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 FIPS 186-4: Digital Signature Standard (DSS):

https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf

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 inexplicable NSA-selected constant)

Trait Implementations

impl AffineArithmetic for NistP256

Available on crate feature arithmetic only.

type AffinePoint = AffinePoint<NistP256>

Elliptic curve point in affine coordinates.

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 copy of the value.

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

Performs copy-assignment from source.

impl Curve for NistP256

type UInt = UInt<_>

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).

n = FFFFFFFF 00000000 FFFFFFFF FFFFFFFF BCE6FAAD A7179E84 F3B9CAC2 FC632551

Calculating the order

One way to calculate the order is with GP/PARI:

p = (2^224) * (2^32 - 1) + 2^192 + 2^96 - 1
b = 41058363725152142129326129780047268409114441015993725554835256314039467401291
E = ellinit([Mod(-3, p), Mod(b, p)])
default(parisize, 120000000)
n = ellsea(E)
isprime(n)

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 DigestPrimitive for NistP256

Available on crate features ecdsa-core and 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 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]],
    dst: &'a [u8]
) -> Result<Self::ProjectivePoint, Error>where
    X: ExpandMsg<'a>,

Computes the hash to curve routine.

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

Computes the encode to curve routine.

impl JwkParameters for NistP256

Available on crate feature jwk only.

const CRV: &'static str = "P-256"

The crv parameter which identifies a particular elliptic curve as defined in RFC 7518 Section 6.2.1.1: https://tools.ietf.org/html/rfc7518#section-6.2.1.1

impl Ord for NistP256

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

const EQUATION_A: FieldElement = _

a = -3

const GENERATOR: (FieldElement, FieldElement) = _

Base point of P-256.

Defined in FIPS 186-4 § D.1.2.3:

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.

const ZERO: FieldElement = FieldElement::ZERO

Zero element of the base field.

const ONE: FieldElement = FieldElement::ONE

Multiplicative identity of the base field.

const EQUATION_B: FieldElement = _

Coefficient b in the curve equation.

impl ProjectiveArithmetic for NistP256

Available on crate feature arithmetic only.

type ProjectivePoint = ProjectivePoint<NistP256>

Elliptic curve point in projective coordinates.

impl ScalarArithmetic for NistP256

Available on crate feature arithmetic only.

type Scalar = Scalar

Scalar field type.

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 VerifyPrimitive<NistP256> for AffinePoint

Available on crate features ecdsa-core and ecdsa only.

fn verify_prehashed(
    &self,
    z: GenericArray<u8, <<C as Curve>::UInt as ArrayEncoding>::ByteSize>,
    sig: &Signature<C>
) -> Result<(), Error>

Verify the prehashed message against the provided signature

fn verify_digest<D>(&self, msg_digest: D, sig: &Signature<C>) -> Result<(), Error>where
    D: FixedOutput<OutputSize = <<C as Curve>::UInt as ArrayEncoding>::ByteSize>,

Available on crate feature digest only.

Verify message digest against the provided signature.

impl VoprfParameters for NistP256

Available on crate feature voprf only.

const ID: u16 = 3u16

See https://www.ietf.org/archive/id/draft-irtf-cfrg-voprf-08.html#section-4.3-1.3.

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

See https://www.ietf.org/archive/id/draft-irtf-cfrg-voprf-08.html#section-4.3-1.2.

impl Copy for NistP256

impl Eq for NistP256

impl PrimeCurve for NistP256

impl StructuralEq for NistP256

impl StructuralPartialEq for NistP256