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11
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 ..."
Abstract

Cited by 50 (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
Algebraic feedback shift registers
 Theoretical Comp. Sci
, 1999
"... A general framework for the design of feedback registers based on algebra over complete rings is described. These registers generalize linear feedback shift registers and feedback with carry shift registers. Basic properties of the output sequences are studied: relations to the algebra of the underl ..."
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Cited by 9 (3 self)
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A general framework for the design of feedback registers based on algebra over complete rings is described. These registers generalize linear feedback shift registers and feedback with carry shift registers. Basic properties of the output sequences are studied: relations to the algebra of the underlying ring; synthesis of the register from the sequence (which has implications for cryptanalysis); and basic statistical properties. These considerations lead to security measures for stream ciphers, analogous to the notion of linear complexity that arises from linear feedback shift registers. We also show that when the underlying ring is a polynomial ring over a finite field, the new registers can be simulated by linear feedback shift registers with small nonlinear filters. Key words: cryptography; feedback shift register; complete ring; stream cipher; pseudorandom number generator. 1
A Systematic Procedure for Applying Fast Correlation Attacks to Combiners with Memory
, 1997
"... A systematic procedure for applying fast correlation attacks to combiners with memory is introduced. This procedure consists of the following four stages: identifying correlated linear input and output transforms with maximum possible or relatively large correlation coefficient, calculating loww ..."
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Cited by 4 (0 self)
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A systematic procedure for applying fast correlation attacks to combiners with memory is introduced. This procedure consists of the following four stages: identifying correlated linear input and output transforms with maximum possible or relatively large correlation coefficient, calculating lowweight polynomial multiples based on the identified input linear transform, applying an iterative error correction algorithm to the linear transform of the observed keystream and solving several sets of linear equations to determine the initial state of the input LFSRs. This procedure is successfully applied to three keystream generators, namely, the summation generators with three and five inputs, the nonlinear filter generator and the multiplexed sequence generator. 1 Introduction A wellknown type of keystream generator for stream cipher applications consists of a number of linear feedback shift registers (LFSRs) combined by a memoryless nonlinear function. The keystream sequences pr...
Algebraic Attacks on Summation Generators
 In FSE 2004, number 3017 in Lecture Notes in Computer Science
, 2003
"... We apply the algebraic attacks on stream ciphers with memories to the summation generator. For a summation generator that uses n LFSRs, an algebraic equation relating the key stream bits and LFSR output bits can be made to be of degree less than or equal to 2 , using dlog 2 ne + 1 consecutive ..."
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Cited by 4 (1 self)
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We apply the algebraic attacks on stream ciphers with memories to the summation generator. For a summation generator that uses n LFSRs, an algebraic equation relating the key stream bits and LFSR output bits can be made to be of degree less than or equal to 2 , using dlog 2 ne + 1 consecutive key stream bits. This is much lower than the upper bound given by previous general results. We also show that the techniques of [5] can be applied to summation generators using 2 LFSRs to reduce the eective degree of the algebraic equation.
Correlation Analysis of Summation Generator
"... Abstract: J. Dj. Golić applied linear sequential circuit approximation (LSCA) method to analyze the summation generator with an arbitrary number of inputs. He conjectured that he could obtain all pairs of mutually correlated input and output linear functions with the maximum possible absolute value ..."
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Abstract: J. Dj. Golić applied linear sequential circuit approximation (LSCA) method to analyze the summation generator with an arbitrary number of inputs. He conjectured that he could obtain all pairs of mutually correlated input and output linear functions with the maximum possible absolute value of the correlation coefficient by this method, but he did not give any proof. By using Walsh Transformation technique, the conjecture is proved for even n in this paper. The “total correlation ” of summation generator is studied which is very similar to that of combiners with one bit memory. Key words: summation generator; correlation coefficient; memory; stream cipher 摘 要: J. Dj. Golić 运用线性序列电路逼进的方法来分析具有任意个输入的求和生成器.他猜想可以通过这种方 法来获得所有具有最大相关系数的输入和输出线性函数对,但是他未给出证明.利 用 Walsh 变换技术证明了 当 n 是
Research Summary
"... models for answering questions on the existence of secure families of sequence generators. 5. Design and analysis of families of sequences for secure spreadspectrum communications. These sequences include geometric sequences and dform sequences (the latter invented by me). ..."
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models for answering questions on the existence of secure families of sequence generators. 5. Design and analysis of families of sequences for secure spreadspectrum communications. These sequences include geometric sequences and dform sequences (the latter invented by me).
NESSIE D13  Security Evaluation of NESSIE First Phase
 Commission of the European Communities IST199912324
, 2001
"... A preliminary security assessment of cryptographic primitives submitted to the NESSIE project is given in this deliverable. ..."
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A preliminary security assessment of cryptographic primitives submitted to the NESSIE project is given in this deliverable.