns a LegendreSymbol, which indicates whether this field element is 1 : a quadratic residue 0 : equal to 0 -1 : a quadratic non-residue

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<'a, P: Fp448Parameters> Sub<&'a Fp448<P>> for Fp448<P>

type Output = Self

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, P: Fp448Parameters> Sub<&'a mut Fp448<P>> for Fp448<P>

type Output = Self

The resulting type after applying the - operator.

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

Performs the - operation.

impl<P: Fp448Parameters> Sub<Fp448<P>> for Fp448<P>

type Output = Self

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, P: Fp448Parameters> SubAssign<&'a Fp448<P>> for Fp448<P>

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

Performs the -= operation.

impl<'a, P: Fp448Parameters> SubAssign<&'a mut Fp448<P>> for Fp448<P>

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

Performs the -= operation.

impl<P: Fp448Parameters> SubAssign<Fp448<P>> for Fp448<P>

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<'a, P: Fp448Parameters> Sum<&'a Fp448<P>> for Fp448<P>

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

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<P: Fp448Parameters> Sum<Fp448<P>> for Fp448<P>

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

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<P: Fp448Parameters> ToBytes for Fp448<P>

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

Serializes self into writer.

impl<P: Fp448Parameters> Zero for Fp448<P>

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl<P: Fp448Parameters> Zeroize for Fp448<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 for Fp448<P>

impl<P> Eq for Fp448<P>