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Fibonacci and Galois Representations of FeedbackWithCarry Shift Registers
 IEEE Trans. Inform. Theory
, 2002
"... A feedbackwithcarry shift register (FCSR) with "Fibonacci" architecture is a shift register provided with a small amount of memory which is used in the feedback algorithm. Like the linear feedback shift register (LFSR), the FCSR provides a simple and predictable method for the fast generation of p ..."
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Cited by 20 (2 self)
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A feedbackwithcarry shift register (FCSR) with "Fibonacci" architecture is a shift register provided with a small amount of memory which is used in the feedback algorithm. Like the linear feedback shift register (LFSR), the FCSR provides a simple and predictable method for the fast generation of pseudorandom sequences with good statistical properties and large periods. In this paper, we describe and analyze an alternative architecture for the FCSR which is similar to the "Galois" architecture for the LFSR. The Galois architecture is more efficient than the Fibonacci architecture because the feedback computations are performed in parallel. We also describe the output sequences generated by theFCSR, a slight modification of the (Fibonacci) FCSR architecture in which the feedback bit is delayed for clock cycles before being returned to the first cell of the shift register. We explain how these devices may be configured so as to generate sequences with large periods. We show that the FCSR also admits a more efficient "Galois" architecture.
ON THE DISTINCTNESS OF MODULAR REDUCTIONS OF MAXIMAL LENGTH SEQUENCES MODULO ODD
"... Abstract. We discuss the distinctness problem of the reductions modulo M of maximal length sequences modulo powers of an odd prime p, where the integer M has a prime factor different from p. For any two different maximal length sequences generated by the same polynomial, we prove that their reductio ..."
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Cited by 2 (2 self)
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Abstract. We discuss the distinctness problem of the reductions modulo M of maximal length sequences modulo powers of an odd prime p, where the integer M has a prime factor different from p. For any two different maximal length sequences generated by the same polynomial, we prove that their reductions modulo M are distinct. In other words, the reduction modulo M of a maximal length sequence is proved to contain all the information of the original sequence. 1.
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).
Search algorithms for FCSR architectures and properties of the FCSR combiner generator
, 2005
"... The feedbackwithcarry shift register (FCSR) is an important primitive in the design of stream ciphers. In the first part of this thesis, we propose efficient methods to search for FCSR architectures of guaranteed period and 2adic complexity. We devise extended versions of these methods that yield ..."
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The feedbackwithcarry shift register (FCSR) is an important primitive in the design of stream ciphers. In the first part of this thesis, we propose efficient methods to search for FCSR architectures of guaranteed period and 2adic complexity. We devise extended versions of these methods that yield architectures of guaranteed period and 2adic complexity, given additional design constraints such as a fixed number of feedback tap connections. We also propose a search algorithm for a generalisation of the basic FCSR architecture called the dFCSR, and discuss the difficulty of finding valid architectures for values of the parameter d other than d = 2.