How to calculate `x^3 + ax + b mod p` with Golang big.Int

Question

I'm trying to find the Y coordinate for an elliptic point. I understand the formula is y^2≡x^3+ax+b mod p.

However I'm unsure of how I would actually program this in Go.

xCubed.Exp(X, 3, nil)
AX.Mul(A,X)

N.Add(XPow3, AX) // x^3 + ax
N.Mod(N, P) // mod p
N.Add(N, B) // (x^3 + ax) + b
N.Mod(N, P) // mod p

return N

Where xCubed,X,N,P,B are *big.Int and N represents y^2

I'm a noob to modular arithmetic, so my assumption mod P is applied to each operation; Is this the correct way to to calculate x^3 + ax + b mod p?

edit: should I have added AX.Mod(p) ?

you might want to take a look at this Java implementation: there is a method `getY`: https://github.com/google/tink/blob/master/java/src/main/java/com/google/crypto/tink/subtle/EllipticCurves.java? — Stephan Schlecht, Jan 05 '19 at 19:45

score 1 · Accepted Answer · answered Jan 05 '19 at 19:47

1

I figured it out, by scouting some code in the elliptic lib

func GetY(x *big.Int, curve *elliptic.CurveParams) *big.Int {


    x3 := new(big.Int).Mul(x, x)
    x3.Mul(x3, x)

    threeX := new(big.Int).Lsh(x, 1)
    threeX.Add(threeX, x)

    x3.Sub(x3, threeX)
    x3.Add(x3, curve.B)
    x3.Mod(x3, curve.P)

    return x3.ModSqrt(x3, curve.P)
}

answered Jan 05 '19 at 19:47

NotAnApple

21
4

If you are just picking random x's and plugging them in you must be prepared for the possibility the square root does not exist, and `ModSqrt` returns nil. – President James K. Polk Jan 06 '19 at 03:16

How to calculate `x^3 + ax + b mod p` with Golang big.Int

1 Answers1