Struct halo2curves::bn256::Fq

pub struct Fq(_);

This represents an element of $\mathbb{F}_q$ where

p = 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47

is the base field of the BN254 curve.

Implementations

impl Fq

pub const fn zero() -> Fq

Returns zero, the additive identity.

pub const fn one() -> Fq

Returns one, the multiplicative identity.

pub const fn from_raw(val: [u64; 4]) -> Self

Converts from an integer represented in little endian into its (congruent) $field representation.

pub fn from_bytes(bytes: &[u8; 32]) -> CtOption<Fq>

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

pub fn to_bytes(&self) -> [u8; 32]

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

impl Fq

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

Adds rhs to self, returning the result.

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

Multiplies rhs by self, returning the result.

impl Fq

pub const fn double(&self) -> Fq

Doubles this field element.

pub const fn square(&self) -> Fq

Squares this element.

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

Subtracts rhs from self, returning the result.

pub const fn neg(&self) -> Self

Negates self.

impl Fq

pub const fn size() -> usize

pub fn legendre(&self) -> LegendreSymbol

Trait Implementations

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

type Output = Fq

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Fq

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Fq

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<Fq> for Fq

type Output = Fq

The resulting type after applying the + operator.

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

Performs the + operation.

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

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

Performs the += operation.

impl AddAssign<Fq> for Fq

fn add_assign(&mut self, rhs: Fq)

Performs the += operation.

impl Clone for Fq

fn clone(&self) -> Fq

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for Fq

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 Fq

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

Determine if two items are equal.

impl Debug for Fq

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

Formats the value using the given formatter.

impl Default for Fq

fn default() -> Self

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Fq

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>where
    __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Field for Fq

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

Computes the square root of this element, if it exists.

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

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

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 double(&self) -> Self

Doubles this element.

fn square(&self) -> Self

Squares this element.

fn is_zero(&self) -> Choice

Returns true iff this 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 Fq

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

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

const MODULUS: &'static str = MODULUS_STR

Modulus of the field written as a string for display purposes

const TWO_INV: Self = TWO_INV

Inverse of $2$ in the field.

const ROOT_OF_UNITY_INV: Self = ROOT_OF_UNITY_INV

Inverse of PrimeField::root_of_unity()

const DELTA: Self = DELTA

Generator of the $t-order$ multiplicative subgroup

const ZETA: Self = ZETA

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 Fq> for [u8; 32]

fn from(value: &'a Fq) -> [u8; 32]

Converts to this type from the input type.

impl From<[u64; 4]> for Fq

fn from(digits: [u64; 4]) -> Self

Converts to this type from the input type.

impl From<Fq> for [u64; 4]

fn from(elt: Fq) -> [u64; 4]

Converts to this type from the input type.

impl From<Fq> for [u8; 32]

fn from(value: Fq) -> [u8; 32]

Converts to this type from the input type.

impl From<Fq> for i128

fn from(value: Fq) -> i128

Converts to this type from the input type.

impl From<bool> for Fq

fn from(bit: bool) -> Fq

Converts to this type from the input type.

impl From<u64> for Fq

fn from(val: u64) -> Fq

Converts to this type from the input type.

impl Group for Fq

type Scalar = Fq

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 Fq

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 Fq> for &'a Fq

type Output = Fq

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Fq

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Fq

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Fq> for Fq

type Output = Fq

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Performs the *= operation.

impl MulAssign<Fq> for Fq

fn mul_assign(&mut self, rhs: Fq)

Performs the *= operation.

impl<'a> Neg for &'a Fq

type Output = Fq

The resulting type after applying the - operator.

fn neg(self) -> Fq

Performs the unary - operation.

impl Neg for Fq

type Output = Fq

The resulting type after applying the - operator.

fn neg(self) -> Fq

Performs the unary - operation.

impl Ord for Fq

fn cmp(&self, other: &Self) -> 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<Fq> for Fq

fn eq(&self, other: &Fq) -> 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<Fq> for Fq

fn partial_cmp(&self, other: &Self) -> 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 Fq

type Repr = [u8; 32]

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 Fq

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 Fq

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 Fq

const T_MINUS1_OVER2: [u64; 4] = _

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

fn get_lower_32(&self) -> u32

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

fn pow_by_t_minus1_over2(&self) -> Self

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

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 Fq> for &'a Fq

type Output = Fq

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Fq

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Fq

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<Fq> for Fq

type Output = Fq

The resulting type after applying the - operator.

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

Performs the - operation.

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

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

Performs the -= operation.

impl SubAssign<Fq> for Fq

fn sub_assign(&mut self, rhs: Fq)

Performs the -= operation.

impl Copy for Fq

impl Eq for Fq

impl StructuralEq for Fq

impl StructuralPartialEq for Fq