Struct FieldElement 

pub struct FieldElement(pub(crate) ConstMontyForm<MODULUS, { MODULUS::LIMBS }>);

Tuple Fields

0: ConstMontyForm<MODULUS, { MODULUS::LIMBS }>

Implementations

impl FieldElement

pub const A_PLUS_TWO_OVER_FOUR: Self

pub const DECAF_FACTOR: Self

pub const EDWARDS_D: Self

pub const J: Self

pub const MINUS_ONE: Self

pub const NEG_EDWARDS_D: Self

pub const NEG_FOUR_TIMES_TWISTED_D: Self

pub const ONE: Self

pub const TWO: Self

pub const TWISTED_D: Self

pub const TWO_TIMES_TWISTED_D: Self

pub const Z: Self

pub const ZERO: Self

pub fn is_negative(&self) -> Choice

pub fn is_zero(&self) -> Choice

pub fn invert(&self) -> Self

Inverts a field element

pub fn square(&self) -> Self

fn square_n<const N: u32>(&self) -> FieldElement

Squares a field element n times

pub fn is_square(&self) -> Choice

pub fn unchecked_sqrt(&self) -> FieldElement

pub fn to_bytes(self) -> [u8; 56]

pub fn to_bytes_extended(self) -> [u8; 57]

pub fn from_bytes(bytes: &[u8; 56]) -> Self

pub fn from_bytes_extended(bytes: &[u8; 57]) -> Self

pub fn from_repr(bytes: &[u8; 56]) -> CtOption<Self>

pub fn double(&self) -> Self

pub(crate) fn inverse_square_root(&self) -> (FieldElement, Choice)

Computes the inverse square root of a field element Returns the result and a boolean to indicate whether self was a Quadratic residue

pub(crate) fn sqrt_ratio( u: &FieldElement, v: &FieldElement, ) -> (FieldElement, Choice)

Computes the square root ratio of two elements

pub(crate) fn div_by_2(&self) -> FieldElement

pub(crate) fn map_to_curve_elligator2(&self) -> AffinePoint

pub(crate) fn map_to_curve_decaf448(&self) -> TwistedExtendedPoint

Trait Implementations

impl Add for FieldElement

type Output = FieldElement

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = FieldElement

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<&FieldElement> for &FieldElement

type Output = FieldElement

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = FieldElement

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign for FieldElement

fn add_assign(&mut self, other: FieldElement)

Performs the += operation.

impl AddAssign<&FieldElement> for FieldElement

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

Performs the += operation.

impl BatchInvert for FieldElement

fn batch_invert_in_place( elements: &mut [Self], scratch_space: &mut [Self], ) -> Self

Inverts each field element in elements (when non-zero). Zero-valued elements are left as zero.

fn batch_invert_in_place_vartime( elements: &mut [Self], scratch_space: &mut [Self], ) -> Self

Variable-time batch inversion.

impl Clone for FieldElement

fn clone(&self) -> FieldElement

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for FieldElement

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 FieldElement

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 Copy for FieldElement

impl Debug for FieldElement

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

Formats the value using the given formatter.

impl Default for FieldElement

fn default() -> FieldElement

Returns the “default value” for a type.

impl DefaultIsZeroes for FieldElement

impl Display for FieldElement

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

Formats the value using the given formatter.

impl Eq for FieldElement

impl Field for FieldElement

const ZERO: Self = Self::ZERO

The zero element of the field, the additive identity.

const ONE: Self = Self::ONE

The one element of the field, the multiplicative identity.

fn try_random<R: TryRng + ?Sized>(rng: &mut R) -> Result<Self, R::Error>

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

fn square(&self) -> Self

Squares this element.

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 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 random<R>(rng: &mut R) -> Self

where R: Rng + ?Sized,

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

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 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 LowerHex for FieldElement

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

Formats the value using the given formatter.

impl Mul for FieldElement

type Output = FieldElement

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = FieldElement

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<&FieldElement> for &FieldElement

type Output = FieldElement

The resulting type after applying the * operator.

fn mul(self, other: &FieldElement) -> FieldElement

Performs the * operation.

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

type Output = FieldElement

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign for FieldElement

fn mul_assign(&mut self, other: FieldElement)

Performs the *= operation.

impl MulAssign<&FieldElement> for FieldElement

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

Performs the *= operation.

impl Neg for &FieldElement

type Output = FieldElement

The resulting type after applying the - operator.

fn neg(self) -> FieldElement

Performs the unary - operation.

impl Neg for FieldElement

type Output = FieldElement

The resulting type after applying the - operator.

fn neg(self) -> FieldElement

Performs the unary - operation.

impl PartialEq for FieldElement

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

Equality operator ==.

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

Inequality operator !=.

impl Product for FieldElement

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

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

impl<'a> Product<&'a FieldElement> for FieldElement

fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self

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

impl Reduce<Array<u8, UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B1>, B0>, B1>, B0>, B0>>> for FieldElement

fn reduce(value: &Array<u8, U84>) -> Self

Reduces self modulo Modulus.

impl Reduce<Array<u8, UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B1>, B1>, B0>, B0>, B0>>> for FieldElement

fn reduce(value: &Array<u8, U56>) -> Self

Reduces self modulo Modulus.

impl Sub for FieldElement

type Output = FieldElement

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = FieldElement

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<&FieldElement> for &FieldElement

type Output = FieldElement

The resulting type after applying the - operator.

fn sub(self, other: &FieldElement) -> FieldElement

Performs the - operation.

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

type Output = FieldElement

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign for FieldElement

fn sub_assign(&mut self, other: FieldElement)

Performs the -= operation.

impl SubAssign<&FieldElement> for FieldElement

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

Performs the -= operation.

impl Sum for FieldElement

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

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

impl<'a> Sum<&'a FieldElement> for FieldElement

fn sum<I: Iterator<Item = &'a FieldElement>>(iter: I) -> Self

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

impl UpperHex for FieldElement

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

Formats the value using the given formatter.