Alice needs to share an already generated numeric secret $s$ with Bob and she doe not want the world to see it. The problem is that she has never contacted Bob before.

I thought Alice and Bob could generate a line à la Shamir Secret Sharing so that $$q(x)=s+\alpha x.$$

To agree with $\alpha$ Alice and Bob could implement the original Diffie-Hellman protocol for key exchange. Finally Alice could just send $q(1)$ to Bob and he could compute $s$ as $$q(1)-\alpha*1=q(1)-\alpha=s.$$

Theoretically even if Eve could see both the values sent in the clear by the Diffie-Hellman protocol and the value $q(1)$, Eve could not compute $s$ from them.

Is this method already used used somewhere? Do you know some literature which prove this to be secure?


This protocol is insecure because the original Diffie-Hellman method can be exploited by man-in-the-middle attacks.

For this reason, you should never use Diffie-Hellman alone.


Your Answer

By clicking "Post Your Answer", you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.