Struct FpElement 

pub struct FpElement<MOD, const LIMBS: usize>
where
    MOD: ConstPrimeMontyParams<LIMBS>,
{ /* private fields */ }

An element of the prime field $\mathbb{F}_p = \mathbb{Z}/p\mathbb{Z}$, stored in Montgomery form.

The internal value uses crypto-bigint’s ConstMontyForm, so arithmetic is performed in Montgomery representation while the public constructors and accessors accept and return canonical integers.

Implementations

impl<MOD, const LIMBS: usize> FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS>,

pub fn from_uint(x: Uint<LIMBS>) -> Self

Goes from an Uint<LIMBS> to an element of $\mathbb{F}_p$

Arguments

• x - An integer (type: Uint<LIMBS>)

Returns

Element of $\mathbb{F}_p$ (type: Self)

pub fn from_words(words: [u64; LIMBS]) -> Self

Goes from an [u64; LIMBS] to an element of $\mathbb{F}_p$

Arguments

• words - A vec of u64 (type: [u64; LIMBS])

Returns

Element of $\mathbb{F}_p$ (type: Self)

pub fn from_limbs(limbs: &[u64]) -> Self

Goes from an &[u64] to an element of $\mathbb{F}_p$

Arguments

• limbs - A vec of u64 (type: &[u64])

Returns

Element of $\mathbb{F}_p$ (type: Self)

pub fn from_u64(val: u64) -> Self

Goes from an u64 to an element of $\mathbb{F}_p$

Arguments

• val - A u64 int (type: u64)

Returns

Element of $\mathbb{F}_p$ (type: Self)

pub fn as_uint(&self) -> Uint<LIMBS>

Goes from an element of $\mathbb{F}_p$ to the corresponding Uint

Arguments

• &self - Element of $\mathbb{F}_p$ (type: Self)

Returns

The corresponding Uint (type: Uint<LIMBS>)

pub fn as_limbs(&self) -> [u64; LIMBS]

Goes from an element of $\mathbb{F}_p$ to the limbs

Arguments

• &self - Element of $\mathbb{F}_p$ (type: Self)

Returns

The limbs giving the integer (type: [u64; LIMBS])

pub fn to_montgomery(&self) -> Uint<LIMBS>

Gives a montgomery Uint<LIMBS> from an $\mathbb{F}_p$ element

Arguments

• &self - Element of $\mathbb{F}_p$ (type: Self)

Returns

Integer in montgomery from (type: Uint<LIMBS>)

pub fn from_montgomery(mont: Uint<LIMBS>) -> Self

Gives an element of $\mathbb{F}_p$ from the Montgomery representation.

Arguments

• mont - The input montgomery value (type: Uint<LIMBS>)

Returns

Corresponding element of $\mathbb{F}_p$ (type: Self)

Trait Implementations

impl<MOD, const LIMBS: usize> Add for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS>,

type Output = FpElement<MOD, LIMBS>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<MOD, const LIMBS: usize> Clone for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS> + Clone,

fn clone(&self) -> FpElement<MOD, LIMBS>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<MOD, const LIMBS: usize> ConditionallySelectable for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS>,

fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self

Select a or b according to choice.

fn conditional_assign(&mut self, other: &Self, choice: Choice)

Conditionally assign other to self, according to choice.

fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice)

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves.

impl<MOD, const LIMBS: usize> ConstantTimeEq for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS>,

fn ct_eq(&self, other: &Self) -> Choice

Determine if two items are equal.

fn ct_ne(&self, other: &Self) -> Choice

Determine if two items are NOT equal.

impl<MOD, const LIMBS: usize> Debug for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS> + Debug,

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

Formats the value using the given formatter.

impl<MOD, const LIMBS: usize> Default for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS>,

fn default() -> Self

Returns the “default value” for a type.

impl<MOD, const LIMBS: usize> Display for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS>,

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

Formats the value using the given formatter.

impl<MOD, const LIMBS: usize> FieldFromRepr for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS>,

type Repr = Uint<LIMBS>

The representation type accepted by this field.

fn from_repr(x: Self::Repr) -> Self

Constructs a field element from the given representation.

impl<MOD, const LIMBS: usize> FieldOps for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS>,

fn zero() -> Self

Create the constant zero

fn one() -> Self

Create the constant one

fn from_u64(x: u64) -> Self

Convert u64 to the field.

fn is_zero(&self) -> Choice

Check if element is zero

fn is_one(&self) -> Choice

Check if element is one

fn negate(&self) -> Self

Negate self to -self

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

Add rhs to self

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

Sub rhs from self

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

Multipliy self by rhs

fn square(&self) -> Self

Square self

fn double(&self) -> Self

Double self

fn invert(&self) -> CtOption<Self>

Invert self

fn frobenius(&self) -> Self

Compute self^p the frobenius acting on self

fn norm(&self) -> Self

compute the norm of self down to $\mathbb{F}_p$ (as an element of type Self)

fn trace(&self) -> Self

compute the trace of self down to $\mathbb{F}_p$ (as an element of type Self)

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

Returns a squareroot if it exists

fn legendre(&self) -> i8

Computes the “Legendre symbol” i.e., if 0,1,-1 depending if self is 0, a square or a nonsquare.

fn characteristic() -> Vec<u64>

Returns the characteristic of the field.

fn degree() -> u32

Returns the extension degree of the field.

fn div(&self, rhs: &Self) -> CtOption<Self>

Divide self by rhs

fn pow_vartime(&self, exp: &[u64]) -> Self

self^exp using square-and multiply (litte-endian bit order)

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

self^pow in constant time using a Montgomery ladder

fn frobenius_pow(&self, k: u32) -> Self

Compute self^{p^k} a power of the frobenius

fn inverse_and_sqrt(&self) -> (CtOption<Self>, CtOption<Self>)

Computes the inverse and square root of self

fn inv_sqrt(&self) -> CtOption<Self>

Computes the square root the inverse of self

fn invertme_sqrtother(&self, rhs: &Self) -> (CtOption<Self>, CtOption<Self>)

Computes the inverse of self and square root of rhs

fn sqrt_ratio(&self, rhs: &Self) -> CtOption<Self>

Computes the squareroot of a ratio self/rhs

impl<MOD, const LIMBS: usize> FieldRandom for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS>,

fn random(rng: &mut (impl CryptoRng + Rng)) -> Self

Sample a uniformly random element of Fp using a CSPRNG.

impl<MOD, const LIMBS: usize> Mul for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS>,

type Output = FpElement<MOD, LIMBS>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<MOD, const LIMBS: usize> Neg for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS>,

type Output = FpElement<MOD, LIMBS>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<MOD, const LIMBS: usize> PartialEq for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS> + PartialEq,

fn eq(&self, other: &FpElement<MOD, LIMBS>) -> 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<MOD, const LIMBS: usize> Sub for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS>,

type Output = FpElement<MOD, LIMBS>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<MOD, const LIMBS: usize> Copy for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS> + Copy,

impl<MOD, const LIMBS: usize> Eq for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS> + Eq,

impl<MOD, const LIMBS: usize> StructuralPartialEq for FpElement<MOD, LIMBS>

where MOD: ConstPrimeMontyParams<LIMBS>,