ec.go

package ec

import (
	big "math/big"
)

type Point struct {
	X *big.Int
	Y *big.Int
}

//x^2 + y^2 == 1 + dx^2y^2
type Curve struct {
	MaxPrime *big.Int
	D        *big.Int
}

// https://www.youtube.com/watch?v=l6jTFxQaUJA
func (c *Curve) Add(a, b *Point) *Point {
	x1, y1 := a.X, a.Y
	x2, y2 := b.X, b.Y

	x3 := c.x3(x1, x2, y1, y2)
	y3 := c.y3(x1, x2, y1, y2)

	return &Point{X: x3, Y: y3}
}

func (c *Curve) x3(x1, x2, y1, y2 *big.Int) *big.Int {
	numerator := c.xNumerator(x1, x2, y1, y2)
	denominator := c.xDenominator(x1, x2, y1, y2)

	x3 := numerator.Div(numerator, denominator)
	return x3.Mod(x3, c.MaxPrime)
}

func (c *Curve) y3(x1, x2, y1, y2 *big.Int) *big.Int {
	numerator := c.yNumerator(x1, x2, y1, y2)
	denominator := c.yDenominator(x1, x2, y1, y2)

	y3 := numerator.Div(numerator, denominator)
	return y3.Mod(y3, c.MaxPrime)
}

//calculates  (x1 * y2 + y1 * x2) % MaxPrime
func (c *Curve) xNumerator(x1, x2, y1, y2 *big.Int) *big.Int {
	calc := big.NewInt(0)

	r := calc.Mul(x1, y2)
	calc.Add(r, calc.Mul(y1, x2))

	return r.Mod(r, c.MaxPrime)
}

// 1 * d * x1 * x2 * y1 * y2
func (c *Curve) xDenominator(x1, x2, y1, y2 *big.Int) *big.Int {
	r := big.NewInt(1)
	r.Add(r, c.denominatorComponent(x1, x2, y1, y2))

	return r.Mod(r, c.MaxPrime)
}

// y1 * y2 - x1 * x2
func (c *Curve) yNumerator(x1, x2, y1, y2 *big.Int) *big.Int {
	calc := big.NewInt(0)

	r := calc.Mul(y1, y2)
	calc.Sub(r, calc.Mul(x1, x2))

	return r.Mod(r, c.MaxPrime)
}

// 1- d*x1*x2*y1*y2
func (c *Curve) yDenominator(x1, x2, y1, y2 *big.Int) *big.Int {
	r := big.NewInt(1)
	r.Add(r, c.denominatorComponent(x1, x2, y1, y2))

	return r.Mod(r, c.MaxPrime)
}

//calculates d*x1*x2*y1*y2
func (c *Curve) denominatorComponent(x1, x2, y1, y2 *big.Int) *big.Int {
	r := big.NewInt(0)
	r.Mul(c.D, x1).Mul(r, x2).Mul(r, y1).Mul(r, y2)
	return r.Mod(r, c.MaxPrime)
}