Construction of Transition Matrices for Binary FCSRs

Zhiqiang Lin; Dingyi Pei; Dongdai Lin

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 $q = det (I - 2 A)$ . In this paper, we show how to calculate the determinant 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 -sequences 2-adic ring FCSRs transition 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}
}