Struct k256::Scalar

pub struct Scalar(_);

This is supported on crate feature arithmetic only.

Scalars are elements in the finite field modulo n.

Trait impls

Much of the important functionality of scalars is provided by traits from the ff crate, which is re-exported as k256::elliptic_curve::ff:

• Field - represents elements of finite fields and provides:
  • Field::random - generate a random scalar
  • double, square, and invert operations
  • Bounds for Add, Sub, Mul, and Neg (as well as *Assign equivalents)
  • Bounds for ConditionallySelectable from the subtle crate
• PrimeField - represents elements of prime fields and provides:
  • from_repr/to_repr for converting field elements from/to big integers.
  • char_le_bits, multiplicative_generator, root_of_unity constants.
• PrimeFieldBits - operations over field elements represented as bits (requires bits feature)

Please see the documentation for the relevant traits for more information.

Implementations

impl Scalar

pub const fn zero() -> Self

Returns the zero scalar.

pub const fn one() -> Scalar

Returns the multiplicative identity.

pub fn is_zero(&self) -> Choice

Checks if the scalar is zero.

pub fn truncate_to_u32(&self) -> u32

Returns the value of the scalar truncated to a 32-bit unsigned integer.

pub fn from_bytes_reduced(bytes: &FieldBytes) -> Self

Parses the given byte array as a scalar.

Subtracts the modulus when the byte array is larger than the modulus.

pub fn to_bytes(&self) -> FieldBytes

Returns the SEC1 encoding of this scalar.

pub fn is_high(&self) -> Choice

Is this scalar greater than or equal to n / 2?

pub fn negate(&self) -> Self

Negates the scalar.

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

Modulo adds two scalars

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

Modulo subtracts one scalar from the other.

pub fn mul(&self, rhs: &Scalar) -> Scalar

Modulo multiplies two scalars.

pub fn square(&self) -> Self

Modulo squares the scalar.

pub fn rshift(&self, shift: usize) -> Scalar

Right shifts the scalar. Note: not constant-time in shift.

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

Inverts the scalar.

pub fn generate_biased(rng: impl CryptoRng + RngCore) -> Self

Returns a (nearly) uniformly-random scalar, generated in constant time.

pub fn generate_vartime(rng: impl RngCore) -> Self

Returns a uniformly-random scalar, generated using rejection sampling.

pub fn conditional_add_bit(&self, bit: usize, flag: Choice) -> Self

If flag evaluates to true, adds (1 << bit) to self.

pub fn mul_shift_var(&self, b: &Scalar, shift: usize) -> Self

Multiplies self by b (without modulo reduction) divide the result by 2^shift (rounding to the nearest integer). Variable time in shift.

Trait Implementations

impl Add<&'_ Scalar> for &Scalar

type Output = Scalar

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<&'_ Scalar> for Scalar

type Output = Scalar

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<Scalar> for Scalar

type Output = Scalar

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<Scalar> for &Scalar

type Output = Scalar

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign<&'_ Scalar> for Scalar

fn add_assign(&mut self, rhs: &Scalar)

Performs the += operation.

impl AddAssign<Scalar> for Scalar

fn add_assign(&mut self, rhs: 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.

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

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 is_zero(&self) -> bool

Returns true iff this element is zero.

#[must_use]

fn square(&self) -> Self

Squares this element.

#[must_use]

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.

#[must_use]

fn cube(&self) -> Self

Cubes this element.

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<&'_ Scalar> for FieldBytes

fn from(scalar: &Scalar) -> Self

Performs the conversion.

impl From<Scalar> for FieldBytes

fn from(scalar: Scalar) -> Self

Performs the conversion.

impl From<u32> for Scalar

fn from(k: u32) -> Self

Performs the conversion.

impl From<u64> for Scalar

fn from(k: u64) -> Self

Performs the conversion.

impl FromDigest<Secp256k1> for Scalar

This is supported on crate feature digest only.

fn from_digest<D>(digest: D) -> Self where
    D: Digest<OutputSize = U32>, 

Convert the output of a digest algorithm into a Scalar reduced modulo n.

impl Mul<&'_ Scalar> for AffinePoint

type Output = ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, scalar: &Scalar) -> ProjectivePoint

Performs the * operation.

impl Mul<&'_ Scalar> for &ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<&'_ Scalar> for ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<&'_ Scalar> for &Scalar

type Output = Scalar

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<&'_ Scalar> for Scalar

type Output = Scalar

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Scalar> for AffinePoint

type Output = ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, scalar: Scalar) -> ProjectivePoint

Performs the * operation.

impl Mul<Scalar> for ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Scalar> for Scalar

type Output = Scalar

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign<&'_ Scalar> for ProjectivePoint

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

Performs the *= operation.

impl MulAssign<&'_ Scalar> for Scalar

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

Performs the *= operation.

impl MulAssign<Scalar> for ProjectivePoint

fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation.

impl MulAssign<Scalar> for Scalar

fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation.

impl Neg for Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Scalar

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 NormalizeLow for Scalar

This is supported on crate feature ecdsa-core only.

fn normalize_low(&self) -> (Self, bool)

Normalize scalar to the lower half of the field (i.e. negate it if it’s larger than half the curve’s order). Returns a tuple with the new scalar and a boolean indicating whether the given scalar was in the higher half.

impl PartialEq<Scalar> for Scalar

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

This method tests for self and other values to be equal, and is used by ==.

#[must_use]

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

This method tests for !=.

impl PrimeField for Scalar

fn from_repr(bytes: FieldBytes) -> Option<Self>

Attempts to parse the given byte array as an SEC1-encoded scalar.

Returns None if the byte array does not contain a big-endian integer in the range [0, p).

type Repr = FieldBytes

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

const NUM_BITS: u32

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

const CAPACITY: u32

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

const S: u32

An integer s satisfying the equation 2^s * t = modulus - 1 with t odd.

fn to_repr(&self) -> FieldBytes

Converts an element of the prime field into the standard byte representation for this field.

fn is_odd(&self) -> bool

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(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 is_even(&self) -> bool

Returns true iff this element is even.

impl RecoverableSignPrimitive<Secp256k1> for Scalar

This is supported on crate feature ecdsa-core only.

fn try_sign_recoverable_prehashed<K>(
    &self,
    ephemeral_scalar: &K,
    z: &Scalar
) -> Result<(Signature, bool), Error> where
    K: Borrow<Scalar> + Invert<Output = Scalar>, 

Try to sign the prehashed message.

impl Shr<usize> for Scalar

type Output = Self

The resulting type after applying the >> operator.

fn shr(self, rhs: usize) -> Self::Output

Performs the >> operation.

impl Shr<usize> for &Scalar

type Output = Scalar

The resulting type after applying the >> operator.

fn shr(self, rhs: usize) -> Self::Output

Performs the >> operation.

impl Sub<&'_ Scalar> for &Scalar

type Output = Scalar

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<&'_ Scalar> for Scalar

type Output = Scalar

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<Scalar> for Scalar

type Output = Scalar

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign<&'_ Scalar> for Scalar

fn sub_assign(&mut self, rhs: &Scalar)

Performs the -= operation.

impl SubAssign<Scalar> for Scalar

fn sub_assign(&mut self, rhs: Scalar)

Performs the -= operation.

impl Zeroize for Scalar

fn zeroize(&mut self)

Zero out this object from memory using Rust intrinsics which ensure the zeroization operation is not “optimized away” by the compiler.

impl Copy for Scalar

impl Eq for Scalar