Struct dalek_ff_group::FieldElement

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

A constant-time implementation of the Ed25519 field.

Implementations

impl FieldElement

pub fn from_square(value: [u8; 32]) -> FieldElement

Interpret the value as a little-endian integer, square it, and reduce it into a FieldElement.

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

Perform an exponentiation.

pub fn sqrt_ratio_i(u: FieldElement, v: FieldElement) -> (Choice, FieldElement)

The square root of u/v, as used for Ed25519 point decoding (RFC 8032 5.1.3) and within Ristretto (5.1 Extracting an Inverse Square Root).

The result is only a valid square root if the Choice is true. RFC 8032 simply fails if there isn’t a square root, leaving any return value undefined. Ristretto explicitly returns 0 or sqrt((SQRT_M1 * u) / v).

Trait Implementations

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

type Output = FieldElement

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add for FieldElement

type Output = FieldElement

The resulting type after applying the + operator.

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

Performs the + operation.

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

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

Performs the += operation.

impl AddAssign for FieldElement

fn add_assign(&mut self, other: FieldElement)

Performs the += operation.

impl Clone for FieldElement

fn clone(&self) -> FieldElement

Returns a copy 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 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 Field for FieldElement

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(u: &FieldElement, v: &FieldElement) -> (Choice, FieldElement)

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 FieldElement

fn from(a: u128) -> FieldElement

Converts to this type from the input type.

impl From<u16> for FieldElement

fn from(a: u16) -> FieldElement

Converts to this type from the input type.

impl From<u32> for FieldElement

fn from(a: u32) -> FieldElement

Converts to this type from the input type.

impl From<u64> for FieldElement

fn from(a: u64) -> FieldElement

Converts to this type from the input type.

impl From<u8> for FieldElement

fn from(a: u8) -> FieldElement

Converts to this type from the input type.

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

type Output = FieldElement

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul for FieldElement

type Output = FieldElement

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Performs the *= operation.

impl MulAssign for FieldElement

fn mul_assign(&mut self, other: FieldElement)

Performs the *= operation.

impl<'a> Neg for &'a FieldElement

type Output = FieldElement

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Neg for FieldElement

type Output = FieldElement

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl PartialEq for FieldElement

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

type Repr = [u8; 32]

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

const MODULUS: &'static str = "7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed"

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

const NUM_BITS: u32 = 255u32

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

const CAPACITY: u32 = 254u32

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 = 2u32

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: [u8; 32]) -> 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) -> [u8; 32]

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_u128(num: u128) -> Self

Obtains a field element congruent to the integer v.

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 PrimeFieldBits for FieldElement

type ReprBits = [u8; 32]

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 FieldElement> for FieldElement

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

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

impl Product for FieldElement

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

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

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

type Output = FieldElement

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub for FieldElement

type Output = FieldElement

The resulting type after applying the - operator.

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

Performs the - operation.

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

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

Performs the -= operation.

impl SubAssign for FieldElement

fn sub_assign(&mut self, other: FieldElement)

Performs the -= operation.

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

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

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

impl Sum for FieldElement

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

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

impl Copy for FieldElement

impl Eq for FieldElement

impl StructuralPartialEq for FieldElement