### Faster Computation of Self-pairings

Chang-An Zhao, Fangguo Zhang, and Dongqing Xie

##### 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 $one$.

Available format(s)
Category
Implementation
Publication info
Published elsewhere. Unknown where it was published
Contact author(s)
changanzhao @ gmail com
History
Short URL
https://ia.cr/2010/399

CC BY

BibTeX

@misc{cryptoeprint:2010/399,
author = {Chang-An Zhao and Fangguo Zhang and Dongqing Xie},
title = {Faster Computation of Self-pairings},
howpublished = {Cryptology ePrint Archive, Paper 2010/399},
year = {2010},
note = {\url{https://eprint.iacr.org/2010/399}},
url = {https://eprint.iacr.org/2010/399}
}

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