Trait FieldElement

pub trait FieldElement:
    Add<Output = Self>
    + AddAssign
    + Div<Output = Self>
    + Mul<Output = Self>
    + MulAssign
    + Neg<Output = Self>
    + Sub<Output = Self>
    + SubAssign
    + FromStr<Err = Error>
    + PartialEq
    + Clone
    + Hash
    + Debug
    + From<u64>
    + Display {
    // Required methods
    fn byte_len() -> usize;
    fn name_str() -> &'static str;
    fn from_bytes_le(bytes: &[u8]) -> Self;
    fn to_bytes_le(&self) -> Vec<u8> ;

    // Provided methods
    fn zero() -> Self { ... }
    fn one() -> Self { ... }
    fn prime() -> BigUint { ... }
    fn from_usize(value: usize) -> Self { ... }
    fn to_biguint(&self) -> BigUint { ... }
    fn from_biguint(v: &BigUint) -> Self { ... }
    fn lower60_string(&self) -> String { ... }
    fn log_floor(&self, b: Self) -> u32 { ... }
    fn legendre(&self) -> i32 { ... }
    fn sqrt(&self) -> Self { ... }
}

A generic representation of a scalar finite field element. For use in internal module logic. Supports field operations using builtin operators (*-+/) and other convenience traits. Handles serialization and deserialization to a reasonable string representation.

Required Methods

fn byte_len() -> usize

Minimum number of bytes needed to represent an element.

fn name_str() -> &'static str

A short string identifier for the field.

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

Parse an element from a byte representation. Panics if the byte representation is too long. e.g. if the bytes represent a value > Self::prime().

fn to_bytes_le(&self) -> Vec<u8>

Convert a field element to a byte representation. The number of bytes may be variable, but is guaranteed to be accepted by from_bytes_le for the same curve.

Provided Methods

fn zero() -> Self

Get the zero element.

fn one() -> Self

Get the one element.

fn prime() -> BigUint

The prime modulus of the field as an arbitrary precision integer.

fn from_usize(value: usize) -> Self

Parse an element from a usize throws if the field size is smaller than the usize on the machine.

fn to_biguint(&self) -> BigUint

Get a num_bigint::BigUint representation for arbitrary precision operations.

fn from_biguint(v: &BigUint) -> Self

Convert a num_bigint::BigUint into a field element precision operations. Numbers will be converted % self.prime()

fn lower60_string(&self) -> String

A string representation of a field element using only the lower 60 bits of the element. A normal decimal representation will be given if it’s shorter than the lower 60 bit representation. This is a lossy representation.

fn log_floor(&self, b: Self) -> u32

Take a logarithm using a custom base and return the floored value. O(logb(n)) time complexity where n is the size of the element.

fn legendre(&self) -> i32

Calculate the legendre symbol for a field element. Used to determine if the element is a quadratic residue.

fn sqrt(&self) -> Self

Kumar 08 prime field square root implementation. Always returns the smaller root e.g. the positive root.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors