Struct EdwardsPoint 

pub struct EdwardsPoint {
    pub(crate) X: FieldElement,
    pub(crate) Y: FieldElement,
    pub(crate) Z: FieldElement,
    pub(crate) T: FieldElement,
}

Represent points on the (untwisted) edwards curve using Extended Homogenous Projective Co-ordinates (x, y) -> (X/Z, Y/Z, Z, T) a = 1, d = -39081 XXX: Make this more descriptive Should this be renamed to EdwardsPoint so that we are consistent with Dalek crypto? Necessary as ExtendedPoint is not regular lingo?

Fields

X: FieldElement

Y: FieldElement

Z: FieldElement

T: FieldElement

Implementations

impl EdwardsPoint

pub const GENERATOR: Self = GOLDILOCKS_BASE_POINT

Generator for the prime subgroup

pub const IDENTITY: Self

Identity point

pub fn to_montgomery(&self) -> MontgomeryPoint

Convert this point to MontgomeryPoint

pub fn scalar_mul(&self, scalar: &EdwardsScalar) -> Self

Generic scalar multiplication to compute s*P

pub fn add(&self, other: &EdwardsPoint) -> Self

Add two points

pub fn double(&self) -> Self

Double this point

pub fn is_on_curve(&self) -> Choice

Check if this point is on the curve

pub fn to_affine(&self) -> AffinePoint

Convert this point to an AffinePoint.

pub(crate) fn to_twisted(self) -> TwistedExtensiblePoint

pub fn negate(&self) -> Self

Compute the negation of this point’s x-coordinate.

pub fn torque(&self) -> Self

Compute the negation of this point’s y-coordinate.

pub fn is_torsion_free(&self) -> Choice

Determine if this point is “torsion-free”, i.e., is contained in the prime-order subgroup.

Return

• true if self has zero torsion component and is in the prime-order subgroup;
• false if self has a nonzero torsion component and is not in the prime-order subgroup.

Trait Implementations

impl Add<&AffinePoint> for &EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the + operator.

fn add(self, other: &AffinePoint) -> EdwardsPoint

Performs the + operation.

impl<'b> Add<&'b AffinePoint> for EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the + operator.

fn add(self, rhs: &'b AffinePoint) -> EdwardsPoint

Performs the + operation.

impl Add<&EdwardsPoint> for &AffinePoint

type Output = EdwardsPoint

The resulting type after applying the + operator.

fn add(self, other: &EdwardsPoint) -> EdwardsPoint

Performs the + operation.

impl Add<&EdwardsPoint> for &EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the + operator.

fn add(self, other: &EdwardsPoint) -> EdwardsPoint

Performs the + operation.

impl<'b> Add<&'b EdwardsPoint> for AffinePoint

type Output = EdwardsPoint

The resulting type after applying the + operator.

fn add(self, rhs: &'b EdwardsPoint) -> EdwardsPoint

Performs the + operation.

impl<'b> Add<&'b EdwardsPoint> for EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the + operator.

fn add(self, rhs: &'b EdwardsPoint) -> EdwardsPoint

Performs the + operation.

impl<'a> Add<AffinePoint> for &'a EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the + operator.

fn add(self, rhs: AffinePoint) -> EdwardsPoint

Performs the + operation.

impl Add<AffinePoint> for EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the + operator.

fn add(self, rhs: AffinePoint) -> EdwardsPoint

Performs the + operation.

impl<'a> Add<EdwardsPoint> for &'a AffinePoint

type Output = EdwardsPoint

The resulting type after applying the + operator.

fn add(self, rhs: EdwardsPoint) -> EdwardsPoint

Performs the + operation.

impl<'a> Add<EdwardsPoint> for &'a EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the + operator.

fn add(self, rhs: EdwardsPoint) -> EdwardsPoint

Performs the + operation.

impl Add<EdwardsPoint> for AffinePoint

type Output = EdwardsPoint

The resulting type after applying the + operator.

fn add(self, rhs: EdwardsPoint) -> EdwardsPoint

Performs the + operation.

impl Add for EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the + operator.

fn add(self, rhs: EdwardsPoint) -> EdwardsPoint

Performs the + operation.

impl AddAssign<&AffinePoint> for EdwardsPoint

fn add_assign(&mut self, rhs: &AffinePoint)

Performs the += operation.

impl AddAssign<&EdwardsPoint> for AffinePoint

fn add_assign(&mut self, rhs: &EdwardsPoint)

Performs the += operation.

impl<'b> AddAssign<&'b EdwardsPoint> for EdwardsPoint

fn add_assign(&mut self, _rhs: &'b EdwardsPoint)

Performs the += operation.

impl AddAssign<AffinePoint> for EdwardsPoint

fn add_assign(&mut self, rhs: AffinePoint)

Performs the += operation.

impl AddAssign<EdwardsPoint> for AffinePoint

fn add_assign(&mut self, rhs: EdwardsPoint)

Performs the += operation.

impl AddAssign for EdwardsPoint

fn add_assign(&mut self, rhs: EdwardsPoint)

Performs the += operation.

impl BatchNormalize<[EdwardsPoint]> for EdwardsPoint

Available on crate feature alloc only.

type Output = Vec<<EdwardsPoint as Curve>::Affine>

The output of the batch normalization; a container of affine points.

fn batch_normalize(points: &[Self]) -> Vec<<Self as CurveGroup>::Affine>

Perform a batched conversion to affine representation on a sequence of projective points at an amortized cost that should be practically as efficient as a single conversion. Internally, implementors should rely upon InvertBatch.

fn batch_normalize_vartime(points: &Points) -> Self::Output

Perform a batched conversion to affine representation on a sequence of projective points in variable-time.

impl<const N: usize> BatchNormalize<[EdwardsPoint; N]> for EdwardsPoint

type Output = [<EdwardsPoint as Curve>::Affine; N]

The output of the batch normalization; a container of affine points.

fn batch_normalize(points: &[Self; N]) -> [<Self as CurveGroup>::Affine; N]

Perform a batched conversion to affine representation on a sequence of projective points at an amortized cost that should be practically as efficient as a single conversion. Internally, implementors should rely upon InvertBatch.

fn batch_normalize_vartime(points: &Points) -> Self::Output

Perform a batched conversion to affine representation on a sequence of projective points in variable-time.

impl Clone for EdwardsPoint

fn clone(&self) -> EdwardsPoint

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl CofactorGroup for EdwardsPoint

type Subgroup = EdwardsPoint

The large prime-order subgroup in which cryptographic operations are performed. If Self implements PrimeGroup, then Self::Subgroup may be Self.

fn clear_cofactor(&self) -> Self::Subgroup

Maps self to the prime-order subgroup by multiplying this element by some k-multiple of the cofactor.

fn into_subgroup(self) -> CtOption<Self::Subgroup>

Returns self if it is contained in the prime-order subgroup.

fn is_torsion_free(&self) -> Choice

Determines if this element is “torsion free”, i.e., is contained in the prime-order subgroup.

fn is_small_order(&self) -> Choice

Determines if this element is of small order.

impl ConditionallySelectable for EdwardsPoint

fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self

Select a or b according to choice.

fn conditional_assign(&mut self, other: &Self, choice: Choice)

Conditionally assign other to self, according to choice.

fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice)

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves.

impl ConstantTimeEq for EdwardsPoint

fn ct_eq(&self, other: &Self) -> Choice

Determine if two items are equal.

fn ct_ne(&self, other: &Self) -> Choice

Determine if two items are NOT equal.

impl CtEq for EdwardsPoint

fn ct_eq(&self, other: &Self) -> Choice

Determine if self is equal to other in constant-time.

fn ct_ne(&self, other: &Rhs) -> Choice

Determine if self is NOT equal to other in constant-time.

impl CtSelect for EdwardsPoint

fn ct_select(&self, other: &Self, choice: Choice) -> Self

Select between self and other based on choice, returning a copy of the value.

fn ct_swap(&mut self, other: &mut Self, choice: Choice)

Conditionally swap self and other if choice is Choice::TRUE.

impl Curve for EdwardsPoint

type Affine = AffinePoint

The affine representation for this elliptic curve.

fn to_affine(&self) -> AffinePoint

Converts this element into its affine representation.

fn batch_normalize(projective: &[Self], affine: &mut [Self::Affine])

Converts a batch of projective elements into affine elements. This function will panic if p.len() != q.len().

impl Debug for EdwardsPoint

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

Formats the value using the given formatter.

impl Default for EdwardsPoint

fn default() -> Self

Returns the “default value” for a type.

impl Display for EdwardsPoint

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

Formats the value using the given formatter.

impl From<&AffinePoint> for EdwardsPoint

fn from(value: &AffinePoint) -> Self

Converts to this type from the input type.

impl From<&DecafPoint> for EdwardsPoint

fn from(point: &DecafPoint) -> Self

Converts to this type from the input type.

impl From<&EdwardsPoint> for [u8; 57]

fn from(value: &EdwardsPoint) -> Self

Converts to this type from the input type.

impl From<&EdwardsPoint> for AffinePoint

fn from(value: &EdwardsPoint) -> Self

Converts to this type from the input type.

impl From<&EdwardsPoint> for DecafPoint

fn from(point: &EdwardsPoint) -> Self

Converts to this type from the input type.

impl From<&EdwardsPoint> for Vec<u8>

Available on crate feature alloc only.

fn from(value: &EdwardsPoint) -> Self

Converts to this type from the input type.

impl From<AffinePoint> for EdwardsPoint

fn from(value: AffinePoint) -> Self

Converts to this type from the input type.

impl From<DecafPoint> for EdwardsPoint

fn from(point: DecafPoint) -> Self

Converts to this type from the input type.

impl From<EdwardsPoint> for [u8; 57]

fn from(value: EdwardsPoint) -> Self

Converts to this type from the input type.

impl From<EdwardsPoint> for AffinePoint

fn from(value: EdwardsPoint) -> Self

Converts to this type from the input type.

impl From<EdwardsPoint> for DecafPoint

fn from(point: EdwardsPoint) -> Self

Converts to this type from the input type.

impl From<EdwardsPoint> for Vec<u8>

Available on crate feature alloc only.

fn from(value: EdwardsPoint) -> Self

Converts to this type from the input type.

impl From<NonIdentity<EdwardsPoint>> for EdwardsPoint

fn from(p: NonIdentity<EdwardsPoint>) -> Self

Converts to this type from the input type.

impl Generate for EdwardsPoint

fn try_generate_from_rng<R: TryCryptoRng + ?Sized>( rng: &mut R, ) -> Result<Self, R::Error>

Generate random key using the provided TryCryptoRng.

fn generate_from_rng<R>(rng: &mut R) -> Self

where R: CryptoRng + ?Sized,

Generate random key using the provided CryptoRng.

fn try_generate() -> Result<Self, Error>

Randomly generate a value of this type using the system’s ambient cryptographically secure random number generator.

fn generate() -> Self

Randomly generate a value of this type using the system’s ambient cryptographically secure random number generator.

impl Group for EdwardsPoint

type Scalar = Scalar<Ed448>

Scalars modulo the order of this group’s scalar field.

fn try_random<R>(rng: &mut R) -> Result<Self, R::Error>

where R: TryRng + ?Sized,

Returns an element chosen uniformly at random from the non-identity elements of this group using a user-provided fallible RNG.

fn identity() -> Self

Returns the additive identity, also known as the “neutral element”.

fn generator() -> Self

Returns a fixed generator of the prime-order subgroup.

fn is_identity(&self) -> Choice

Determines if this point is the identity.

fn double(&self) -> Self

Doubles this element.

fn random<R>(rng: &mut R) -> Self

where R: Rng + ?Sized,

Returns an element chosen uniformly at random from the non-identity elements of this group using a user-provided infallible RNG.

fn mul_by_generator(scalar: &Self::Scalar) -> Self

Multiply by the generator of the prime-order subgroup.

impl GroupEncoding for EdwardsPoint

type Repr = Array<u8, UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B1>, B1>, B0>, B0>, B1>>

The encoding of group elements.

fn from_bytes(bytes: &Self::Repr) -> CtOption<Self>

Attempts to deserialize a group element from its encoding.

fn from_bytes_unchecked(bytes: &Self::Repr) -> CtOption<Self>

Attempts to deserialize a group element, not checking if the element is valid.

fn to_bytes(&self) -> Self::Repr

Converts this element into its byte encoding. This may or may not support encoding the identity.

impl LinearCombination<[(EdwardsPoint, Scalar<Ed448>)]> for EdwardsPoint

fn lincomb(points_and_scalars: &PointsAndScalars) -> Self

Calculates x1 * k1 + ... + xn * kn.

fn lincomb_vartime(points_and_scalars: &PointsAndScalars) -> Self

Calculates x1 * k1 + ... + xn * kn.

impl<const N: usize> LinearCombination<[(EdwardsPoint, Scalar<Ed448>); N]> for EdwardsPoint

fn lincomb(points_and_scalars: &PointsAndScalars) -> Self

Calculates x1 * k1 + ... + xn * kn.

fn lincomb_vartime(points_and_scalars: &PointsAndScalars) -> Self

Calculates x1 * k1 + ... + xn * kn.

impl LowerHex for EdwardsPoint

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

Formats the value using the given formatter.

impl Mul<&Scalar<Ed448>> for &EdwardsPoint

fn mul(self, scalar: &EdwardsScalar) -> EdwardsPoint

Scalar multiplication: compute scalar * self.

type Output = EdwardsPoint

The resulting type after applying the * operator.

impl<'b> Mul<&'b Scalar<Ed448>> for EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, rhs: &'b EdwardsScalar) -> EdwardsPoint

Performs the * operation.

impl<'a> Mul<Scalar<Ed448>> for &'a EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, rhs: EdwardsScalar) -> EdwardsPoint

Performs the * operation.

impl Mul<Scalar<Ed448>> for EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, rhs: EdwardsScalar) -> EdwardsPoint

Performs the * operation.

impl<'b> MulAssign<&'b Scalar<Ed448>> for EdwardsPoint

fn mul_assign(&mut self, scalar: &'b EdwardsScalar)

Performs the *= operation.

impl MulAssign<Scalar<Ed448>> for EdwardsPoint

fn mul_assign(&mut self, rhs: EdwardsScalar)

Performs the *= operation.

impl MulByGeneratorVartime for EdwardsPoint

fn mul_by_generator_vartime(scalar: &Self::Scalar) -> Self

Multiply by the generator of the prime-order subgroup.

fn mul_by_generator_and_mul_add_vartime( a: &Self::Scalar, b: &Self::Scalar, p: &Self, ) -> Self

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<&Scalar<Ed448>> for &EdwardsPoint

fn mul_vartime(self, scalar: &EdwardsScalar) -> EdwardsPoint

Multiply self by rhs in variable-time.

impl MulVartime<&Scalar<Ed448>> for EdwardsPoint

fn mul_vartime(self, scalar: &EdwardsScalar) -> EdwardsPoint

Multiply self by rhs in variable-time.

impl MulVartime<Scalar<Ed448>> for EdwardsPoint

fn mul_vartime(self, scalar: EdwardsScalar) -> EdwardsPoint

Multiply self by rhs in variable-time.

impl Neg for &EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the - operator.

fn neg(self) -> EdwardsPoint

Performs the unary - operation.

impl Neg for EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the - operator.

fn neg(self) -> EdwardsPoint

Performs the unary - operation.

impl PartialEq for EdwardsPoint

fn eq(&self, other: &EdwardsPoint) -> 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 Sub<&AffinePoint> for &EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the - operator.

fn sub(self, other: &AffinePoint) -> EdwardsPoint

Performs the - operation.

impl<'b> Sub<&'b AffinePoint> for EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the - operator.

fn sub(self, rhs: &'b AffinePoint) -> EdwardsPoint

Performs the - operation.

impl Sub<&EdwardsPoint> for &AffinePoint

type Output = EdwardsPoint

The resulting type after applying the - operator.

fn sub(self, other: &EdwardsPoint) -> EdwardsPoint

Performs the - operation.

impl Sub<&EdwardsPoint> for &EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the - operator.

fn sub(self, other: &EdwardsPoint) -> EdwardsPoint

Performs the - operation.

impl<'b> Sub<&'b EdwardsPoint> for AffinePoint

type Output = EdwardsPoint

The resulting type after applying the - operator.

fn sub(self, rhs: &'b EdwardsPoint) -> EdwardsPoint

Performs the - operation.

impl<'b> Sub<&'b EdwardsPoint> for EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the - operator.

fn sub(self, rhs: &'b EdwardsPoint) -> EdwardsPoint

Performs the - operation.

impl<'a> Sub<AffinePoint> for &'a EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the - operator.

fn sub(self, rhs: AffinePoint) -> EdwardsPoint

Performs the - operation.

impl Sub<AffinePoint> for EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the - operator.

fn sub(self, rhs: AffinePoint) -> EdwardsPoint

Performs the - operation.

impl<'a> Sub<EdwardsPoint> for &'a AffinePoint

type Output = EdwardsPoint

The resulting type after applying the - operator.

fn sub(self, rhs: EdwardsPoint) -> EdwardsPoint

Performs the - operation.

impl<'a> Sub<EdwardsPoint> for &'a EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the - operator.

fn sub(self, rhs: EdwardsPoint) -> EdwardsPoint

Performs the - operation.

impl Sub<EdwardsPoint> for AffinePoint

type Output = EdwardsPoint

The resulting type after applying the - operator.

fn sub(self, rhs: EdwardsPoint) -> EdwardsPoint

Performs the - operation.

impl Sub for EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the - operator.

fn sub(self, rhs: EdwardsPoint) -> EdwardsPoint

Performs the - operation.

impl SubAssign<&AffinePoint> for EdwardsPoint

fn sub_assign(&mut self, rhs: &AffinePoint)

Performs the -= operation.

impl SubAssign<&EdwardsPoint> for AffinePoint

fn sub_assign(&mut self, rhs: &EdwardsPoint)

Performs the -= operation.

impl<'b> SubAssign<&'b EdwardsPoint> for EdwardsPoint

fn sub_assign(&mut self, _rhs: &'b EdwardsPoint)

Performs the -= operation.

impl SubAssign<AffinePoint> for EdwardsPoint

fn sub_assign(&mut self, rhs: AffinePoint)

Performs the -= operation.

impl SubAssign<EdwardsPoint> for AffinePoint

fn sub_assign(&mut self, rhs: EdwardsPoint)

Performs the -= operation.

impl SubAssign for EdwardsPoint

fn sub_assign(&mut self, rhs: EdwardsPoint)

Performs the -= operation.

impl<T> Sum<T> for EdwardsPoint

where T: Borrow<EdwardsPoint>,

fn sum<I>(iter: I) -> Self

where I: Iterator<Item = T>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl TryFrom<&[u8]> for EdwardsPoint

type Error = &'static str

The type returned in the event of a conversion error.

fn try_from(value: &[u8]) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<&[u8; 57]> for EdwardsPoint

type Error = &'static str

The type returned in the event of a conversion error.

fn try_from(value: &[u8; 57]) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<&Vec<u8>> for EdwardsPoint

Available on crate feature alloc only.

type Error = &'static str

The type returned in the event of a conversion error.

fn try_from(value: &Vec<u8>) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<[u8; 57]> for EdwardsPoint

type Error = &'static str

The type returned in the event of a conversion error.

fn try_from(value: [u8; 57]) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<Box<[u8]>> for EdwardsPoint

Available on crate feature alloc only.

type Error = &'static str

The type returned in the event of a conversion error.

fn try_from(value: Box<[u8]>) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<EdwardsPoint> for NonIdentity<EdwardsPoint>

The constant-time alternative is available at NonIdentity::new().

type Error = Error

The type returned in the event of a conversion error.

fn try_from(point: EdwardsPoint) -> Result<Self, Error>

Performs the conversion.

impl TryFrom<Vec<u8>> for EdwardsPoint

Available on crate feature alloc only.

type Error = &'static str

The type returned in the event of a conversion error.

fn try_from(value: Vec<u8>) -> Result<Self, Self::Error>

Performs the conversion.

impl UpperHex for EdwardsPoint

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

Formats the value using the given formatter.

impl Copy for EdwardsPoint

impl DefaultIsZeroes for EdwardsPoint

impl Eq for EdwardsPoint

impl PrimeGroup for EdwardsPoint