Cryptology ePrint Archive: Report 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.

Category / Keywords: foundations / stream cipher, $l$-sequences, 2-adic ring, FCSRs, transition matrix.

Date: received 8 Dec 2015

Contact author: linzhiqiang at iie ac cn

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Version: 20151213:041039 (All versions of this report)

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