Trait ff::PrimeField

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

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

    fn from_repr(_: Self::Repr) -> Option<Self>;
    fn to_repr(&self) -> Self::Repr;
    fn is_odd(&self) -> bool;
    fn char() -> Self::Repr;
    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 ReprEndianness: Endianness

This indicates the endianness of PrimeField::Repr.

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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.

const S: u32

2^s * t = char() - 1 with t odd.

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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 endianness defined by PrimeField::ReprEndianness.

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 defined by PrimeField::ReprEndianness.

fn is_odd(&self) -> bool

Returns true iff this element is odd.

fn char() -> Self::Repr

Returns the field characteristic; the modulus.

fn multiplicative_generator() -> Self

Returns the multiplicative generator of char() - 1 order. This element must also be quadratic nonresidue.

fn root_of_unity() -> Self

Returns the 2^s root of unity computed by exponentiating the multiplicative_generator() by t.

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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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