Paper 2009/304
Factor-4 and 6 Compression of Cyclotomic Subgroups
Koray Karabina
Abstract
Bilinear pairings derived from supersingular elliptic curves of embedding degrees 4 and 6 over finite fields of characteristic two and three, respectively, have been used to implement pairing-based cryptographic protocols. The pairing values lie in certain prime-order subgroups of certain cyclotomic subgroups. It was previously known how to compress the pairing values over characteristic two fields by a factor of 2, and the pairing values over characteristic three fields by a factor of 6. In this paper, we show how the pairing values over characteristic two fields can be compressed by a factor of 4. Moreover, we present and compare several algorithms for performing exponentiation in the prime-order subgroups using the compressed representations. In particular, in the case where the base is fixed, we expect to gain at least a 54% speed up over the fastest previously known exponentiation algorithm that uses factor-6 compressed representations.
Metadata
- Available format(s)
-
PDF
PS
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Finite field compressioncyclotomic subgroupspairing-based cryptography
- Contact author(s)
- kkarabin @ uwaterloo ca
- History
- 2010-04-27: last of 4 revisions
- 2009-06-24: received
- See all versions
- Short URL
- https://ia.cr/2009/304
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2009/304,
author = {Koray Karabina},
title = {Factor-4 and 6 Compression of Cyclotomic Subgroups},
howpublished = {Cryptology {ePrint} Archive, Paper 2009/304},
year = {2009},
url = {https://eprint.iacr.org/2009/304}
}
