Is it possible to add two secp256k1 points to get a "shared key"?

0

As I know from the Elliptic Curve Diffie Hellman (ECDH), you can create a "Shared Key": https://asecuritysite.com/encryption/ecdh2

This will look like this:

dA × dB × G = Shared Key

QB = dB × G

QA = dA × G

But is it possible to get the sum of dA and dB? (Plusing the value of each private key?)

dA + dB × G = ???

How to get a "Shared Key" when adding each private key (plus)?

Izi Tors

Posted 2019-10-25T09:47:17.940

Reputation: 19

Answers

1

Yes, QA + QB = (dA + dB) × G, but this isn't used in ECDH as QA + QB can be calculated by third parties.

You can read about this property here.

MCCCS

Posted 2019-10-25T09:47:17.940

Reputation: 5 827

QA + QB can not be calculated by third parties? That is, the point G does not allow this to be done. Or how can QA + QB be calculated? Maybe in a different way?Izi Tors 2019-10-25T10:24:25.593

If you know the points QA and QB, what you should do is draw the curve, mark the points QA and QB, connect them with a line, find where the line intersects the curve (apart from QA and QB). The third intersection will be -(QA + QB). You can then reflect the point over the X axis to find the point QA + QB. You can read more about addition here. (note that there are also some modulo operations) @IziTors

MCCCS 2019-10-25T10:45:12.803

How on the graph of the curve can they get the sum of the total private keys (dA + dB) by calculating QA + QB?Izi Tors 2019-10-25T11:19:06.393

It’s assumed to be impossible to find dA + dB from QA + QB, but you can find (dA + dB) x G if you know QA and QB by adding them. If you know QA and QB or QA + QB you can’t find dA or dB or their sum.MCCCS 2019-10-25T12:03:18.450

And there are minus points QA - QB, and accordingly minus (dA - dB) x G ?Izi Tors 2019-11-01T12:27:02.017

@IziTors Yes. it's correct.MCCCS 2019-11-01T15:03:41.363