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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2015/1181}},
      url = {https://eprint.iacr.org/2015/1181}
}
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