Thread: Finite field subtraction, i.e. additive inverse of a geometric point

Hello

I hope someone can help me with this.

Let's imagine I want to perform the following subtraction operation -

(7, 1) - (2, 3)

Both are geometric points on an elliptic curve.

As far as I know, finite field subtraction is simply finite field addition using the additive inverse of the bit I want to subtract, i.e. (7, 1) + [additiveInverse(2, 3)]

Is this correct?

Does anyone know how I can calculate the additive inverse of a point?

Is it simply (-2, -3)?

Any help greatly appreciated.

Thanks!

I think in order to answer this equation you need to say which finite field you are working in.
And also what elliptic curve you are dealing with.

I guess that if is the elliptic curve and then . This gives us infromation to solve for and determine the curve. Now we just need to know what is.

Thanks for your reply.

I think there was some misunderstanding though.

All I'm asking is this: is the additive inverse of (2, 3) simply (-2, -3)?

Thanks.

Hmmm. I'm after finding this on the internet:

J = (Xj, Yj)
K = (Xk, Yk)

J - K = J + (-K)
where -K = (Xk, Xk + Yk)

Does this ring any bells with anyone?

Thanks

That looks correct. I been just gazing for curves over for motivation. If you have on the curve then the line joining and passes through . Thus, the inverse of is . Therefore, if we have a point over a finite field then it seems .

Perfect! Thank you.