Struct Fp 

pub struct Fp(/* private fields */);

Trait Implementations

impl<'r> Add<&'r Fp> for Fp

type Output = Fp

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add for Fp

type Output = Fp

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'r> AddAssign<&'r Fp> for Fp

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

Performs the += operation.

impl AddAssign for Fp

fn add_assign(&mut self, other: Fp)

Performs the += operation.

impl Clone for Fp

fn clone(&self) -> Fp

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for Fp

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

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 ConstantTimeEq for Fp

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

Determine if two items are equal.

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

Determine if two items are NOT equal.

impl Debug for Fp

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

Formats the value using the given formatter.

impl Default for Fp

fn default() -> Fp

Returns the “default value” for a type.

impl Field for Fp

fn random(rng: impl RngCore) -> Self

Computes a uniformly random element using rejection sampling.

const ZERO: Self

The zero element of the field, the additive identity.

const ONE: Self = R

The one element of the field, the multiplicative identity.

fn is_zero_vartime(&self) -> bool

Returns true iff this element is zero.

fn double(&self) -> Self

Doubles this element.

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

Computes the multiplicative inverse of this element, failing if the element is zero.

fn square(&self) -> Self

Squares this element.

fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self)

Computes:

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

Returns the square root of the field element, if it is quadratic residue.

fn is_zero(&self) -> Choice

Returns true iff this element is zero.

fn cube(&self) -> Self

Cubes this element.

fn sqrt_alt(&self) -> (Choice, Self)

Equivalent to Self::sqrt_ratio(self, one()).

fn pow<S>(&self, exp: S) -> Self

where S: AsRef<[u64]>,

Exponentiates self by exp, where exp is a little-endian order integer exponent.

fn pow_vartime<S>(&self, exp: S) -> Self

where S: AsRef<[u64]>,

Exponentiates self by exp, where exp is a little-endian order integer exponent.

impl<'a> From<&'a Fp> for FpRepr

fn from(e: &'a Fp) -> FpRepr

Converts to this type from the input type.

impl From<Fp> for FpRepr

fn from(e: Fp) -> FpRepr

Converts to this type from the input type.

impl From<Fp> for Vec<u64>

fn from(s: Fp) -> Vec<u64>

Converts to this type from the input type.

impl From<Fp> for Vec<u8>

fn from(s: Fp) -> Vec<u8>

Converts to this type from the input type.

impl From<u64> for Fp

fn from(val: u64) -> Fp

Converts to this type from the input type.

impl<'r> Mul<&'r Fp> for Fp

type Output = Fp

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul for Fp

type Output = Fp

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'r> MulAssign<&'r Fp> for Fp

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

Performs the *= operation.

impl MulAssign for Fp

fn mul_assign(&mut self, other: Fp)

Performs the *= operation.

impl Neg for Fp

type Output = Fp

The resulting type after applying the - operator.

fn neg(self) -> Fp

Performs the unary - operation.

impl Ord for Fp

Elements are ordered lexicographically.

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

This method returns an Ordering between self and other.

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

where Self: Sized,

Compares and returns the maximum of two values.

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

where Self: Sized,

Compares and returns the minimum of two values.

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

where Self: Sized,

Restrict a value to a certain interval.

impl PartialEq for Fp

fn eq(&self, other: &Fp) -> 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 PartialOrd for Fp

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

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

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

Tests less than (for self and other) and is used by the < operator.

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

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

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

Tests greater than (for self and other) and is used by the > operator.

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

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

impl PrimeField for Fp

const MODULUS: &'static str = MODULUS_STR

Modulus of the field written as a string for debugging purposes.

const NUM_BITS: u32 = 129u32

How many bits are needed to represent an element of this field.

const CAPACITY: u32 = 128u32

How many bits of information can be reliably stored in the field element.

const TWO_INV: Self = TWO_INV

Inverse of $2$ in the field.

const MULTIPLICATIVE_GENERATOR: Self = GENERATOR

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

const S: u32 = 1u32

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

const ROOT_OF_UNITY: Self = ROOT_OF_UNITY

The 2^s root of unity.

const ROOT_OF_UNITY_INV: Self = ROOT_OF_UNITY_INV

Inverse of Self::ROOT_OF_UNITY.

const DELTA: Self = DELTA

Generator of the t-order multiplicative subgroup.

type Repr = FpRepr

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

fn from_repr(r: FpRepr) -> CtOption<Fp>

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).

fn from_repr_vartime(r: FpRepr) -> Option<Fp>

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).

fn to_repr(&self) -> FpRepr

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

fn is_odd(&self) -> Choice

Returns true iff this element is odd.

fn from_str_vartime(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 from_u128(v: u128) -> Self

Obtains a field element congruent to the integer v.

fn is_even(&self) -> Choice

Returns true iff this element is even.

impl<T: Borrow<Fp>> Product<T> for Fp

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

Takes an iterator and generates Self from the elements by multiplying the items.

impl<'r> Sub<&'r Fp> for Fp

type Output = Fp

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub for Fp

type Output = Fp

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'r> SubAssign<&'r Fp> for Fp

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

Performs the -= operation.

impl SubAssign for Fp

fn sub_assign(&mut self, other: Fp)

Performs the -= operation.

impl<T: Borrow<Fp>> Sum<T> for Fp

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

Takes an iterator and generates Self from the elements by “summing up” the items.

impl Zeroize for Fp

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 Copy for Fp

impl Eq for Fp