Paper 2015/1181
Construction of Transition Matrices for Binary FCSRs
Zhiqiang Lin, Dingyi Pei, and Dongdai Lin
Abstract
Stream ciphers based on Linear Feedback Shift Registers (LFSRs) have faced algebraic attacks. To avoid this kind of attacks, Feedback with Carry Shift Registers (FCSRs) have been proposed as an alternative. In order to eliminate a so-called LFSRization weakness, FCSRs have been implemented using ring representation instead of the Galois one. A ring FCSR is determined by its transition matrix $A$. Its connection integer, which is related to the properties of the output sequences, is $q=\mbox{det}(I-2A)$. In this paper, we show how to calculate the determinant $\mbox{det}(I-2A)$ of transition matrices with a critical path of length 1 and fan-out 2. Moreover, we propose algorithms to construct such transition matrices (binary case) based on searching target connection integers.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- stream cipher$l$-sequences2-adic ringFCSRstransition matrix.
- Contact author(s)
- linzhiqiang @ iie ac cn
- History
- 2015-12-13: received
- Short URL
- https://ia.cr/2015/1181
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2015/1181,
author = {Zhiqiang Lin and Dingyi Pei and Dongdai Lin},
title = {Construction of Transition Matrices for Binary {FCSRs}},
howpublished = {Cryptology {ePrint} Archive, Paper 2015/1181},
year = {2015},
url = {https://eprint.iacr.org/2015/1181}
}
