Paper 2005/241 Original: eprint.iacr.org/2005/241 ↗
On the binary sequences with high $GF(2)$ linear complexities and low $GF(p)$ linear complexities
Abstract
Klapper [1] showed that there are binary sequences of period $q^n-1$ ($q$ is a prime power $p^m$, $p$ is an odd prime) with the maximal possible linear complexity $q^n-1$ when considered as sequences over $GF(2)$, while the sequences have very low linear complexities when considered as sequences over $GF(p)$. This suggests that the binary sequences with high $GF(2)$ linear complexities and low $GF(p)$ linear complexities are note secure in cryptography. In this note we give some simple constructions of the binary sequences with high $GF(2)$ linear complexities and low $GF(p)$ linear complexities. We also prove some lower bounds on the $GF(p)$ linear complexities of binary sequences and a lower bound on the number of the binary sequences with high $GF(2)$ linear complexities and low $GF(p)$ linear complexities .
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2005-07-30: last updated
- 2005-07-30: published
- Short URL
- https://ia.cr/2005/241
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2005/241,
author = {Hao Chen and Liqing Xu},
title = {On the binary sequences with high $GF(2)$ linear complexities and low $GF(p)$ linear complexities},
howpublished = {Cryptology {ePrint} Archive, Paper 2005/241},
year = {2005},
url = {https://eprint.iacr.org/2005/241}
}