Paper 2013/562

Self-pairings on supersingular elliptic curves with embedding degree $three$

Binglong Chen and Chang-An Zhao

Abstract

Self-pairings are a special subclass of pairings and have interesting applications in cryptographic schemes and protocols. In this paper, we explore the computation of the self-pairings on supersingular elliptic curves with embedding degree $k = 3$. We construct a novel self-pairing which has the same Miller loop as the Eta/Ate pairing. However, the proposed self-pairing has a simple final exponentiation. Our results suggest that the proposed self-pairings are more efficient than the other ones on the corresponding curves. We compare the efficiency of self-pairing computations on different curves over large characteristic and estimate that the proposed self-pairings on curves with $k=3$ require $44\%$ less field multiplications than the fastest ones on curves with $k=2$ at AES 80-bit security level.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
Elliptic curveTate pairingWeil pairingSelf-pairingPairing based cryptography.
Contact author(s)
zhaochan3 @ mail sysu edu cn
History
2013-09-05: received
Short URL
https://ia.cr/2013/562
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2013/562,
      author = {Binglong Chen and Chang-An Zhao},
      title = {Self-pairings on supersingular elliptic curves with embedding degree $three$},
      howpublished = {Cryptology ePrint Archive, Paper 2013/562},
      year = {2013},
      note = {\url{https://eprint.iacr.org/2013/562}},
      url = {https://eprint.iacr.org/2013/562}
}
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