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Struct p256::NistP256

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pub struct NistP256;
Expand description

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)

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impl AssociatedOid for NistP256

Available on crate feature pkcs8 only.
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const OID: ObjectIdentifier = _

The OID associated with this type.
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impl Clone for NistP256

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fn clone(&self) -> NistP256

Returns a copy of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl Curve for NistP256

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

32-byte serialized field elements.

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

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

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const ORDER: U256 = _

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

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impl CurveArithmetic for NistP256

Available on crate feature arithmetic only.
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type AffinePoint = AffinePoint<NistP256>

Elliptic curve point in affine coordinates.
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type ProjectivePoint = ProjectivePoint<NistP256>

Elliptic curve point in projective coordinates. Read more
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type Scalar = Scalar

Scalar field modulo this curve’s order. Read more
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impl Debug for NistP256

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

Formats the value using the given formatter. Read more
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impl Default for NistP256

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fn default() -> NistP256

Returns the “default value” for a type. Read more
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impl DigestPrimitive for NistP256

Available on crate features ecdsa-core and sha256 only.
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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.
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impl FieldBytesEncoding<NistP256> for U256

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fn decode_field_bytes(field_bytes: &FieldBytes) -> Self

Decode unsigned integer from serialized field element. Read more
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fn encode_field_bytes(&self) -> FieldBytes

Encode unsigned integer into serialized field element. Read more
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impl GroupDigest for NistP256

Available on crate features hash2curve and arithmetic only.
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type FieldElement = FieldElement

The field element representation for a group value with multiple elements
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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. Read more
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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. Read more
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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. Read more
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impl JwkParameters for NistP256

Available on crate feature jwk only.
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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 Read more
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impl Ord for NistP256

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

This method returns an Ordering between self and other. Read more
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fn max(self, other: Self) -> Selfwhere Self: Sized,

Compares and returns the maximum of two values. Read more
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fn min(self, other: Self) -> Selfwhere Self: Sized,

Compares and returns the minimum of two values. Read more
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fn clamp(self, min: Self, max: Self) -> Selfwhere Self: Sized + PartialOrd<Self>,

Restrict a value to a certain interval. Read more
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impl PartialEq<NistP256> for NistP256

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

This method tests for self and other values to be equal, and is used by ==.
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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.
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impl PartialOrd<NistP256> for NistP256

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

This method returns an ordering between self and other values if one exists. Read more
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fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator. Read more
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fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more
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fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator. Read more
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fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more
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impl PointCompaction for NistP256

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const COMPACT_POINTS: bool = false

NIST P-256 points are typically uncompressed.

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impl PointCompression for NistP256

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const COMPRESS_POINTS: bool = false

NIST P-256 points are typically uncompressed.

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impl PrimeCurveArithmetic for NistP256

Available on crate feature arithmetic only.
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type CurveGroup = ProjectivePoint<NistP256>

Prime order elliptic curve group.
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impl PrimeCurveParams for NistP256

Available on crate feature arithmetic only.

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

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const EQUATION_A: FieldElement = _

a = -3

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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
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type FieldElement = FieldElement

Base field element type.
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type PointArithmetic = EquationAIsMinusThree

Point arithmetic implementation, might be optimized for this specific curve
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const EQUATION_B: FieldElement = _

Coefficient b in the curve equation.
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impl SignPrimitive<NistP256> for Scalar

Available on crate features ecdsa-core and ecdsa only.
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fn try_sign_prehashed<K>( &self, k: K, z: &GenericArray<u8, <C as Curve>::FieldBytesSize> ) -> Result<(Signature<C>, Option<RecoveryId>), Error>where K: AsRef<Self> + Invert<Output = CtOption<Self>>,

Try to sign the prehashed message. Read more
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fn try_sign_prehashed_rfc6979<D>( &self, z: &GenericArray<u8, <C as Curve>::FieldBytesSize>, ad: &[u8] ) -> Result<(Signature<C>, Option<RecoveryId>), Error>where Self: From<ScalarPrimitive<C>> + Invert<Output = CtOption<Self>>, D: Digest<OutputSize = <C as Curve>::FieldBytesSize> + BlockSizeUser + FixedOutput + FixedOutputReset,

Available on crate feature rfc6979 only.
Try to sign the given message digest deterministically using the method described in RFC6979 for computing ECDSA ephemeral scalar k. Read more
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impl VerifyPrimitive<NistP256> for AffinePoint

Available on crate features ecdsa-core and ecdsa only.
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fn verify_prehashed( &self, z: &GenericArray<u8, <C as Curve>::FieldBytesSize>, sig: &Signature<C> ) -> Result<(), Error>

Verify the prehashed message against the provided signature Read more
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fn verify_digest<D>( &self, msg_digest: D, sig: &Signature<C> ) -> Result<(), Error>where D: FixedOutput<OutputSize = <C as Curve>::FieldBytesSize>,

Available on crate feature digest only.
Verify message digest against the provided signature.
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impl VoprfParameters for NistP256

Available on crate feature voprf only.
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const ID: &'static str = "P256-SHA256"

See https://www.ietf.org/archive/id/draft-irtf-cfrg-voprf-19.html#section-4.3.

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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.

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impl Copy for NistP256

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impl Eq for NistP256

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impl PrimeCurve for NistP256

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impl StructuralEq for NistP256

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impl StructuralPartialEq for NistP256

Auto Trait Implementations§

Blanket Implementations§

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impl<T> Any for Twhere T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for Twhere T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for Twhere T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<T> Conv for T

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fn conv<T>(self) -> Twhere Self: Into<T>,

Converts self into T using Into<T>. Read more
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impl<T> DynAssociatedOid for Twhere T: AssociatedOid,

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fn oid(&self) -> ObjectIdentifier

Get the OID associated with this value.
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impl<T> FmtForward for T

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fn fmt_binary(self) -> FmtBinary<Self>where Self: Binary,

Causes self to use its Binary implementation when Debug-formatted.
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fn fmt_display(self) -> FmtDisplay<Self>where Self: Display,

Causes self to use its Display implementation when Debug-formatted.
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fn fmt_lower_exp(self) -> FmtLowerExp<Self>where Self: LowerExp,

Causes self to use its LowerExp implementation when Debug-formatted.
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fn fmt_lower_hex(self) -> FmtLowerHex<Self>where Self: LowerHex,

Causes self to use its LowerHex implementation when Debug-formatted.
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fn fmt_octal(self) -> FmtOctal<Self>where Self: Octal,

Causes self to use its Octal implementation when Debug-formatted.
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fn fmt_pointer(self) -> FmtPointer<Self>where Self: Pointer,

Causes self to use its Pointer implementation when Debug-formatted.
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fn fmt_upper_exp(self) -> FmtUpperExp<Self>where Self: UpperExp,

Causes self to use its UpperExp implementation when Debug-formatted.
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fn fmt_upper_hex(self) -> FmtUpperHex<Self>where Self: UpperHex,

Causes self to use its UpperHex implementation when Debug-formatted.
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fn fmt_list(self) -> FmtList<Self>where &'a Self: for<'a> IntoIterator,

Formats each item in a sequence. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for Twhere U: From<T>,

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fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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fn pipe<R>(self, func: impl FnOnce(Self) -> R) -> Rwhere Self: Sized,

Pipes by value. This is generally the method you want to use. Read more
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Borrows self and passes that borrow into the pipe function. Read more
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Mutably borrows self and passes that borrow into the pipe function. Read more
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Borrows self, then passes self.borrow() into the pipe function. Read more
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Mutably borrows self, then passes self.deref_mut() into the pipe function.
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type Output = T

Should always be Self
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impl<T> Tap for T

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fn tap(self, func: impl FnOnce(&Self)) -> Self

Immutable access to a value. Read more
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Mutable access to a value. Read more
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impl<C> ValidatePublicKey for Cwhere C: CurveArithmetic, <C as CurveArithmetic>::AffinePoint: FromEncodedPoint<C> + ToEncodedPoint<C>, <C as Curve>::FieldBytesSize: ModulusSize,

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fn validate_public_key( secret_key: &SecretKey<C>, public_key: &EncodedPoint<<C as Curve>::FieldBytesSize> ) -> Result<(), Error>

Validate that the given EncodedPoint is a valid public key for the provided secret value.