Struct Fq2

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

An element of Fq2, represented by c0 + c1 * u; where u^2 = -1.

Fields

c0: Fq

c1: Fq

Implementations

impl Fq2

pub const fn zero() -> Fq2

pub const fn one() -> Fq2

pub const fn new(c0: Fq, c1: Fq) -> Self

pub const fn size() -> usize

pub fn from_bytes(bytes: &[u8; 64]) -> CtOption<Fq2>

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

pub fn to_bytes(&self) -> [u8; 64]

Converts an element of Fq into a byte representation in little-endian byte order.

pub fn mul_assign(&mut self, other: &Self)

pub fn square_assign(&mut self)

pub fn double(&self) -> Self

pub fn double_assign(&mut self)

pub fn add(&self, other: &Self) -> Self

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

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

pub fn square(&self) -> Self

pub fn neg(&self) -> Self

pub fn conjugate(&mut self)

pub fn frobenius_map(&mut self, power: usize)

pub fn mul_by_nonresidue(&mut self)

Multiply this element by quadratic nonresidue 9 + u.

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

Trait Implementations

impl<'a, 'b> Add<&'b Fq2> for &'a Fq2

type Output = Fq2

The resulting type after applying the + operator.

fn add(self, rhs: &'b Fq2) -> Fq2

Performs the + operation.

impl<'b> Add<&'b Fq2> for Fq2

type Output = Fq2

The resulting type after applying the + operator.

fn add(self, rhs: &'b Fq2) -> Fq2

Performs the + operation.

impl<'a> Add<Fq2> for &'a Fq2

type Output = Fq2

The resulting type after applying the + operator.

fn add(self, rhs: Fq2) -> Fq2

Performs the + operation.

impl Add for Fq2

type Output = Fq2

The resulting type after applying the + operator.

fn add(self, rhs: Fq2) -> Fq2

Performs the + operation.

impl<'b> AddAssign<&'b Fq2> for Fq2

fn add_assign(&mut self, rhs: &'b Fq2)

Performs the += operation.

impl AddAssign for Fq2

fn add_assign(&mut self, rhs: Fq2)

Performs the += operation.

impl Clone for Fq2

fn clone(&self) -> Fq2

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for Fq2

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 Fq2

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 Fq2

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

Formats the value using the given formatter.

impl Default for Fq2

fn default() -> Self

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Fq2

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Field for Fq2

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

Computes:

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

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

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<'a> From<&'a Fq2> for [u8; 64]

fn from(value: &'a Fq2) -> [u8; 64]

Converts to this type from the input type.

impl From<Fq2> for [u8; 64]

fn from(value: Fq2) -> [u8; 64]

Converts to this type from the input type.

impl From<bool> for Fq2

fn from(bit: bool) -> Fq2

Converts to this type from the input type.

impl From<u64> for Fq2

fn from(val: u64) -> Self

Converts to this type from the input type.

impl FromUniformBytes<64> for Fq2

fn from_uniform_bytes(bytes: &[u8; 64]) -> Self

Returns a field element that is congruent to the provided little endian unsigned byte representation of an integer.

impl Legendre for Fq2

fn legendre(&self) -> i64

fn ct_quadratic_non_residue(&self) -> Choice

fn ct_quadratic_residue(&self) -> Choice

impl<'a, 'b> Mul<&'b Fq2> for &'a Fq2

type Output = Fq2

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fq2) -> Fq2

Performs the * operation.

impl<'b> Mul<&'b Fq2> for Fq2

type Output = Fq2

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fq2) -> Fq2

Performs the * operation.

impl<'a> Mul<Fq2> for &'a Fq2

type Output = Fq2

The resulting type after applying the * operator.

fn mul(self, rhs: Fq2) -> Fq2

Performs the * operation.

impl Mul for Fq2

type Output = Fq2

The resulting type after applying the * operator.

fn mul(self, rhs: Fq2) -> Fq2

Performs the * operation.

impl<'b> MulAssign<&'b Fq2> for Fq2

fn mul_assign(&mut self, rhs: &'b Fq2)

Performs the *= operation.

impl MulAssign for Fq2

fn mul_assign(&mut self, rhs: Fq2)

Performs the *= operation.

impl<'a> Neg for &'a Fq2

type Output = Fq2

The resulting type after applying the - operator.

fn neg(self) -> Fq2

Performs the unary - operation.

impl Neg for Fq2

type Output = Fq2

The resulting type after applying the - operator.

fn neg(self) -> Fq2

Performs the unary - operation.

impl Ord for Fq2

Fq2 elements are ordered lexicographically.

fn cmp(&self, other: &Fq2) -> 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 Fq2

fn eq(&self, other: &Fq2) -> 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 Fq2

fn partial_cmp(&self, other: &Fq2) -> 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 Fq2

const MODULUS: &'static str = "0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47"

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

const MULTIPLICATIVE_GENERATOR: Self = _

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

const NUM_BITS: u32 = 254u32

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

const CAPACITY: u32 = 253u32

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

const S: u32 = 0u32

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

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: Self = _

Inverse of $2$ in the field.

type Repr = Fq2Bytes

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

fn from_repr(repr: 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.

impl<T: Borrow<Fq2>> Product<T> for Fq2

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

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

impl SerdeObject for Fq2

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

The purpose of unchecked functions is to read the internal memory representation of a type from bytes as quickly as possible. No sanitization checks are performed to ensure the bytes represent a valid object. As such this function should only be used internally as an extension of machine memory. It should not be used to deserialize externally provided data.

fn from_raw_bytes(bytes: &[u8]) -> Option<Self>

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

fn read_raw_unchecked<R: Read>(reader: &mut R) -> Self

The purpose of unchecked functions is to read the internal memory representation of a type from disk as quickly as possible. No sanitization checks are performed to ensure the bytes represent a valid object. This function should only be used internally when some machine state cannot be kept in memory (e.g., between runs) and needs to be reloaded as quickly as possible.

fn read_raw<R: Read>(reader: &mut R) -> Result<Self>

fn write_raw<W: Write>(&self, writer: &mut W) -> Result<()>

impl Serialize for Fq2

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<'a, 'b> Sub<&'b Fq2> for &'a Fq2

type Output = Fq2

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Fq2) -> Fq2

Performs the - operation.

impl<'b> Sub<&'b Fq2> for Fq2

type Output = Fq2

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Fq2) -> Fq2

Performs the - operation.

impl<'a> Sub<Fq2> for &'a Fq2

type Output = Fq2

The resulting type after applying the - operator.

fn sub(self, rhs: Fq2) -> Fq2

Performs the - operation.

impl Sub for Fq2

type Output = Fq2

The resulting type after applying the - operator.

fn sub(self, rhs: Fq2) -> Fq2

Performs the - operation.

impl<'b> SubAssign<&'b Fq2> for Fq2

fn sub_assign(&mut self, rhs: &'b Fq2)

Performs the -= operation.

impl SubAssign for Fq2

fn sub_assign(&mut self, rhs: Fq2)

Performs the -= operation.

impl<T: Borrow<Fq2>> Sum<T> for Fq2

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 Fq2

const ZETA: Self = _

A field element of small multiplicative order $N$.

impl Copy for Fq2

impl Eq for Fq2

impl StructuralPartialEq for Fq2