Trait ff::PrimeField

pub trait PrimeField: Field + From<u64> {
    type Repr: Default + AsRef<[u8]> + AsMut<[u8]> + From<Self> + for<'r> From<&'r Self>;
    type ReprBits: BitView + Send + Sync;

    const NUM_BITS: u32;
    const CAPACITY: u32;
    const S: u32;

    fn from_repr(_: Self::Repr) -> Option<Self>;
    fn to_repr(&self) -> Self::Repr;
    fn to_le_bits(&self) -> BitArray<Lsb0, Self::ReprBits>;
    fn is_odd(&self) -> bool;
    fn char_le_bits() -> BitArray<Lsb0, Self::ReprBits>;
    fn multiplicative_generator() -> Self;
    fn root_of_unity() -> Self;

    fn from_str(s: &str) -> Option<Self> { ... }
    fn is_even(&self) -> bool { ... }
}

This represents an element of a prime field.

Associated Types

type Repr: Default + AsRef<[u8]> + AsMut<[u8]> + From<Self> + for<'r> From<&'r Self>

The prime field can be converted back and forth into this binary representation.

type ReprBits: BitView + Send + Sync

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

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Associated Constants

const NUM_BITS: u32

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.

This is usually Self::NUM_BITS - 1.

const S: u32

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

This is the number of leading zero bits in the little-endian bit representation of modulus - 1.

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Required methods

fn from_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).

The byte representation is interpreted with the same endianness as elements returned by PrimeField::to_repr.

fn to_repr(&self) -> Self::Repr

Converts an element of the prime field into the standard byte representation for this field.

The endianness of the byte representation is implementation-specific. Generic encodings of field elements should be treated as opaque.

fn to_le_bits(&self) -> BitArray<Lsb0, Self::ReprBits>

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

fn is_odd(&self) -> bool

Returns true iff this element is odd.

fn char_le_bits() -> BitArray<Lsb0, Self::ReprBits>

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

fn multiplicative_generator() -> Self

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

It can be calculated using SageMath as GF(modulus).primitive_element().

Implementations of this method MUST ensure that this is the generator used to derive Self::root_of_unity.

fn root_of_unity() -> Self

Returns the 2^s root of unity.

It can be calculated by exponentiating Self::multiplicative_generator by t, where t = (modulus - 1) >> Self::S.

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Provided methods

fn from_str(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 is_even(&self) -> bool

Returns true iff this element is even.

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Implementors

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