Struct p256::FieldElement

pub struct FieldElement(_);

Available on crate features arithmetic and expose-field only.

An element in the finite field modulo p = 2^{224}(2^{32} − 1) + 2^{192} + 2^{96} − 1.

The internal representation is in little-endian order. Elements are always in Montgomery form; i.e., FieldElement(a) = aR mod p, with R = 2^256.

Implementations

impl FieldElement

pub const ZERO: Self = _

Zero element.

pub const ONE: Self = _

Multiplicative identity.

pub fn from_bytes(repr: &FieldBytes) -> CtOption<Self>

Create a FieldElement from a canonical big-endian representation.

pub fn from_slice(slice: &[u8]) -> Result<Self>

Decode FieldElement from a big endian byte slice.

pub fn from_uint(uint: U256) -> CtOption<Self>

Decode FieldElement from U256 converting it into Montgomery form:

w * R^2 * R^-1 mod p = wR mod p

pub const fn from_u64(w: u64) -> Self

Convert a u64 into a FieldElement.

pub fn to_bytes(self) -> FieldBytes

Returns the big-endian encoding of this FieldElement.

pub const fn to_canonical(self) -> U256

Translate FieldElement out of the Montgomery domain, returning a U256 in canonical form.

pub fn is_odd(&self) -> Choice

Determine if this FieldElement is odd in the SEC1 sense: self mod 2 == 1.

Returns

If odd, return Choice(1). Otherwise, return Choice(0).

pub fn is_even(&self) -> Choice

Determine if this FieldElement is even in the SEC1 sense: self mod 2 == 0.

Returns

If even, return Choice(1). Otherwise, return Choice(0).

pub fn is_zero(&self) -> Choice

Determine if this FieldElement is zero.

Returns

If zero, return Choice(1). Otherwise, return Choice(0).

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

Add elements.

pub const fn double(&self) -> Self

Double element (add it to itself).

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

Subtract elements.

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

Multiply elements.

pub const fn neg(&self) -> Self

Negate element.

pub const fn square(&self) -> Self

Compute modular square.

pub const fn pow_vartime(&self, exp: &[u64]) -> Self

Returns self^exp, where exp is a little-endian integer exponent.

This operation is variable time with respect to the exponent.

If the exponent is fixed, this operation is effectively constant time.

impl FieldElement

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

Returns the multiplicative inverse of self, if self is non-zero.

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

Returns the square root of self mod p, or None if no square root exists.

Trait Implementations

impl Add<&FieldElement> for &FieldElement

type Output = FieldElement

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<&FieldElement> for FieldElement

type Output = FieldElement

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<FieldElement> for FieldElement

type Output = FieldElement

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign<&FieldElement> 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 AsRef<[u32; 8]> for FieldElement

fn as_ref(&self) -> &[u32; 8]

Converts this type into a shared reference of the (usually inferred) input type.

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.

impl ConstantTimeGreater for FieldElement

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

Determine whether self > other.

impl ConstantTimeLess for FieldElement

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

Determine whether self < other.

impl Debug for FieldElement

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

Formats the value using the given formatter.

impl Default for FieldElement

fn default() -> Self

Returns the “default value” for a type.

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 random(rng: impl RngCore) -> Self

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

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 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_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) -> Selfwhere S: AsRef<[u64]>,

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

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 From<u128> for FieldElement

fn from(n: u128) -> FieldElement

Converts to this type from the input type.

impl From<u32> for FieldElement

fn from(n: u32) -> FieldElement

Converts to this type from the input type.

impl From<u64> for FieldElement

fn from(n: u64) -> FieldElement

Converts to this type from the input type.

impl FromOkm for FieldElement

Available on crate feature hash2curve only.

type Length = UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B1>, B0>, B0>, B0>, B0>

The number of bytes needed to convert to a field element.

fn from_okm(data: &GenericArray<u8, Self::Length>) -> Self

Convert a byte sequence into a field element.

impl MapToCurve for FieldElement

Available on crate feature hash2curve only.

type Output = ProjectivePoint<NistP256>

The output point

fn map_to_curve(&self) -> Self::Output

Map a field element into a point

impl Mul<&FieldElement> for &FieldElement

type Output = FieldElement

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<&FieldElement> for FieldElement

type Output = FieldElement

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<FieldElement> for FieldElement

type Output = FieldElement

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign<&FieldElement> 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 OsswuMap for FieldElement

Available on crate feature hash2curve only.

const PARAMS: OsswuMapParams<Self> = _

The OSSWU parameters for mapping the field to affine points. For Weierstrass curves having A==0 or B==0, the parameters should be for isogeny where A≠0 and B≠0.

fn sqrt_ratio_3mod4(u: Self, v: Self) -> (Choice, Self)

Optimized sqrt_ratio for q = 3 mod 4.

fn osswu(&self) -> (Self, Self)

Convert this field element into an affine point on the elliptic curve returning (X, Y). For Weierstrass curves having A==0 or B==0 the result is a point on an isogeny.

impl PartialEq<FieldElement> for FieldElement

fn eq(&self, rhs: &Self) -> 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 = GenericArray<u8, <NistP256 as Curve>::FieldBytesSize>

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

const MODULUS: &'static str = MODULUS_HEX

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

const NUM_BITS: u32 = 256u32

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

const CAPACITY: u32 = 255u32

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: FieldBytes) -> 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) -> FieldBytes

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

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

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

impl Product<FieldElement> for FieldElement

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

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

impl Sgn0 for FieldElement

Available on crate feature hash2curve only.

fn sgn0(&self) -> Choice

Return the parity of the field 1 == negative 0 == non-negative

impl Sub<&FieldElement> for &FieldElement

type Output = FieldElement

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<&FieldElement> for FieldElement

type Output = FieldElement

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<FieldElement> for FieldElement

type Output = FieldElement

The resulting type after applying the - operator.

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

Performs the - operation.

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

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

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

impl Sum<FieldElement> for FieldElement

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

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

impl Copy for FieldElement

impl DefaultIsZeroes for FieldElement

impl Eq for FieldElement