Struct NistP521 

pub struct NistP521;

NIST P-521 elliptic curve.

Trait Implementations

impl AssociatedOid for NistP521

Available on crate feature pkcs8 only.

const OID: ObjectIdentifier

The OID associated with this type.

impl Clone for NistP521

fn clone(&self) -> NistP521

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Curve for NistP521

const ORDER: Odd<Uint>

Order of NIST P-521’s elliptic curve group (i.e. scalar modulus).

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

66-byte serialized field elements.

type Uint = Uint<crypto_bigint::::uint::U576::{constant#0}>

521-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 NistP521

type AffinePoint = AffinePoint<NistP521>

Elliptic curve point in affine coordinates.

type ProjectivePoint = ProjectivePoint<NistP521>

Elliptic curve point in projective coordinates.

type Scalar = Scalar

Scalar field modulo this curve’s order.

impl Debug for NistP521

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

Formats the value using the given formatter.

impl Default for NistP521

fn default() -> NistP521

Returns the “default value” for a type.

impl DigestAlgorithm for NistP521

Available on crate feature sha512 only.

type Digest = Sha512

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 NistP521

const NORMALIZE_S: bool = false

Does this curve use low-S normalized signatures?

impl FieldArithmetic for NistP521

type FieldElement = FieldElement

Base field element type.

impl Mul<&<NistP521 as CurveArithmetic>::AffinePoint> for &Scalar

type Output = <NistP521 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: &AffinePoint<NistP521>) -> ProjectivePoint<NistP521>

Performs the * operation.

impl Mul<&<NistP521 as CurveArithmetic>::AffinePoint> for Scalar

type Output = <NistP521 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: &AffinePoint<NistP521>) -> ProjectivePoint<NistP521>

Performs the * operation.

impl Mul<&<NistP521 as CurveArithmetic>::ProjectivePoint> for &Scalar

type Output = <NistP521 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: &ProjectivePoint<NistP521>) -> ProjectivePoint<NistP521>

Performs the * operation.

impl Mul<&<NistP521 as CurveArithmetic>::ProjectivePoint> for Scalar

type Output = <NistP521 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: &ProjectivePoint<NistP521>) -> ProjectivePoint<NistP521>

Performs the * operation.

impl Mul<<NistP521 as CurveArithmetic>::AffinePoint> for &Scalar

type Output = <NistP521 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: AffinePoint<NistP521>) -> ProjectivePoint<NistP521>

Performs the * operation.

impl Mul<<NistP521 as CurveArithmetic>::AffinePoint> for Scalar

type Output = <NistP521 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: AffinePoint<NistP521>) -> ProjectivePoint<NistP521>

Performs the * operation.

impl Mul<<NistP521 as CurveArithmetic>::ProjectivePoint> for &Scalar

type Output = <NistP521 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: ProjectivePoint<NistP521>) -> ProjectivePoint<NistP521>

Performs the * operation.

impl Mul<<NistP521 as CurveArithmetic>::ProjectivePoint> for Scalar

type Output = <NistP521 as CurveArithmetic>::ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, rhs: ProjectivePoint<NistP521>) -> ProjectivePoint<NistP521>

Performs the * operation.

impl MulBackend<NistP521> 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<&<NistP521 as CurveArithmetic>::AffinePoint> for &Scalar

fn mul_vartime(self, rhs: &AffinePoint<NistP521>) -> ProjectivePoint<NistP521>

Multiply self by rhs in variable-time.

impl MulVartime<&<NistP521 as CurveArithmetic>::AffinePoint> for Scalar

fn mul_vartime(self, rhs: &AffinePoint<NistP521>) -> ProjectivePoint<NistP521>

Multiply self by rhs in variable-time.

impl MulVartime<&<NistP521 as CurveArithmetic>::ProjectivePoint> for &Scalar

fn mul_vartime( self, rhs: &ProjectivePoint<NistP521>, ) -> ProjectivePoint<NistP521>

Multiply self by rhs in variable-time.

impl MulVartime<&<NistP521 as CurveArithmetic>::ProjectivePoint> for Scalar

fn mul_vartime( self, rhs: &ProjectivePoint<NistP521>, ) -> ProjectivePoint<NistP521>

Multiply self by rhs in variable-time.

impl MulVartime<<NistP521 as CurveArithmetic>::AffinePoint> for &Scalar

fn mul_vartime(self, rhs: AffinePoint<NistP521>) -> ProjectivePoint<NistP521>

Multiply self by rhs in variable-time.

impl MulVartime<<NistP521 as CurveArithmetic>::AffinePoint> for Scalar

fn mul_vartime(self, rhs: AffinePoint<NistP521>) -> ProjectivePoint<NistP521>

Multiply self by rhs in variable-time.

impl MulVartime<<NistP521 as CurveArithmetic>::ProjectivePoint> for &Scalar

fn mul_vartime( self, rhs: ProjectivePoint<NistP521>, ) -> ProjectivePoint<NistP521>

Multiply self by rhs in variable-time.

impl MulVartime<<NistP521 as CurveArithmetic>::ProjectivePoint> for Scalar

fn mul_vartime( self, rhs: ProjectivePoint<NistP521>, ) -> ProjectivePoint<NistP521>

Multiply self by rhs in variable-time.

impl Ord for NistP521

fn cmp(&self, other: &NistP521) -> 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 NistP521

fn eq(&self, other: &NistP521) -> 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 NistP521

fn partial_cmp(&self, other: &NistP521) -> 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 NistP521

const COMPACT_POINTS: bool = false

NIST P-521 points are typically uncompacted.

impl PointCompression for NistP521

const COMPRESS_POINTS: bool = false

NIST P-521 points are typically uncompressed.

impl PrimeCurveArithmetic for NistP521

type CurveGroup = ProjectivePoint<NistP521>

Prime order elliptic curve group.

impl PrimeCurveParams for NistP521

Adapted from NIST SP 800-186 § 3.2.1.5: P-521.

const EQUATION_A: FieldElement

a = -3 (0x1ff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffc)

const EQUATION_B: FieldElement

b = 0x051 953eb961 8e1c9a1f 929a21a0 b68540ee a2da725b 99b315f3 b8b48991 8ef109e1 56193951 ec7e937b 1652c0bd 3bb1bf07 3573df88 3d2c34f1 ef451fd4 6b503f00

const GENERATOR: (FieldElement, FieldElement)

Base point of P-521.

Gₓ = 0x0c6 858e06b7 0404e9cd 9e3ecb66 2395b442 9c648139 053fb521
           f828af60 6b4d3dba a14b5e77 efe75928 fe1dc127 a2ffa8de
           3348b3c1 856a429b f97e7e31 c2e5bd66
Gᵧ = 0x118 39296a78 9a3bc004 5c8a5fb4 2c7d1bd9 98f54449 579b4468
           17afbd17 273e662c 97ee7299 5ef42640 c550b901 3fad0761
           353c7086 a272c240 88be9476 9fd16650

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 NistP521

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

Basepoint table for this curve.

impl Copy for NistP521

impl Eq for NistP521

impl PrimeCurve for NistP521

impl StructuralPartialEq for NistP521