# Pairings of Elliptic Curves

We were missing two things – an HH that supports both addition and multiplication that is needed for the verifier’s checks, and a transition from an interactive protocol to a non-interactive proof system.

Now we will see that using elliptic curves we can obtain a limited, but sufficient for our purposes, form of HH that supports multiplication. We will then show that this limited HH also suffices to convert our protocol to the desired non-interactive system.

We begin by introducing elliptic curves and explaining how they give us the necessary HH.

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