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Feedback shift registers, 2adic span, and combiners with memory
 Journal of Cryptology
, 1997
"... Feedback shift registers with carry operation (FCSR’s) are described, implemented, and analyzed with respect to memory requirements, initial loading, period, and distributional properties of their output sequences. Many parallels with the theory of linear feedback shift registers (LFSR’s) are presen ..."
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Cited by 51 (7 self)
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Feedback shift registers with carry operation (FCSR’s) are described, implemented, and analyzed with respect to memory requirements, initial loading, period, and distributional properties of their output sequences. Many parallels with the theory of linear feedback shift registers (LFSR’s) are presented, including a synthesis algorithm (analogous to the BerlekampMassey algorithm for LFSR’s) which, for any pseudorandom sequence, constructs the smallest FCSR which will generate the sequence. These techniques are used to attack the summation cipher. This analysis gives a unified approach to the study of pseudorandom sequences, arithmetic codes, combiners with memory, and the MarsagliaZaman random number generator. Possible variations on the FCSR architecture are indicated at the end. Index Terms – Binary sequence, shift register, stream cipher, combiner with memory, cryptanalysis, 2adic numbers, arithmetic code, 1/q sequence, linear span. 1
Cryptographically Strong de Bruijn Sequences with Large Periods
, 2012
"... In this paper we first refine Mykkeltveit et al.’s technique for producing de Bruijn sequences through compositions. We then conduct an analysis on an approximation of the feedback functions that generate de Bruijn sequences. The cycle structures of the approximated feedback functions and the linea ..."
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Cited by 3 (0 self)
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In this paper we first refine Mykkeltveit et al.’s technique for producing de Bruijn sequences through compositions. We then conduct an analysis on an approximation of the feedback functions that generate de Bruijn sequences. The cycle structures of the approximated feedback functions and the linear complexity of a sequence produced by an approximated feedback function are determined. Furthermore, we present a compact algebraic representation of an (n + 16)stage nonlinear feedback shift register (NLFSR) and a few examples of de Bruijn sequences of period 2 n, 35 ≤ n ≤ 40, which are generated by the recursively constructed NLFSR together with the evaluation of their implementation.
Cryptographic Dmorphic Analysis and Fast Implementations of Composited De Bruijn Sequences
, 2012
"... Recently, Mandal and Gong [23] refined and analyzed the recursive method by Lempel and Mykkeltveit et al. for generating de Bruijn sequences, where the recursive feedback function is the sum of a feedback function with kth order composition and a sum of (k + 1) productofsum terms. In this paper ..."
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Recently, Mandal and Gong [23] refined and analyzed the recursive method by Lempel and Mykkeltveit et al. for generating de Bruijn sequences, where the recursive feedback function is the sum of a feedback function with kth order composition and a sum of (k + 1) productofsum terms. In this paper we first determine the linear complexity of a composited de Bruijn sequence. We then conduct a profound analysis of the recursive construction by introducing the notion of the higher order Dmorphism of a binary sequence. In the analysis, we consider both linearly and nonlinearly generated composited de Bruijn sequences and calculate the success probability of obtaining a kth order Dmorphic order n de Bruijn preimages ((n, k)DMDP) of length (2 n + k) and a kth order Dmorphic order n msequence preimages ((n, k)DMMP) of length (2n + k) as one of (n, k)DMMP and (n, k)DMDP allows one to construct the starting de Bruijn sequence and to recover the feedback function. Moreover, we investigate the hardness of producing the whole composited de Bruijn sequence from a known (n, k)DMDP of the composited de Bruijn sequence. Furthermore, we present a new iterative technique with its parallel extension for computing the productofsum terms of the feedback function where a productofsum term is calculated in an iteration. In addition, we present three de Bruijn sequences of period 2 64 together with their software implementations and performances.
Algebraic Shift Register Sequences
, 2009
"... and The Institute for Advanced Study, where he was a visitor during part of the writing of this book. His participation in the writing of this book was partially supported by NSF grant CCF ..."
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and The Institute for Advanced Study, where he was a visitor during part of the writing of this book. His participation in the writing of this book was partially supported by NSF grant CCF
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"... The purpose of this paper is to consider a number of general encoding schemes for a twodimensional positionsensing scheme. The general idea of the scheme is to write a pattern onto a planar, rectangular surface in such a way that, given any small part of the pattern (of predetermined nature), the ..."
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The purpose of this paper is to consider a number of general encoding schemes for a twodimensional positionsensing scheme. The general idea of the scheme is to write a pattern onto a planar, rectangular surface in such a way that, given any small part of the pattern (of predetermined nature), the exact location of this partpattern on the surface can be
Study on Pseudorandom Sequences with Applications in Cryptography and Telecommunications
"... Abstract. Pseudorandom sequences have many applications in cryptography and spread spectrum communications. In this dissertation, on one hand we develop tools for assessing the randomness of a sequence, and on the other hand we propose new constructions of pseudorandom sequences. More precisely, we ..."
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Abstract. Pseudorandom sequences have many applications in cryptography and spread spectrum communications. In this dissertation, on one hand we develop tools for assessing the randomness of a sequence, and on the other hand we propose new constructions of pseudorandom sequences. More precisely, we develop tools for computing the first order approximation of a binary sequence with the minimum linear complexity, we propose two efficient algorithms for computing the second order complexity (quadratic span) of a binary sequence, and we consider and solve the problem of computing the maximum nonlinear complexity (span) of a sequence. Finally, we investigate the properties of a family of sequences constructed as the direct sum of two sequences with ideal autocorrelation, like the GMW sequences. 1