# Using ECDH for authentication

I've found this method for using ECDH for asymmetric encryption.

Is there a similar method for using ECDH (rather than the more usual ECDSA, let's say my hardware can do ECDH but not ECDSA) to accomplish authentication?

• ECDH is basically a point multplication and a KDF. I assume your hypotetical hardware can do the point multiplication by itself? And what do you mean by "authentication", do you need a digital signature like ECDSA? – Conrado Apr 9 at 18:50
• Yes, the hardware can do multiplication by itself. I mean authentication in the same way that ECDSA can be used: I want Alice to be able to prove that's she's really Alice to Bob, assuming Bob knows the public key of Alice. – Kristof Provost Apr 10 at 6:55

You van use DH over elliptic curve or over Zp for authentication. If the authenticating party has a fixed DH key and published in advance the public part $$g^a$$ (or multiplication for ECDH). When we want to authenticate we can create a mutual DH key $$g^{ab}$$ and then the authenticator can prove knowledge of this in many ways. encrypt a challenge with this as key would be a simple way. Could equally decrypt a challenge, or hash a challenge with the key prepended. Or something fancier like socialist millionaire which gives zero knowledge proof both sides have the same key. And if both sides have the other side public dh key it supplies authentication of both sides.