An Improvement of Tate Paring with Supersingular Curve

Vector decomposition problem has been proposed on some supersingular curves whose embedding degree is 2 for example. In order to apply the problem as a trapdoor for some innovative cryptosystems, it is necessary to make pairing-related calculations more efficient. Our previous work has considered an approach for Tate pairing on a supersingular curve of embedding degree 2 over extension field of extension degree 2. It improved both Miller´s algorithm and final exponentiation that was required for the Tate pairing. In detail, one multiplication in the calculation of Miller´s loop was eliminated by using a twist mapping. This paper shows a more improved calculation of pairing with some experimental result for the efficiency discussion.