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.
  • multiplicative_generator and 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.

serde support

When the serde feature of this crate is enabled, the Serialize and Deserialize traits are impl’d for this type.

The serialization is a fixed-width big endian encoding. When used with textual formats, the binary data is encoded as hexadecimal.

Implementations

impl Scalar

pub const ZERO: Self

Zero scalar.

pub const ONE: Self

Multiplicative identity.

pub fn is_zero(&self) -> Choice

Checks if the scalar is zero.

pub fn to_bytes(&self) -> FieldBytes

Returns the SEC1 encoding of this scalar.

pub const fn negate(&self) -> Self

Negates the scalar.

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

Returns self + rhs mod n.

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

Returns self - rhs mod n.

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

Modulo multiplies two scalars.

pub fn square(&self) -> Self

Modulo squares the scalar.

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

Right shifts the scalar.

Note: not constant-time with respect to the shift parameter.

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.

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 sqrt(&self) -> CtOption<Self>

Tonelli-Shank’s algorithm for q mod 16 = 1 https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)

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 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 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 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 ScalarCore<Secp256k1>

fn from(scalar: &Scalar) -> ScalarCore<Secp256k1>

Performs the conversion.

impl From<&'_ Scalar> for FieldBytes

fn from(scalar: &Scalar) -> Self

Performs the conversion.

impl From<&'_ ScalarCore<Secp256k1>> for Scalar

fn from(scalar: &ScalarCore<Secp256k1>) -> Scalar

Performs the conversion.

impl From<Scalar> for ScalarCore<Secp256k1>

fn from(scalar: Scalar) -> ScalarCore<Secp256k1>

Performs the conversion.

impl From<Scalar> for U256

fn from(scalar: Scalar) -> U256

Performs the conversion.

impl From<Scalar> for FieldBytes

fn from(scalar: Scalar) -> Self

Performs the conversion.

impl From<ScalarCore<Secp256k1>> for Scalar

fn from(scalar: ScalarCore<Secp256k1>) -> Scalar

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 IsHigh for Scalar

fn is_high(&self) -> Choice

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

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 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 ==.

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

This method tests for !=.

impl PrimeField for Scalar

fn from_repr(bytes: FieldBytes) -> CtOption<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) -> Choice

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_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 Reduce<UInt<{_: usize}>> for Scalar

fn from_uint_reduced(w: U256) -> Self

Perform a modular reduction, returning a field element.

fn from_be_bytes_reduced(
    bytes: GenericArray<u8, <UInt as ArrayEncoding>::ByteSize>
) -> Self

Interpret the given byte array as a big endian integer and perform a modular reduction.

fn from_le_bytes_reduced(
    bytes: GenericArray<u8, <UInt as ArrayEncoding>::ByteSize>
) -> Self

Interpret the given byte array as a little endian integer and perform a modular reduction.

impl Reduce<UInt<{_: usize}>> for Scalar

fn from_uint_reduced(w: U512) -> Self

Perform a modular reduction, returning a field element.

fn from_be_bytes_reduced(
    bytes: GenericArray<u8, <UInt as ArrayEncoding>::ByteSize>
) -> Self

Interpret the given byte array as a big endian integer and perform a modular reduction.

fn from_le_bytes_reduced(
    bytes: GenericArray<u8, <UInt as ArrayEncoding>::ByteSize>
) -> Self

Interpret the given byte array as a little endian integer and perform a modular reduction.

impl ReduceNonZero<UInt<{_: usize}>> for Scalar

fn from_uint_reduced_nonzero(w: U256) -> Self

Perform a modular reduction, returning a field element.

impl ReduceNonZero<UInt<{_: usize}>> for Scalar

fn from_uint_reduced_nonzero(w: U512) -> Self

Perform a modular reduction, returning a field element.

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 SignPrimitive<Secp256k1> for Scalar

This is supported on crate feature ecdsa-core only.

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

Try to sign the prehashed message.

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 Copy for Scalar

impl DefaultIsZeroes for Scalar

impl Eq for Scalar