Faster Computation of Self-pairings

Chang-An Zhao; Fangguo Zhang; Dongqing Xie

Paper 2010/399

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 $η_{T}$ 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 .

Metadata

Available format(s): PDF PS
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): changanzhao @ gmail com
History: 2010-07-16: received
Short URL: https://ia.cr/2010/399
License: 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},
      url = {https://eprint.iacr.org/2010/399}
}