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Binomial Characterization of Cryptographic Sequences

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Computational Science and Its Applications – ICCSA 2019 (ICCSA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11619))

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Abstract

The generalized self-shrinking generator is a sequence generator that produces binary sequences with good cryptographic properties. On the other hand, the binomial sequences are a well-defined class of sequences that can be obtained considering infinite successions of binomial coefficients modulo 2. In this work, we see that the generalized sequences can be computed as a finite binary sum of binomial sequences. Moreover, the cryptographic parameters of the generalized sequences can be studied in terms of the binomial sequences.

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References

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Acknowledgements

Research partially supported by Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación, and Fondo Europeo de Desarrollo Regional (FEDER, UE) under project COPCIS (TIN2017-84844-C2-1-R) and by Comunidad de Madrid (Spain) under project CYNAMON (P2018/TCS-4566), also co-funded by European Union FEDER funds. The first author was supported by CAPES (Brazil).

Author information

Authors and Affiliations

  1. Instituto de Matemática, Estatística e Computação Científica, UNICAMP, R. Sérgio Buarque de Holanda, 651, Campinas, SP, 13083-859, Brazil

    Sara D. Cardell

  2. Instituto de Tecnologías Físicas y de la Información, C.S.I.C., Serrano 144, 28006, Madrid, Spain

    Amparo Fúster-Sabater

Authors
  1. Sara D. Cardell
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  2. Amparo Fúster-Sabater
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Corresponding author

Correspondence to Sara D. Cardell .

Editor information

Editors and Affiliations

  1. Covenant University, Ota, Nigeria

    Sanjay Misra

  2. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  3. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  4. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  5. Saint Petersburg State University, Saint Petersburg, Russia

    Vladimir Korkhov

  6. Polytechnic University of Bari, Bari, Italy

    Carmelo Torre

  7. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  8. Monash University, Clayton, VIC, Australia

    David Taniar

  9. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  10. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

Appendices

Appendix A

figure a

Appendix B

$$\text {GSS-sequences for }p(x)=1+x+x^6$$
figure b

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Cardell, S.D., Fúster-Sabater, A. (2019). Binomial Characterization of Cryptographic Sequences. In: Misra, S., et al. Computational Science and Its Applications – ICCSA 2019. ICCSA 2019. Lecture Notes in Computer Science(), vol 11619. Springer, Cham. https://doi.org/10.1007/978-3-030-24289-3_59

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  • DOI: https://doi.org/10.1007/978-3-030-24289-3_59

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24288-6

  • Online ISBN: 978-3-030-24289-3

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