Struct p256::Scalar

pub struct Scalar(_);

Available 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 p256::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 to_bytes(&self) -> FieldBytes

Returns the SEC1 encoding of this scalar.

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

Returns self + rhs mod n

pub const fn double(&self) -> Self

Returns 2*self.

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

Returns self - rhs mod n.

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

Returns self * rhs mod n

pub const fn square(&self) -> Self

Returns self * self mod p

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

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

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

Faster inversion using Stein’s algorithm

pub fn is_odd(&self) -> Choice

Is integer representing equivalence class odd?

pub fn is_even(&self) -> Choice

Is integer representing equivalence class even?

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 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 Borrow<Scalar> for BlindedScalar

fn borrow(&self) -> &Scalar

Immutably borrows from an owned value.

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<'de> Deserialize<'de> for Scalar

Available on crate feature serde only.

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>where
    D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

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) -> Selfwhere
    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

Converts to this type from the input type.

impl From<&Scalar> for ScalarBits

Available on crate feature bits only.

fn from(scalar: &Scalar) -> ScalarBits

Converts to this type from the input type.

impl From<&Scalar> for ScalarCore<NistP256>

fn from(scalar: &Scalar) -> ScalarCore<NistP256>

Converts to this type from the input type.

impl From<&Scalar> for U256

fn from(scalar: &Scalar) -> U256

Converts to this type from the input type.

impl From<&ScalarCore<NistP256>> for Scalar

fn from(scalar: &ScalarCore<NistP256>) -> Scalar

Converts to this type from the input type.

impl From<&SecretKey<NistP256>> for Scalar

fn from(secret_key: &SecretKey) -> Scalar

Converts to this type from the input type.

impl From<Scalar> for FieldBytes

fn from(scalar: Scalar) -> Self

Converts to this type from the input type.

impl From<Scalar> for ScalarCore<NistP256>

fn from(scalar: Scalar) -> ScalarCore<NistP256>

Converts to this type from the input type.

impl From<Scalar> for U256

fn from(scalar: Scalar) -> U256

Converts to this type from the input type.

impl From<ScalarCore<NistP256>> for Scalar

fn from(scalar: ScalarCore<NistP256>) -> Scalar

Converts to this type from the input type.

impl From<u128> for Scalar

fn from(k: u128) -> Self

Converts to this type from the input type.

impl From<u32> for Scalar

fn from(k: u32) -> Self

Converts to this type from the input type.

impl From<u64> for Scalar

fn from(k: u64) -> Self

Converts to this type from the input type.

impl FromOkm for Scalar

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 IsHigh for Scalar

fn is_high(&self) -> Choice

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

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 Scalar

type Output = Scalar

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign<&Scalar> for Scalar

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<'a> Neg for &'a 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 Ord for Scalar

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Selfwhere
    Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Selfwhere
    Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Selfwhere
    Self: Sized + PartialOrd<Self>,

Restrict a value to a certain interval.

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 !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd<Scalar> for Scalar

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

This method tests less than (for self and other) and is used by the < operator.

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

This method tests less than or equal to (for self and other) and is used by the <= operator.

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

This method tests greater than (for self and other) and is used by the > operator.

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

This method tests greater than or equal to (for self and other) and is used by the >= operator.

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 = GenericArray<u8, <<NistP256 as Curve>::UInt as ArrayEncoding>::ByteSize>

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

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 S: u32 = 4u32

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 PrimeFieldBits for Scalar

Available on crate feature bits only.

type ReprBits = [u64; 4]

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

fn to_le_bits(&self) -> ScalarBits

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

fn char_le_bits() -> ScalarBits

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

impl Reduce<UInt<_>> 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.

fn from_be_digest_reduced<D>(digest: D) -> Selfwhere
    D: FixedOutput<OutputSize = <UInt as ArrayEncoding>::ByteSize>,

Available on crate feature digest only.

Interpret a digest as a big endian integer and perform a modular reduction.

fn from_le_digest_reduced<D>(digest: D) -> Selfwhere
    D: FixedOutput<OutputSize = <UInt as ArrayEncoding>::ByteSize>,

Available on crate feature digest only.

Interpret a digest as a little endian integer and perform a modular reduction.

impl ReduceNonZero<UInt<_>> for Scalar

fn from_uint_reduced_nonzero(w: U256) -> Self

Perform a modular reduction, returning a field element.

impl Serialize for Scalar

Available on crate feature serde only.

fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>where
    S: Serializer,

Serialize this value into the given Serde serializer.

impl SignPrimitive<NistP256> for Scalar

Available on crate features ecdsa-core and ecdsa only.

fn try_sign_prehashed<K>(
    &self,
    k: K,
    z: GenericArray<u8, <<C as Curve>::UInt as ArrayEncoding>::ByteSize>
) -> Result<(Signature<C>, Option<RecoveryId>), Error>where
    K: Borrow<Self> + Invert<Output = CtOption<Self>>,

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