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A new algorithm on the minimal rational fraction representation of feedback with carry shift registers

  • Yubo Li
  • Zhichao Yang
  • Kangquan Li
  • Longjiang QuEmail author
Article
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Abstract

In 1994, Klapper and Goresky (Proceedings of the 1993 Cambridge Security Workshop, Lecture Notes in Computer Science, vol 809, Cambridge, pp 174–178, 1994) proposed a new device called feedback with carry shift register to generate pseudo-random sequences instead of using the traditional device linear feedback shift register. They raised an algorithm called as rational approximation algorithm to recover the device for a given sequence (Klapper and Goresky, Advances in Cryptology, Crypto’95, Lecture Notes in Computer Science, vol 963, Springer, Berlin, pp 262–274, 1995). In this paper, we propose a new algorithm by introducing a new parameter and get the best rational approximation of the sequence much more quickly, especially when the size of the sequence increases dramatically. Unlike most of known algorithms, we can solve the minimal lattice basis instead of one shortest vector. Besides, we can prove that the solution of each step is optimal regardless of the length of the input sequence theoretically.

Keywords

Sequence FCSR Lattice Rational approximation Rational fraction representation 

Mathematics Subject Classification

94A55 94A60 03G10 11P21 
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Notes

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Liberal Arts and SciencesNational University of Defense TechnologyChangshaChina
  2. 2.College of ComputerNational University of Defense TechnologyChangshaChina
  3. 3.State Key Laboratory of CryptologyBeijingChina

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