Struct Point

pub struct Point<C>(/* private fields */);

A point on an elliptic curve curve, possibly at infinity.

Implementations

impl<C: Curve> Point<C>

pub fn new(x: Num, y: Num) -> Result<Self, InvalidPoint>

pub fn infinity() -> Self

pub fn coordinates(&self) -> Coordinates

Trait Implementations

impl<C: Curve> Add for Point<C>

Elliptic curve points are added together by first constructing a line through the two points, then finding the intersection of that line with the curve. The intersection is the result. If the two points are equal, a tangent should be constructed instead of a line.

If the points are not equal: $$ (x_1, y_1) + (x_2, y_2) = (x_3, y_3) \\ H = \frac{y_2 - y_1}{x_2 - x_1} \\ x_3 = H^2 - x_1 - x_2 \\ y_3 = H(x_1 - x_3) - y_1 \\ $$

If the points are equal: $$ 2 \cdot (x_1, y_1) = (x_3, y_3) \\ H = \frac{3x_1^2 + a}{2y_1} \\ x_3 = H^2 - 2x_1 \\ y_3 = H(x_1 - x_3) - y_1 \\ $$

type Output = Point<C>

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl<C: Curve> AddAssign for Point<C>

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl<C> Clone for Point<C>

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<C: Debug> Debug for Point<C>

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

Formats the value using the given formatter.

impl<C: Curve> Mul<Point<C>> for Num

Multiply the point by a scalar.

This uses the square-and-multiply method. For example, to calculate $x^{19}$, start with $y = x$ and multiply $y$ with itself, resulting in $y = y \cdot y = x^2$. Then, multiply $y$ with itself again, resulting in $y = y \cdot y = x^4$. Repeat this until it can no longer be done, at which point $y = x^{16}$ and there have been four multiplications thus far. Finally, multiply $y$ with $x$ three more times to get the desired result.

With this method, $x^{19}$ was calculated in only seven multiplications, compared to the naive algorithm which would execute 19 multiplications.

In the case of elliptic curve points, the “square” is equivalent to doubling, and “multiply” is equivalent to addition.

type Output = Point<C>

The resulting type after applying the * operator.

fn mul(self, rhs: Point<C>) -> Self::Output

Performs the * operation.

impl<C> PartialEq for Point<C>

fn eq(&self, other: &Self) -> 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<C> Copy for Point<C>

impl<C> Eq for Point<C>