Struct curve25519_dalek::curve::ExtendedPoint

pub struct ExtendedPoint {
    pub X: FieldElement,
    pub Y: FieldElement,
    pub Z: FieldElement,
    pub T: FieldElement,
}

An ExtendedPoint is a point on the curve in 𝗣³(𝔽ₚ). A point (x,y) in the affine model corresponds to (x:y:1:xy).

Fields

X: FieldElement

Y: FieldElement

Z: FieldElement

T: FieldElement

Methods

impl ExtendedPoint

fn to_projective_niels(&self) -> ProjectiveNielsPoint

Convert to a ProjectiveNielsPoint

fn to_affine_niels(&self) -> AffineNielsPoint

Dehomogenize to a AffineNielsPoint. Mainly for testing.

fn compress_edwards(&self) -> CompressedEdwardsY

Compress this point to CompressedEdwardsY format.

fn compress_montgomery(&self) -> Option<CompressedMontgomeryU>

Convert this point to a CompressedMontgomeryU. Note that this discards the sign.

Return

• None if self is the identity point;
• Some(CompressedMontgomeryU) otherwise.

impl ExtendedPoint

fn double(&self) -> ExtendedPoint

Add this point to itself.

impl ExtendedPoint

fn mult_by_cofactor(&self) -> ExtendedPoint

Multiply by the cofactor: compute 8 * self.

Convenience wrapper around mult_by_pow_2.

fn mult_by_pow_2(&self, k: u32) -> ExtendedPoint

Compute 2^k * self by successive doublings. Requires k > 0.

fn is_small_order(&self) -> bool

Determine if this point is of small order.

The order of the group of points on the curve Ɛ is |Ɛ| = 8q. Thus, to check if a point P is of small order, we multiply by 8 and then test if the result is equal to the identity.

Return

True if it is of small order; false otherwise.

impl ExtendedPoint

fn to_uniform_representative(&self) -> Option<[u8; 32]>

Use Elligator2 to try to convert self to a uniformly random string.

Returns Some<[u8;32]> if self is in the image of the Elligator2 map. For a random point on the curve, this happens with probability 1/2. Otherwise, returns None.

fn from_uniform_representative(bytes: &[u8; 32]) -> ExtendedPoint

Use Elligator2 to convert a uniformly random string to a curve point.

Trait Implementations

impl Copy for ExtendedPoint

impl Clone for ExtendedPoint

fn clone(&self) -> ExtendedPoint

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Identity for ExtendedPoint

fn identity() -> ExtendedPoint

Returns the identity element of the curve. Can be used as a constructor.

impl ValidityCheck for ExtendedPoint

fn is_valid(&self) -> bool

Checks whether the point is on the curve. Not CT.

impl CTEq for ExtendedPoint

fn ct_eq(&self, other: &ExtendedPoint) -> u8

Determine if two items are equal in constant time.

impl<'a, 'b> Add<&'b ProjectiveNielsPoint> for &'a ExtendedPoint

type Output = CompletedPoint

The resulting type after applying the + operator

fn add(self, other: &'b ProjectiveNielsPoint) -> CompletedPoint

The method for the + operator

impl<'a, 'b> Sub<&'b ProjectiveNielsPoint> for &'a ExtendedPoint

type Output = CompletedPoint

The resulting type after applying the - operator

fn sub(self, other: &'b ProjectiveNielsPoint) -> CompletedPoint

The method for the - operator

impl<'a, 'b> Add<&'b AffineNielsPoint> for &'a ExtendedPoint

type Output = CompletedPoint

The resulting type after applying the + operator

fn add(self, other: &'b AffineNielsPoint) -> CompletedPoint

The method for the + operator

impl<'a, 'b> Sub<&'b AffineNielsPoint> for &'a ExtendedPoint

type Output = CompletedPoint

The resulting type after applying the - operator

fn sub(self, other: &'b AffineNielsPoint) -> CompletedPoint

The method for the - operator

impl<'a, 'b> Add<&'b ExtendedPoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the + operator

fn add(self, other: &'b ExtendedPoint) -> ExtendedPoint

The method for the + operator

impl<'a, 'b> Sub<&'b ExtendedPoint> for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator

fn sub(self, other: &'b ExtendedPoint) -> ExtendedPoint

The method for the - operator

impl<'a> Neg for &'a ExtendedPoint

type Output = ExtendedPoint

The resulting type after applying the - operator

fn neg(self) -> ExtendedPoint

The method for the unary - operator

impl ScalarMult<Scalar> for ExtendedPoint

fn scalar_mult(&self, scalar: &Scalar) -> ExtendedPoint

Scalar multiplication: compute scalar * self.

Uses a window of size 4. Note: for scalar multiplication of the basepoint, basepoint_mult is approximately 4x faster.

impl BasepointMult<Scalar> for ExtendedPoint

fn basepoint() -> ExtendedPoint

Return the basepoint B.

fn basepoint_mult(scalar: &Scalar) -> ExtendedPoint

Compute scalar * B.

impl Debug for ExtendedPoint

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

Formats the value using the given formatter.