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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 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
Efficient prediction of MarsagliaZaman random number generators
 IEEE Transactions on Information Theory
, 1993
"... Abstract—We show that the random number generator of Marsaglia and Zaman produces the successive digits of a rationaladic number. (Theadic number system generalizesadic numbers to an arbitrary integer base.) Using continued fractions, we derive an efficient prediction algorithm for this generator ..."
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Cited by 3 (0 self)
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Abstract—We show that the random number generator of Marsaglia and Zaman produces the successive digits of a rationaladic number. (Theadic number system generalizesadic numbers to an arbitrary integer base.) Using continued fractions, we derive an efficient prediction algorithm for this generator. Index Terms — Continued fractions, inductive inference,adic numbers, pseudorandom sequences.
A Tutorial on padic Arithmetic
"... The padic arithmetic allows errorfree representation of fractions and errorfree arithmetic using fractions. In this tutorial, we describe infiniteprecision padic arithmetic which is more suitable for software implementations and finiteprecision padic arithmetic which is more suitable for hard ..."
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Cited by 1 (0 self)
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The padic arithmetic allows errorfree representation of fractions and errorfree arithmetic using fractions. In this tutorial, we describe infiniteprecision padic arithmetic which is more suitable for software implementations and finiteprecision padic arithmetic which is more suitable for hardware implementations. The finiteprecision padic representation is also called Hensel code which has certain interesting properties and some open problems for research. 1
Implementing Data Parallel Rational MultipleResidue Arithmetic in Eden ⋆ Extended and revisited version
"... Abstract. Residue systems present a wellknown way to reduce computation cost for symbolic computation. However most residue systems are implemented for integers or polynomials. This work combines two known results in a novel manner. Firstly, it lifts an integral residue system to fractions. Secondl ..."
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Abstract. Residue systems present a wellknown way to reduce computation cost for symbolic computation. However most residue systems are implemented for integers or polynomials. This work combines two known results in a novel manner. Firstly, it lifts an integral residue system to fractions. Secondly, it generalises a singleresidue system to a multipleresidue one. Combined, a rational multiresidue system emerges. Due to the independent manner of single “parts ” of the system, this work enables progress in parallel computing. We present a complete implementation of the arithmetic in the parallel Haskell extension Eden. The parallelisation utilises algorithmic skeletons. We compare our approach with Maple. A nontrivial example computation is also supplied.