International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Faster Computation of Self-pairings

Chang-An Zhao
Fangguo Zhang
Dongqing Xie
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Abstract: 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 characteristics. Based on the $\eta_T$ pairing, we propose a generalization of the Ateil pairing, which we call the Ateil$_i$ pairing. The optimal Ateil$_i$ pairing which has the shortest Miller loop is faster than previously known self-pairings on supersingular elliptic curves over finite fields with small characteristics. 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 degree $one$.
  title={Faster Computation of Self-pairings},
  booktitle={IACR Eprint archive},
  keywords={implementation /},
  note={ 14806 received 15 Jul 2010},
  author={Chang-An Zhao and Fangguo Zhang and Dongqing Xie},