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On the frequency of symbols in sequences generated by nonlinear Feedforward generators

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Abstract

Due to their simple construction, LFSRs are commonly used as building blocks in various random number generators. Nonlinear feedforward logic is incorporated in LFSRs to increase the linear complexity of the generated sequences. This work deals with Nonlinear Feedforward Generators (NLFGs) that generate sequences over arbitrary finite fields. We analyze the frequency of symbols in sequences generated by such configurations. Further, we propose a method of using nonlinear feedforward logic with word-based σ-LFSRs wherein vectors over a finite field are seen as elements of an extension field. We then briefly analyze sequences generated by an existing scheme and show that sequences generated by the proposed scheme are statistically more balanced.

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Acknowledgements

The authors are grateful to Prof. Harish K. Pillai, Department of Electrical Engineering, Indian Institute of Technology Bombay, without whom this work would never have been possible.

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Correspondence to Suman Roy.

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Roy, S., Krishnaswamy, S. On the frequency of symbols in sequences generated by nonlinear Feedforward generators. Cryptogr. Commun. 12, 115–126 (2020). https://doi.org/10.1007/s12095-019-00379-1

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Keywords

  • Pesudorandom number generator (PRNG)
  • Linear feedback shift register (LFSR)
  • Nonlinear feedforward generator (NLFG)
  • Balanced distribution
  • Linear complexity

Mathematics Subject Classification (2010)

  • 94A55