How to Sub two EcPoint

manxiaqu · April 26, 2019, 9:32am

I’m a beginner in crypto. Recently I try to do some research on the curve. But I didn’t find any code for Subtraction of two EcPoints.

github.com

golang/go/blob/master/src/crypto/elliptic/elliptic.go#L24


// reverse the transform than to operate in affine coordinates.


import (
	"io"
	"math/big"
	"sync"
)


// A Curve represents a short-form Weierstrass curve with a=-3.
// See https://www.hyperelliptic.org/EFD/g1p/auto-shortw.html
type Curve interface {
	// Params returns the parameters for the curve.
	Params() *CurveParams
	// IsOnCurve reports whether the given (x,y) lies on the curve.
	IsOnCurve(x, y *big.Int) bool
	// Add returns the sum of (x1,y1) and (x2,y2)
	Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int)
	// Double returns 2*(x,y)
	Double(x1, y1 *big.Int) (x, y *big.Int)
	// ScalarMult returns k*(Bx,By) where k is a number in big-endian form.
	ScalarMult(x1, y1 *big.Int, k []byte) (x, y *big.Int)

for example: EcPoint a - EcPoint b.

I have tried something below:

using a + (-1) * b; but the result seems incorrect.
compute negation formulas of b(https://www.hyperelliptic.org/EFD/g1p/auto-shortw.html), and compute a + negation of b. through the negation of b + b is zero. but the negation of b is not on curve and the result is also incorrect.

anyone have some ideas about this, am I doing something wrong?

system · July 25, 2019, 9:32am

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