Struct halo2curves::bn256::Fq2

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

An element of Fq2, represented by c0 + c1 * u.

Fields

c0: Fq

c1: Fq

Implementations

impl 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 legendre(&self) -> LegendreSymbol

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 mul_by_xi(&mut self)

pub fn norm(&self) -> Fq

Norm of Fq2 as extension field in i over Fq

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<Fq2> 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<Fq2> 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.

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

fn random(rng: impl RngCore) -> Self

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

fn zero() -> Self

Returns the zero element of the field, the additive identity.

fn one() -> Self

Returns the one element of the field, the multiplicative identity.

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 is_zero_vartime(&self) -> bool

Returns true iff this element is zero.

fn cube(&self) -> Self

Cubes this element.

fn pow_vartime<S>(&self, exp: S) -> Selfwhere
    S: AsRef<[u64]>,

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

impl FieldExt for Fq2

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

Converts a 512-bit little endian integer into a Fq by reducing by the modulus.

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

Modulus of the field written as a string for display purposes

const ROOT_OF_UNITY_INV: Self = _

Inverse of PrimeField::root_of_unity()

const DELTA: Self = _

Generator of the $t-order$ multiplicative subgroup

const TWO_INV: Self = _

Inverse of $2$ in the field.

const ZETA: Self = _

Element of multiplicative order $3$.

fn from_u128(v: u128) -> Self

Obtains a field element congruent to the integer v.

fn get_lower_128(&self) -> u128

Gets the lower 128 bits of this field element when expressed canonically.

fn pow(&self, by: &[u64; 4]) -> Self

Exponentiates self by by, where by 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 Group for Fq2

type Scalar = Fq2

The group is assumed to be of prime order $p$. Scalar is the associated scalar field of size $p$.

fn group_zero() -> Self

Returns the additive identity of the group.

fn group_add(&mut self, rhs: &Self)

Adds rhs to this group element.

fn group_sub(&mut self, rhs: &Self)

Subtracts rhs from this group element.

fn group_scale(&mut self, by: &Self::Scalar)

Scales this group element by a scalar.

impl Hash for Fq2

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)where
    H: Hasher,
    Self: Sized,

Feeds a slice of this type into the given Hasher.

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<Fq2> 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<Fq2> 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) -> Selfwhere
    Self: Sized,

Compares and returns the maximum of two values.

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

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Selfwhere
    Self: Sized + PartialOrd<Self>,

Restrict a value to a certain interval.

impl PartialEq<Fq2> for Fq2

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

This method tests for self and other values to be equal, and is used by ==.

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

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd<Fq2> 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

This method tests less than (for self and other) and is used by the < operator.

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

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

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

This method tests greater than (for self and other) and is used by the > operator.

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

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

impl PrimeField for Fq2

type Repr = Fq2Bytes

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

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.

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 multiplicative_generator() -> Self

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

fn root_of_unity() -> Self

Returns the 2^s root of unity.

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_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 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 SqrtRatio for Fq2

const T_MINUS1_OVER2: [u64; 4] = _

The value $(T-1)/2$ such that $2^S \cdot T = p - 1$ with $T$ odd.

fn pow_by_t_minus1_over2(&self) -> Self

Raise this field element to the power [Self::T_MINUS1_OVER2].

fn get_lower_32(&self) -> u32

Gets the lower 32 bits of this field element when expressed canonically.

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

Computes:

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

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

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<Fq2> 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<Fq2> for Fq2

fn sub_assign(&mut self, rhs: Fq2)

Performs the -= operation.

impl Copy for Fq2

impl Eq for Fq2

impl StructuralEq for Fq2

impl StructuralPartialEq for Fq2