Struct P256 

pub struct P256;

NIST-P256. 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 duplicate of the value.

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

Performs copy-assignment from source.

impl Curve for NistP256

const ORDER: Uint<crypto_bigint::::uint::U256::{constant#0}>

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.

impl Curve for NistP256

type ScalarSize = <Secp256r1 as Curve>::ScalarSize

The size in bytes of a scalar.

type CompressedSize = <Secp256r1 as Curve>::CompressedSize

The size in bytes of a compressed point.

type UncompressedSize = <Secp256r1 as Curve>::UncompressedSize

The size in bytes of a uncompressed point.

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<(), Error>

Formats the value using the given formatter.

impl Default for NistP256

fn default() -> NistP256

Returns the “default value” for a type.

impl DigestPrimitive for NistP256

Available on crate feature sha256 only.

type Digest = CoreWrapper<CtVariableCoreWrapper<Sha256VarCore, UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, OidSha256>>

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

impl Ecdh for P256

const SCALAR_SIZE: usize = <<P256 as Curve>::ScalarSize>::USIZE

The size in bytes of a scalar.

type PrivateKey = P256PrivateKey

An ECDH private key.

type PublicKey = P256PublicKey

An ECDH public key.

type SharedSecret = SharedSecret<NistP256>

The shared secret (Diffie-Hellman value) computed as the result of the key exchange (Self::ecdh).

fn ecdh( local: &Self::PrivateKey, remote: &Self::PublicKey, ) -> Result<Self::SharedSecret, EcdhError>

Performs ECDH with the local secret key and remote public key.

impl Identified for NistP256

const OID: &'static Oid = SECP256R1

The algorithm’s OID.

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 FieldElement = FieldElement

Base field element type.

type PointArithmetic = EquationAIsMinusThree

Point arithmetic implementation, might be optimized for this specific curve

impl Signature<NistP256> for P256Signature

type Data = SigBytes<Signature<NistP256>>

The fixed-length byte encoding of the signature.

fn export(&self) -> Self::Data

Returns the byte encoding of the signature.

impl Signer for P256

type SigningKey = P256SigningKey

A private key used to create signatures.

type VerifyingKey = P256VerifyingKey

A public key used verify signatures.

type Signature = P256Signature

A digital signature.

fn verify_batch( msgs: &[&[u8]], sigs: &[Self::Signature], pks: &[Self::VerifyingKey], ) -> Result<(), SignerError>

Verifies all (message, signature, verifying key) tuples as a batch.

impl SigningKey<NistP256> for P256SigningKey

fn sign(&self, msg: &[u8]) -> Result<P256Signature, SignerError>

Returns the signature over msg, which must NOT be pre-hashed.

fn public(&self) -> Result<P256VerifyingKey, PkError>

Returns the public half of the key.

impl VerifyingKey<NistP256> for P256VerifyingKey

fn verify(&self, msg: &[u8], sig: &P256Signature) -> Result<(), SignerError>

Reports whether the signature over msg is valid.

impl Copy for NistP256

impl Eq for NistP256

impl PrimeCurve for NistP256

impl StructuralPartialEq for NistP256