Faster Computation of Self-pairings.dvi

Self-pairings have found interesting applications in cryptographic schemes, such as ZSS short signatures and so on. In this paper, we present a novel method for constructing a self-pairing on supersingular elliptic curves with even embedding degrees, which we call the Ateil pairing. This pairing improves the efficiency of the self-pairing computation on supersingular curves over finite fields with large characteristic. On the basis of the ηT pairing, we propose a generalization of the Ateil pairing, which we call the Ateili pairing. The optimal Ateili pairing which has the shortest Miller loop length is faster than previously known self-pairing on supersingular elliptic curves over finite fields with small characteristic. We also propose a new self-pairing based on the Weil pairing which is faster than the previously known self-pairing on ordinary elliptic curves with embedding degree one.