Paper 2011/199
An efficient deterministic test for Kloosterman sum zeros
Omran Ahmadi and Robert Granger
Abstract
We propose a simple deterministic test for deciding whether or not a non-zero element $a \in \F_{2^n}$ or $\F_{3^n}$ is a zero of the corresponding Kloosterman sum over these fields, and analyse its complexity. The test seems to have been overlooked in the literature. For binary fields, the test has an expected operation count dominated by just two $\F_{2^n}$-multiplications when $n$ is odd (with a slightly higher cost for even extension degrees), making its repeated invocation the most efficient method to date to find a non-trivial Kloosterman sum zero in these fields. The analysis depends on the distribution of Sylow $p$-subgroups in two corresponding families of elliptic curves, which we prove using a theorem due to Howe.
Note: Comments welcome
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Published elsewhere. Submitted
- Keywords
- Kloosterman sumselliptic curvesSylow p-subgroups
- Contact author(s)
- rgranger @ computing dcu ie
- History
- 2011-04-25: received
- Short URL
- https://ia.cr/2011/199
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2011/199,
author = {Omran Ahmadi and Robert Granger},
title = {An efficient deterministic test for Kloosterman sum zeros},
howpublished = {Cryptology {ePrint} Archive, Paper 2011/199},
year = {2011},
url = {https://eprint.iacr.org/2011/199}
}
