Boolean-network-based approach for construction of filter generators
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. RESEARCH PAPER .
November 2020, Vol. 63 212206:1–212206:13 https://doi.org/10.1007/s11432-019-2813-7
Boolean-network-based approach for construction of filter generators Bowen LI1,2 & Jianquan LU2* 1
School of Information Science and Engineering, Southeast University, Nanjing 210096, China; 2 School of Mathematics, Southeast University, Nanjing 210096, China
Received 24 November 2019/Revised 14 January 2020/Accepted 5 February 2020/Published online 9 October 2020
Abstract In this paper, we view filter generators as Boolean networks (BNs), and discuss their poweranalysis-based side-channel analysis. An incompletely specified binary sequence always contains some bits called unnecessary bits comprising 1 or 0. Our motivation for considering this type of sequence is to reduce direct dependencies between side-channel information and key sequences. An algorithm is proposed to determine the unnecessary bits to increase the key search time required for adversaries rather than simply turning all unnecessary bits to 0 (or 1). Then, to reduce area dissipation, under the framework of semi-tensor product (STP) of matrices, the problem of constructing filter generators with minimum number of stages is converted into the one of determining the corresponding transition matrices. Compared with the existing results, the lower bound of the minimum number of stages is provided, which can reduce the exhaustive search time required to find it. Finally, one example is used to illustrate the efficacy of the proposed algorithm. Keywords
filter generator, Boolean network, semi-tensor product
Citation Li B W, Lu J Q. Boolean-network-based approach for construction of filter generators. Sci China Inf Sci, 2020, 63(11): 212206, https://doi.org/10.1007/s11432-019-2813-7
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Introduction
With the growth of Internet-of-Things applications, an increasing number of every-day-life applications have become security-critical, demanding high levels of assurance. Stream ciphers having good correlation properties have been widely applied to protect confidential information via Internet communications, error-correcting codes, spread-spectrum communications, etc. These ciphers are generally faster and less complex for hardware devices than block ciphers [1]. Therefore, in 2004, the ECRYPT (European Network of Excellence for Cryptology) launched a program called eSTREAM to identify stream ciphers that could be widely used. Seven algorithms having good applicability were selected. Note that feedback shift registers (FSRs) were the main building blocks in three types of selected stream ciphers: Grain, Trivium and Michkey. An FSR comprises combinational logical circuits, feedback function, and the storage cells (i.e., stages). For the past few decades, the use of FSRs has resulted in a relatively mature theory, and some interesting results have been obtained, such as [2, 3]. Recently, a new linear representation for FSRs was proposed in [4], where FSRs were viewed as Boolean networks (BNs). A BN is a class of logical networks, and was firstly used to
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