## CryptoDB

### Paper: Faster Computation of Self-pairings

Authors: Chang-An Zhao Fangguo Zhang Dongqing Xie URL: http://eprint.iacr.org/2010/399 Search ePrint Search Google 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 $one$.
##### BibTeX
@misc{eprint-2010-23300,
title={Faster Computation of Self-pairings},
booktitle={IACR Eprint archive},
keywords={implementation /},
url={http://eprint.iacr.org/2010/399},
note={ changanzhao@gmail.com 14806 received 15 Jul 2010},
author={Chang-An Zhao and Fangguo Zhang and Dongqing Xie},
year=2010
}