Method doubleJacobian

crypto/secp256k1/curve.go:210–240

doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and returns its double, also in Jacobian form.

(x, y, z *big.Int)

// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and
// returns its double, also in Jacobian form.
func (BitCurve *BitCurve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
	// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l

	a := new(big.Int).Mul(x, x) //X1²
	b := new(big.Int).Mul(y, y) //Y1²
	c := new(big.Int).Mul(b, b) //B²

	d := new(big.Int).Add(x, b) //X1+B
	d.Mul(d, d)                 //(X1+B)²
	d.Sub(d, a)                 //(X1+B)²-A
	d.Sub(d, c)                 //(X1+B)²-A-C
	d.Mul(d, big.NewInt(2))     //2*((X1+B)²-A-C)

	e := new(big.Int).Mul(big.NewInt(3), a) //3*A
	f := new(big.Int).Mul(e, e)             //E²

	x3 := new(big.Int).Mul(big.NewInt(2), d) //2*D
	x3.Sub(f, x3)                            //F-2*D
	x3.Mod(x3, BitCurve.P)

	y3 := new(big.Int).Sub(d, x3)                  //D-X3
	y3.Mul(e, y3)                                  //E*(D-X3)
	y3.Sub(y3, new(big.Int).Mul(big.NewInt(8), c)) //E*(D-X3)-8*C
	y3.Mod(y3, BitCurve.P)

	z3 := new(big.Int).Mul(y, z) //Y1*Z1
	z3.Mul(big.NewInt(2), z3)    //3*Y1*Z1
	z3.Mod(z3, BitCurve.P)

	return x3, y3, z3
}

// ScalarMult does the private scalar.
func (BitCurve *BitCurve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int) {