Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions

Paper 2009/565

Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions

Robert Granger and Michael Scott

Abstract

This paper describes an extremely efficient squaring operation in the so-called `cyclotomic subgroup' of $\F_{q^6}^{\times}$, for $q \equiv 1 \bmod{6}$. This result arises from considering the Weil restriction of scalars of this group from $\F_{q^6}$ to $\F_{q^2}$, and provides efficiency improvements for both pairing-based and torus-based cryptographic protocols.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Keywords: Pairing-based cryptography torus-based cryptography finite field arithmetic.
Contact author(s): rgranger @ computing dcu ie
History: 2009-11-23: received
Short URL: https://ia.cr/2009/565
License: CC BY

BibTeX

@misc{cryptoeprint:2009/565,
      author = {Robert Granger and Michael Scott},
      title = {Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/565},
      year = {2009},
      url = {https://eprint.iacr.org/2009/565}
}