Paper 2004/132

On Small Characteristic Algebraic Tori in Pairing-Based Cryptography

R. Granger, D. Page, and M. Stam

Abstract

The output of the Tate pairing on an elliptic curve over a finite field may be viewed as an element of an algebraic torus. Using this simple observation, we transfer techniques recently developed for torus-based cryptography to pairing-based cryptography, resulting in more efficient computations, and lower bandwidth requirements. To illustrate the efficacy of this approach, we apply the method to pairings on supersingular elliptic curves in characteristic three.

Metadata
Available format(s)
PDF PS
Publication info
Published elsewhere. LMS Journal of Computation and Mathematics
Keywords
Algebraic toriPairing-based cryptography
Contact author(s)
granger @ cs bris ac uk
History
2005-03-18: revised
2004-06-03: received
See all versions
Short URL
https://ia.cr/2004/132
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2004/132,
      author = {R.  Granger and D.  Page and M.  Stam},
      title = {On Small Characteristic Algebraic Tori in Pairing-Based Cryptography},
      howpublished = {Cryptology ePrint Archive, Paper 2004/132},
      year = {2004},
      note = {\url{https://eprint.iacr.org/2004/132}},
      url = {https://eprint.iacr.org/2004/132}
}
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