Struct minimal_ed448::Scalar

pub struct Scalar(/* private fields */);

Ed448 Scalar field element.

Implementations

impl Scalar

pub fn pow(&self, other: Scalar) -> Scalar

Perform an exponentiation.

impl Scalar

pub fn wide_reduce(bytes: [u8; 114]) -> Scalar

Perform a wide reduction to obtain a non-biased Scalar.

Trait Implementations

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

type Output = Scalar

The resulting type after applying the + operator.

fn add(self, other: &'a Scalar) -> Self::Output

Performs the + operation.

impl Add for Scalar

type Output = Scalar

The resulting type after applying the + operator.

fn add(self, other: Scalar) -> Self::Output

Performs the + operation.

impl<'a> AddAssign<&'a Scalar> for Scalar

fn add_assign(&mut self, other: &'a Scalar)

Performs the += operation.

impl AddAssign for Scalar

fn add_assign(&mut self, other: Scalar)

Performs the += operation.

impl Clone for Scalar

fn clone(&self) -> Scalar

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for Scalar

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 Scalar

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 Scalar

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

Formats the value using the given formatter.

impl Default for Scalar

fn default() -> Scalar

Returns the “default value” for a type.

impl Field for Scalar

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 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 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 From<u128> for Scalar

fn from(a: u128) -> Scalar

Converts to this type from the input type.

impl From<u16> for Scalar

fn from(a: u16) -> Scalar

Converts to this type from the input type.

impl From<u32> for Scalar

fn from(a: u32) -> Scalar

Converts to this type from the input type.

impl From<u64> for Scalar

fn from(a: u64) -> Scalar

Converts to this type from the input type.

impl From<u8> for Scalar

fn from(a: u8) -> Scalar

Converts to this type from the input type.

impl Mul<&Scalar> for Point

type Output = Point

The resulting type after applying the * operator.

fn mul(self, other: &Scalar) -> Point

Performs the * operation.

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

type Output = Scalar

The resulting type after applying the * operator.

fn mul(self, other: &'a Scalar) -> Self::Output

Performs the * operation.

impl Mul<Scalar> for Point

type Output = Point

The resulting type after applying the * operator.

fn mul(self, other: Scalar) -> Point

Performs the * operation.

impl Mul for Scalar

type Output = Scalar

The resulting type after applying the * operator.

fn mul(self, other: Scalar) -> Self::Output

Performs the * operation.

impl MulAssign<&Scalar> for Point

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

Performs the *= operation.

impl<'a> MulAssign<&'a Scalar> for Scalar

fn mul_assign(&mut self, other: &'a Scalar)

Performs the *= operation.

impl MulAssign<Scalar> for Point

fn mul_assign(&mut self, other: Scalar)

Performs the *= operation.

impl MulAssign for Scalar

fn mul_assign(&mut self, other: Scalar)

Performs the *= operation.

impl<'a> Neg for &'a Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Neg for Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Scalar

Performs the unary - operation.

impl PartialEq for Scalar

fn eq(&self, other: &Scalar) -> 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 PrimeField for Scalar

type Repr = GenericArray<u8, UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B1>, B1>, B0>, B0>, B1>>

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

const MODULUS: &'static str = MODULUS_STR

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

const NUM_BITS: u32 = 446u32

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

const CAPACITY: u32 = 445u32

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

const TWO_INV: Self = _

Inverse of $2$ in the field.

const MULTIPLICATIVE_GENERATOR: Self = _

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

const S: u32 = 1u32

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.

fn from_repr(bytes: 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 PrimeFieldBits for Scalar

type ReprBits = [u8; 56]

The backing store for a bit representation of a prime field element.

fn to_le_bits(&self) -> FieldBits<Self::ReprBits>

Converts an element of the prime field into a little-endian sequence of bits.

fn char_le_bits() -> FieldBits<Self::ReprBits>

Returns the bits of the field characteristic (the modulus) in little-endian order.

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

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

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl Product for Scalar

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

Method which takes an iterator and generates Self from the elements by multiplying the items.

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

type Output = Scalar

The resulting type after applying the - operator.

fn sub(self, other: &'a Scalar) -> Self::Output

Performs the - operation.

impl Sub for Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn sub(self, other: Scalar) -> Self::Output

Performs the - operation.

impl<'a> SubAssign<&'a Scalar> for Scalar

fn sub_assign(&mut self, other: &'a Scalar)

Performs the -= operation.

impl SubAssign for Scalar

fn sub_assign(&mut self, other: Scalar)

Performs the -= operation.

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

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

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl Sum for Scalar

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

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl Copy for Scalar

impl DefaultIsZeroes for Scalar

impl Eq for Scalar

impl StructuralPartialEq for Scalar