Struct Fq2

pub struct Fq2 {
    pub c0: Fp,
    pub c1: Fp,
}

Fields

c0: Fp

c1: Fp

Implementations

impl Fp2

pub const fn zero() -> Fp2

pub const fn one() -> Fp2

pub fn is_zero(&self) -> Choice

pub fn double(&self) -> Self

pub fn frobenius_map(&self) -> Self

Raises this element to p.

pub fn conjugate(&self) -> Self

pub fn mul_by_nonresidue(&self) -> Fp2

pub fn lexicographically_largest(&self) -> Choice

Returns whether or not this element is strictly lexicographically larger than its negation.

pub const fn square(&self) -> Fp2

pub fn mul(&self, rhs: &Fp2) -> Fp2

pub const fn add(&self, rhs: &Fp2) -> Fp2

pub const fn sub(&self, rhs: &Fp2) -> Fp2

pub const fn neg(&self) -> Fp2

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

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

Computes the multiplicative inverse of this field element, returning None in the case that this element is zero.

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

Although this is labeled “vartime”, it is only variable time with respect to the exponent. It is also not exposed in the public API.

pub fn pow_vartime_extended(&self, by: &[u64]) -> Self

Vartime exponentiation for larger exponents, only used in testing and not exposed through the public API.

pub fn from_bytes(bytes: &[u8; 96]) -> CtOption<Fp2>

Attempts to convert a little-endian byte representation of a scalar into a Fp2, failing if the input is not canonical.

pub fn to_bytes(&self) -> [u8; 96]

Trait Implementations

impl<'a, 'b> Add<&'b Fp2> for &'a Fp2

type Output = Fp2

The resulting type after applying the + operator.

fn add(self, rhs: &'b Fp2) -> Fp2

Performs the + operation.

impl<'b> Add<&'b Fp2> for Fp2

type Output = Fp2

The resulting type after applying the + operator.

fn add(self, rhs: &'b Fp2) -> Fp2

Performs the + operation.

impl<'a> Add<Fp2> for &'a Fp2

type Output = Fp2

The resulting type after applying the + operator.

fn add(self, rhs: Fp2) -> Fp2

Performs the + operation.

impl Add for Fp2

type Output = Fp2

The resulting type after applying the + operator.

fn add(self, rhs: Fp2) -> Fp2

Performs the + operation.

impl<'b> AddAssign<&'b Fp2> for Fp2

fn add_assign(&mut self, rhs: &'b Fp2)

Performs the += operation.

impl AddAssign for Fp2

fn add_assign(&mut self, rhs: Fp2)

Performs the += operation.

impl Clone for Fp2

fn clone(&self) -> Fp2

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for Fp2

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 ConstantTimeEq for Fp2

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 Debug for Fp2

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

Formats the value using the given formatter.

impl Default for Fp2

fn default() -> Self

Returns the “default value” for a type.

impl Field for Fp2

const ZERO: Self = _

The zero element of the field, the additive identity.

const ONE: Self = _

The one element of the field, the multiplicative identity.

fn random(rng: impl RngCore) -> Self

Returns an element chosen uniformly at random using a user-provided RNG.

fn is_zero(&self) -> Choice

Returns true iff this element is zero.

fn square(&self) -> Self

Squares this element.

fn double(&self) -> Self

Doubles this element.

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

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

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

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

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

Computes:

fn is_zero_vartime(&self) -> bool

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 From<Fp> for Fp2

fn from(f: Fp) -> Fp2

Converts to this type from the input type.

impl From<Fp2> for Fp12

fn from(f: Fp2) -> Fp12

Converts to this type from the input type.

impl From<Fp2> for Fp6

fn from(f: Fp2) -> Fp6

Converts to this type from the input type.

impl From<u64> for Fp2

fn from(val: u64) -> Self

Converts to this type from the input type.

impl HashToField for Fp2

type InputLength = UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, B0>, B0>

The length of the data used to produce an individual field element.

fn from_okm(okm: &GenericArray<u8, U128>) -> Fp2

Interprets the given output keying material as a big endian integer, and reduces it into a field element.

fn hash_to_field<X: ExpandMessage>( message: &[u8], dst: &[u8], output: &mut [Self], )

Hashes a byte string of arbitrary length into one or more elements of Self, using ExpandMessage variant X.

impl<'a, 'b> Mul<&'b Fp2> for &'a Fp2

type Output = Fp2

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fp2) -> Fp2

Performs the * operation.

impl<'b> Mul<&'b Fp2> for Fp2

type Output = Fp2

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fp2) -> Fp2

Performs the * operation.

impl<'a> Mul<Fp2> for &'a Fp2

type Output = Fp2

The resulting type after applying the * operator.

fn mul(self, rhs: Fp2) -> Fp2

Performs the * operation.

impl Mul for Fp2

type Output = Fp2

The resulting type after applying the * operator.

fn mul(self, rhs: Fp2) -> Fp2

Performs the * operation.

impl<'b> MulAssign<&'b Fp2> for Fp2

fn mul_assign(&mut self, rhs: &'b Fp2)

Performs the *= operation.

impl MulAssign for Fp2

fn mul_assign(&mut self, rhs: Fp2)

Performs the *= operation.

impl<'a> Neg for &'a Fp2

type Output = Fp2

The resulting type after applying the - operator.

fn neg(self) -> Fp2

Performs the unary - operation.

impl Neg for Fp2

type Output = Fp2

The resulting type after applying the - operator.

fn neg(self) -> Fp2

Performs the unary - operation.

impl Ord for Fp2

fn cmp(&self, other: &Fp2) -> 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 Fp2

fn eq(&self, other: &Self) -> 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 Fp2

fn partial_cmp(&self, other: &Fp2) -> 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 Fp2

const NUM_BITS: u32 = 381u32

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

const CAPACITY: u32 = 380u32

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

const MODULUS: &'static str = "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"

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

const ROOT_OF_UNITY: Self = _

The 2^s root of unity.

const ROOT_OF_UNITY_INV: Self = _

Inverse of Self::ROOT_OF_UNITY.

const DELTA: Self = _

Generator of the t-order multiplicative subgroup.

const TWO_INV: Fp2 = _

Inverse of $2$ in the field.

const S: u32 = 0u32

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

type Repr = Fp2Bytes

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

fn from_repr(r: Self::Repr) -> CtOption<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).

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

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 from_repr_vartime(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).

fn is_even(&self) -> Choice

Returns true iff this element is even.

const MULTIPLICATIVE_GENERATOR: Self

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

impl<T: Borrow<Fp2>> Product<T> for Fp2

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

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

impl<'a, 'b> Sub<&'b Fp2> for &'a Fp2

type Output = Fp2

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Fp2) -> Fp2

Performs the - operation.

impl<'b> Sub<&'b Fp2> for Fp2

type Output = Fp2

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Fp2) -> Fp2

Performs the - operation.

impl<'a> Sub<Fp2> for &'a Fp2

type Output = Fp2

The resulting type after applying the - operator.

fn sub(self, rhs: Fp2) -> Fp2

Performs the - operation.

impl Sub for Fp2

type Output = Fp2

The resulting type after applying the - operator.

fn sub(self, rhs: Fp2) -> Fp2

Performs the - operation.

impl<'b> SubAssign<&'b Fp2> for Fp2

fn sub_assign(&mut self, rhs: &'b Fp2)

Performs the -= operation.

impl SubAssign for Fp2

fn sub_assign(&mut self, rhs: Fp2)

Performs the -= operation.

impl<T: Borrow<Fp2>> Sum<T> for Fp2

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

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

impl WithSmallOrderMulGroup<3> for Fp2

const ZETA: Self = _

A field element of small multiplicative order $N$.

impl Copy for Fp2

impl Eq for Fp2