Decoding a Perturbed Sequence Generated by an LFSR

  • Sara D. Cardell
  • Joan-Josep ClimentEmail author
  • Alicia Roca
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10495)


Given a sequence of bits produced by a linear feedback shift register (LFSR), the Berlekamp-Massey algorithm finds a register of minimal length able to generate the sequence. The situation is different when the sequence is perturbed; for instance, when it is sent through a transmission channel. LFSRs can be described as autonomous systems. A perturbed sequence of bits generated by an LFSR can be interpreted as a codeword in the binary linear code generated by the corresponding observability matrix. The problem of finding the original sequence can then be stated as the decoding problem, “given the received codeword, find the information transmitted”. We propose two decoding algorithms, one based on a brute force attack and the other one based on the representation technique of the syndromes introduced by Becker, Joux, May, and Meurer (2012).


LFSR Correlation attack Keystream sequence Companion matrix Autonomous system Syndrome decoding Decoding representation technique 



The first author was supported by FAPESP with number of process 2015/07246-0. The second author was partially supported by grants MIMECO MTM2015-68805-REDT and MTM2015-69138-REDT. The third author was partially supported by grants MINECO MTM2013-40960-P and MTM2015-68805-REDT.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Sara D. Cardell
    • 1
  • Joan-Josep Climent
    • 2
    Email author
  • Alicia Roca
    • 3
  1. 1.Instituto de Matemática, Estatística e Computação CientíficaUniversidade Estadual de Campinas (UNICAMP)CampinasBrazil
  2. 2.Departament de MatemàtiquesUniversitat d’AlacantAlacantSpain
  3. 3.Departamento de Matemática Aplicada, IMMUniversitat Politècnica de ValènciaValènciaSpain

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