Weak Equivalents for Nonlinear Filtering Functions

  • Amparo Fúster-Sabater
  • Pino Caballero-Gil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8584)


The application of a nonlinear filtering function to a Linear Feedback Shift Register (LFSR) is a general technique for designing pseudorandom sequence generators with cryptographic application. In this paper, we investigate the equivalence between different nonlinear filtering functions applied to distinct LFSRs. It is a well known fact that given a binary sequence generated from a pair (nonlinear filtering function, LFSR), the same sequence can be generated from any other LFSR of the same length by using another filtering function. However, until now no solution has been found for the problem of computing such an equivalent. This paper analyzes the specific case in which the reciprocal LFSR of a given register is used to generate an equivalent of the original nonlinear filtering function. The main advantage of the contribution is that weaker equivalents can be computed for any nonlinear filter, in the sense that such equivalents could be used to cryptanalyze apparently secure generators. Consequently, to evaluate the cryptographic resistance of a sequence generator, the weakest equivalent cipher should be determined and not only a particular instance.


Nonlinear filtering function pseudorandom sequence LFSR stream cipher cryptography 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Amparo Fúster-Sabater
    • 1
  • Pino Caballero-Gil
    • 2
  1. 1.Institute of Physical and Information Technologies (CSIC)MadridSpain
  2. 2.University of La LagunaLa LagunaSpain

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