Struct NistP256 

pub struct NistP256;

NIST P-256 elliptic curve.

This curve is also known as prime256v1 (ANSI X9.62) and secp256r1 (SECG) and is specified in NIST SP 800-186: Recommendations for Discrete Logarithm-based Cryptography: Elliptic Curve Domain Parameters.

It’s included in the US National Security Agency’s “Suite B” and is widely used in protocols like TLS and the associated X.509 PKI.

Its equation is y² = x³ - 3x + b over a ~256-bit prime field where b is the “verifiably random”† constant:

b = 41058363725152142129326129780047268409114441015993725554835256314039467401291

† NOTE: the specific origins of this constant have never been fully disclosed (it is the SHA-1 digest of an unknown NSA-selected constant)

Trait Implementations

impl AssociatedOid for NistP256

Available on crate feature pkcs8 only.

const OID: ObjectIdentifier

The OID associated with this type.

impl Clone for NistP256

fn clone(&self) -> NistP256

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Curve for NistP256

const ORDER: Odd<U256>

Order of NIST P-256’s elliptic curve group (i.e. scalar modulus).

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

32-byte serialized field elements.

type Uint = Uint<crypto_bigint::::uint::U256::{constant#0}>

256-bit integer type used for internally representing field elements.

const FIELD_ENDIANNESS: ByteOrder = ByteOrder::BigEndian

Endianness used for serializing field elements of this curve.

impl CurveArithmetic for NistP256

type AffinePoint = AffinePoint<NistP256>

Elliptic curve point in affine coordinates.

type ProjectivePoint = ProjectivePoint<NistP256>

Elliptic curve point in projective coordinates.

type Scalar = Scalar

Scalar field modulo this curve’s order.

impl Debug for NistP256

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

Formats the value using the given formatter.

impl Default for NistP256

fn default() -> NistP256

Returns the “default value” for a type.

impl DigestAlgorithm for NistP256

Available on crate feature sha256 only.

type Digest = Sha256

Preferred digest to use when computing ECDSA signatures for this elliptic curve. This is typically a member of the SHA-2 family.

impl EcdsaCurve for NistP256

const NORMALIZE_S: bool = false

Does this curve use low-S normalized signatures?

impl FieldArithmetic for NistP256

type FieldElement = FieldElement

Base field element type.

impl Mul<&<NistP256 as CurveArithmetic>::AffinePoint> for &Scalar

type Output = <NistP256 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: &AffinePoint<NistP256>) -> ProjectivePoint<NistP256>

Performs the * operation.

impl Mul<&<NistP256 as CurveArithmetic>::AffinePoint> for Scalar

type Output = <NistP256 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: &AffinePoint<NistP256>) -> ProjectivePoint<NistP256>

Performs the * operation.

impl Mul<&<NistP256 as CurveArithmetic>::ProjectivePoint> for &Scalar

type Output = <NistP256 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: &ProjectivePoint<NistP256>) -> ProjectivePoint<NistP256>

Performs the * operation.

impl Mul<&<NistP256 as CurveArithmetic>::ProjectivePoint> for Scalar

type Output = <NistP256 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: &ProjectivePoint<NistP256>) -> ProjectivePoint<NistP256>

Performs the * operation.

impl Mul<<NistP256 as CurveArithmetic>::AffinePoint> for &Scalar

type Output = <NistP256 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: AffinePoint<NistP256>) -> ProjectivePoint<NistP256>

Performs the * operation.

impl Mul<<NistP256 as CurveArithmetic>::AffinePoint> for Scalar

type Output = <NistP256 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: AffinePoint<NistP256>) -> ProjectivePoint<NistP256>

Performs the * operation.

impl Mul<<NistP256 as CurveArithmetic>::ProjectivePoint> for &Scalar

type Output = <NistP256 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: ProjectivePoint<NistP256>) -> ProjectivePoint<NistP256>

Performs the * operation.

impl Mul<<NistP256 as CurveArithmetic>::ProjectivePoint> for Scalar

type Output = <NistP256 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: ProjectivePoint<NistP256>) -> ProjectivePoint<NistP256>

Performs the * operation.

impl MulBackend<NistP256> for PrecomputedTables

fn mul_by_generator(k: &Scalar) -> ProjectivePoint

Multiplication by the generator.

fn mul_by_generator_vartime(k: &Scalar) -> ProjectivePoint

Variable-time multiplication by the generator.

fn mul_by_generator_and_mul_add_vartime( a: &<C as CurveArithmetic>::Scalar, b_scalar: &<C as CurveArithmetic>::Scalar, b_point: &ProjectivePoint<C>, ) -> ProjectivePoint<C>

Multiply a by the generator of the prime-order subgroup, adding the result to the point P multiplied by the scalar b, i.e. compute aG + bP.

impl MulVartime<&<NistP256 as CurveArithmetic>::AffinePoint> for &Scalar

fn mul_vartime(self, rhs: &AffinePoint<NistP256>) -> ProjectivePoint<NistP256>

Multiply self by rhs in variable-time.

impl MulVartime<&<NistP256 as CurveArithmetic>::AffinePoint> for Scalar

fn mul_vartime(self, rhs: &AffinePoint<NistP256>) -> ProjectivePoint<NistP256>

Multiply self by rhs in variable-time.

impl MulVartime<&<NistP256 as CurveArithmetic>::ProjectivePoint> for &Scalar

fn mul_vartime( self, rhs: &ProjectivePoint<NistP256>, ) -> ProjectivePoint<NistP256>

Multiply self by rhs in variable-time.

impl MulVartime<&<NistP256 as CurveArithmetic>::ProjectivePoint> for Scalar

fn mul_vartime( self, rhs: &ProjectivePoint<NistP256>, ) -> ProjectivePoint<NistP256>

Multiply self by rhs in variable-time.

impl MulVartime<<NistP256 as CurveArithmetic>::AffinePoint> for &Scalar

fn mul_vartime(self, rhs: AffinePoint<NistP256>) -> ProjectivePoint<NistP256>

Multiply self by rhs in variable-time.

impl MulVartime<<NistP256 as CurveArithmetic>::AffinePoint> for Scalar

fn mul_vartime(self, rhs: AffinePoint<NistP256>) -> ProjectivePoint<NistP256>

Multiply self by rhs in variable-time.

impl MulVartime<<NistP256 as CurveArithmetic>::ProjectivePoint> for &Scalar

fn mul_vartime( self, rhs: ProjectivePoint<NistP256>, ) -> ProjectivePoint<NistP256>

Multiply self by rhs in variable-time.

impl MulVartime<<NistP256 as CurveArithmetic>::ProjectivePoint> for Scalar

fn mul_vartime( self, rhs: ProjectivePoint<NistP256>, ) -> ProjectivePoint<NistP256>

Multiply self by rhs in variable-time.

impl Ord for NistP256

fn cmp(&self, other: &NistP256) -> Ordering

This method returns an Ordering between self and other.

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

where Self: Sized,

Compares and returns the maximum of two values.

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

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl PartialEq for NistP256

fn eq(&self, other: &NistP256) -> bool

Tests for self and other values to be equal, and is used by ==.

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

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

impl PartialOrd for NistP256

fn partial_cmp(&self, other: &NistP256) -> Option<Ordering>

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

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

Tests less than (for self and other) and is used by the < operator.

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

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

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

Tests greater than (for self and other) and is used by the > operator.

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

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

impl PointCompaction for NistP256

const COMPACT_POINTS: bool = false

NIST P-256 points are typically uncompressed.

impl PointCompression for NistP256

const COMPRESS_POINTS: bool = false

NIST P-256 points are typically uncompressed.

impl PrimeCurveArithmetic for NistP256

type CurveGroup = ProjectivePoint<NistP256>

Prime order elliptic curve group.

impl PrimeCurveParams for NistP256

Adapted from NIST SP 800-186 § G.1.2: Curve P-256.

const EQUATION_A: FieldElement

a = -3

const GENERATOR: (FieldElement, FieldElement)

Base point of P-256.

Defined in NIST SP 800-186 § G.1.2:

Gₓ = 6b17d1f2 e12c4247 f8bce6e5 63a440f2 77037d81 2deb33a0 f4a13945 d898c296
Gᵧ = 4fe342e2 fe1a7f9b 8ee7eb4a 7c0f9e16 2bce3357 6b315ece cbb64068 37bf51f5

const EQUATION_B: FieldElement

Coefficient b in the curve equation.

type PointArithmetic = EquationAIsMinusThree

Point arithmetic implementation, might be optimized for this specific curve

type Backend = PrecomputedTables

Scalar arithmetic backend implementation.

impl PrimeCurveWithBasepointTable<WINDOW_SIZE> for NistP256

const BASEPOINT_TABLE: &'static BasepointTable<ProjectivePoint, WINDOW_SIZE>

Basepoint table for this curve.

impl Copy for NistP256

impl Eq for NistP256

impl PrimeCurve for NistP256

impl StructuralPartialEq for NistP256