# Shamir Secret Sharing and Diffie-Hellman procedure

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?