Struct p256::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 Clone for NistP256

fn clone(&self) -> NistP256

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Curve for NistP256

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 ORDER: U256 = _

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

impl CurveArithmetic for NistP256

Available on crate feature arithmetic only.

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 FieldBytesEncoding<NistP256> for U256

fn decode_field_bytes(field_bytes: &FieldBytes) -> Self

Decode unsigned integer from serialized field element.

fn encode_field_bytes(&self) -> FieldBytes

Encode unsigned integer into serialized field element.

impl GroupDigest for NistP256

Available on crate features hash2curve and arithmetic only.

type FieldElement = FieldElement

The field element representation for a group value with multiple elements

fn hash_from_bytes<'a, X>( msgs: &[&[u8]], dsts: &'a [&'a [u8]], ) -> Result<Self::ProjectivePoint, Error>

where X: ExpandMsg<'a>,

Computes the hash to curve routine.

fn encode_from_bytes<'a, X>( msgs: &[&[u8]], dsts: &'a [&'a [u8]], ) -> Result<Self::ProjectivePoint, Error>

where X: ExpandMsg<'a>,

Computes the encode to curve routine.

fn hash_to_scalar<'a, X>( msgs: &[&[u8]], dsts: &'a [&'a [u8]], ) -> Result<Self::Scalar, Error>

where X: ExpandMsg<'a>, Self::Scalar: FromOkm,

Computes the hash to field routine according to https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-13.html#section-5 and returns a scalar.

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 + PartialOrd,

Restrict a value to a certain interval.

impl PartialEq for NistP256

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

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 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

Available on crate feature arithmetic only.

type CurveGroup = ProjectivePoint<NistP256>

Prime order elliptic curve group.

impl PrimeCurveParams for NistP256

Available on crate feature arithmetic only.

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

type FieldElement = FieldElement

Base field element type.

type PointArithmetic = EquationAIsMinusThree

Point arithmetic implementation, might be optimized for this specific curve

const EQUATION_B: FieldElement = _

Coefficient b in the curve equation.

impl Copy for NistP256

impl Eq for NistP256

impl PrimeCurve for NistP256

impl StructuralPartialEq for NistP256