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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 ..."
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
Feedback Registers Based on Ramified Extensions of the 2Adic Numbers (Extended Abstract)
 Advances in Cryptology  Eurocrypt 1994. Lecture Notes in Computer Science 718
, 1995
"... A new class of feedback register, based on ramified extensions of the 2adic numbers, is described. An algebraic framework for the analysis of these registers and the sequences they output is given. This framework parallels that of linear feedback shift registers. As one consequence of this, a metho ..."
Abstract

Cited by 11 (4 self)
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A new class of feedback register, based on ramified extensions of the 2adic numbers, is described. An algebraic framework for the analysis of these registers and the sequences they output is given. This framework parallels that of linear feedback shift registers. As one consequence of this, a method for cracking summation ciphers is given. These registers give rise to new measures of cryptologic security.
Cryptanalysis Based on . . .
, 1995
"... This paper presents a new algorithm for cryptanalytically attacking stream ciphers. There is an associated measure of security, the 2adac 8pan. In order for a stream cipher to be secure, its Zadic span must be large. This attack exposes a weakness of Rueppel and Massey's summation combiner. The a ..."
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This paper presents a new algorithm for cryptanalytically attacking stream ciphers. There is an associated measure of security, the 2adac 8pan. In order for a stream cipher to be secure, its Zadic span must be large. This attack exposes a weakness of Rueppel and Massey's summation combiner. The algorithm, based on De Weger and Mahler's rational approximation theory for 2adic numbers, synthesizes a shortest feedback with cam shaft qwter that outputs a particular key stream, given a small number of bits of the key stream. It is adaptive in that it does not neeed to know the number of available bits beforehand.