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

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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.

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Authors and Affiliations

  1. College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, 410073, China

    Yubo Li, Kangquan Li & Longjiang Qu

  2. College of Computer, National University of Defense Technology, Changsha, 410073, China

    Zhichao Yang

  3. State Key Laboratory of Cryptology, Beijing, 100878, China

    Longjiang Qu

Authors
  1. Yubo Li
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  2. Zhichao Yang
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  3. Kangquan Li
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  4. Longjiang Qu
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Corresponding author

Correspondence to Longjiang Qu.

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Communicated by C. Mitchell.

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This work is supported by the Nature Science Foundation of China (NSFC) under Grants 61722213, 11531002, 61572026, and the Open Foundation of State Key Laboratory of Cryptology.

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Li, Y., Yang, Z., Li, K. et al. A new algorithm on the minimal rational fraction representation of feedback with carry shift registers. Des. Codes Cryptogr. 88, 533–552 (2020). https://doi.org/10.1007/s10623-019-00695-w

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  • DOI: https://doi.org/10.1007/s10623-019-00695-w

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