A Fourier Transform Approach to the Linear Complexity of Nonlinearly Filtered Sequences

Massey, James L.; Serconek, Shirlei

doi:10.1007/3-540-48658-5_31

Cited by 37 publications

(20 citation statements)

References 5 publications

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“…A well known result of Key [89] gives an upper bound on the linear span of the resulting sequence. As pointed out in [136] this result is most easily proven using Blahut's theorem. The Hadamard product c = a · b of sequences a, b is the termwise product, c = (a 0 b 0 , a 1 b 1 , · · ·).…”

Section: 5b Nonlinear Filtersmentioning

confidence: 79%

“…The result is credited to R. Blahut by J. Massey in [134] because it appears implicitly in [10]. See also [136] for a self-contained exposition. We use standard facts from Sections 2.3 and 3.2.h concerning the Fourier transform.…”

Section: Blahut's Theoremmentioning

confidence: 99%

“…However, Massey and Serconek have developed a generalization (the GDFT) of the discrete Fourier transform that can be used to analyze the linear span of an arbitrary periodic sequence over a finite field. [136,137]. They refer to the result as the Günther-Blahut theorem because it is equivalent to a result by Günther [70].…”

Section: The Günther-blahut Theoremmentioning

confidence: 99%

“…In this section we review the construction of Günther, Massey and Serconek [70], [136], [137]. Let a = a 0 , a 1 , · · · be a sequence over F of period T = np v for positive integers n and v, with p = char(F ) relatively prime to n. Associate to this sequence the polynomial f (x) = a 0 + a 1 x + · · · + a N −1 x N −1 .…”

Section: 4b the Gdft And Günther Weightmentioning

confidence: 99%

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Algebraic Shift Register Sequences

Goresky

Klapper

2012

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Pseudo-random sequences are essential ingredients of every modern digital communication system including cellular telephones, GPS, secure internet transactions and satellite imagery. Each application requires pseudo-random sequences with specific statistical properties. This book describes the design, mathematical analysis and implementation of pseudo-random sequences, particularly those generated by shift registers and related architectures such as feedback-with-carry shift registers. The earlier chapters may be used as a textbook in an advanced undergraduate mathematics course or a graduate electrical engineering course; the more advanced chapters provide a reference work for researchers in the field. Background material from algebra, beginning with elementary group theory, is provided in an appendix.

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Section: 5b Nonlinear Filtersmentioning

confidence: 79%

Section: Blahut's Theoremmentioning

confidence: 99%

Section: The Günther-blahut Theoremmentioning

confidence: 99%

Section: 4b the Gdft And Günther Weightmentioning

confidence: 99%

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Algebraic Shift Register Sequences

Goresky

Klapper

2012

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“…We can use the Walsh-Hadamard technique [28] to find the best linear approximation for the boolean function g such that:…”

Section: Descriptionmentioning

confidence: 99%

On the Security of Non-Linear HB (NLHB) Protocol against Passive Attack

Abyaneh

2010

2010 IEEE/IFIP International Conference on Embedded and Ubiquitous Computing

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Abstract. As a variant of the HB authentication protocol for RFID systems, which relies on the complexity of decoding linear codes against passive attacks, Madhavan et al. presented Non-Linear HB(NLHB) protocol. In contrast to HB, NLHB relies on the complexity of decoding a class of non-linear codes to render the passive attacks proposed against HB ineffective. Based on the fact that there has been no passive solution for the problem of decoding a random non-linear code, the authors have claimed that NLHB's security margin is very close to its key size. In this paper, we show that passive attacks against HB protocol can still be applicable to NLHB and this protocol does not provide the desired security margin. In our attack, we first linearize the non-linear part of NLHB to obtain a HB equivalent for NLHB, and then exploit the passive attack techniques proposed for the HB to evaluate the security margin of NLHB. The results show that although NLHB's security margin is relatively higher than HB against similar passive attack techniques, it has been overestimated and, in contrary to what is claimed, NLHB is vulnerable to passive attacks against HB, especially when the noise vector in the protocol has a low weight.

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The complexity of binary sequences using logistic chaotic maps

Liu

Miao

2015

Complexity

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The information sources using logistic maps have been studied in this article. We use a particular symmetric binary function to generate the binary sequences due to the generating partition of the logistic maps, which can reflect the dynamics of chaotic real-valued sequences. Using this binary function, we will establish a binary description of the logistic maps, and prove that this description is equivalent with the logistic maps. The probability of all the possible binary sequences generated by this symmetric binary function has been calculated according to this description. Furthermore, the cryptographic complexity of these binary sequences is evaluated theoretically and experimentally, including the correlation functions, the linear complexity, the nonlinear complexity, the Lempel-Ziv complexity and the approximate entropy. Such results show that the logistic binary sequences have good properties of cryptography.

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A Fourier Transform Approach to the Linear Complexity of Nonlinearly Filtered Sequences

Cited by 37 publications

References 5 publications

Algebraic Shift Register Sequences

Algebraic Shift Register Sequences

On the Security of Non-Linear HB (NLHB) Protocol against Passive Attack

The complexity of binary sequences using logistic chaotic maps

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