Faster Computation of Self-Pairings
Chang‐An Zhao, Fangguo Zhang, Dongqing Xie · IEEE Transactions on Information Theory · 2012
Self-pairings have found interesting applications in cryptographic schemes. 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 new pairing improves the efficiency of the self-pairing computation on supersingular curves over finite fields with large characteristic. Based on the ηTpairing, we propose a generalization of the Ateil pairing, which we call the Ateilipairing. The optimal Ateilipairing which has the shortest Miller loop is faster than previously known self-pairings on supersingular elliptic curves over finite fields with small characteristic. We also present a new self-pairing based on the Weil pairing which is faster than the self-pairing based on the Tate pairing on ordinary elliptic curves with embedding degreeone.