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Aspects of Linearity in Cryptographic Sequence Generators

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Computational Science and Its Applications – ICCSA 2013 (ICCSA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7975))

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Abstract

In the present work, it is shown that the sequences obtained from a cryptographic sequence generator, the so-called shrinking generator, are just particular solutions of a kind of linear difference equations. Moreover, all these sequences are simple linear combinations of m-sequences weighted by other primary sequences. This fact establishes a subtle link between irregular decimation and linearity that can be conveniently exploited in the cryptanalysis of such sequence generators. These ideas can be easily extended to other decimation-based cryptographic generators as well as to interleaved sequence generators.

This work was supported by CDTI (Spain) under Project Cenit-HESPERIA as well as by Ministry of Science and Innovation and European FEDER Fund under Project TIN2011-25452/TSI.

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References

  1. Bluetooth, Specifications of the Bluetooth system, Version 1.1, http://www.bluetooth.com/

  2. Coppersmith, D., Krawczyk, H., Mansour, Y.: The Shrinking Generator. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 22–39. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  3. Dickson, L.E.: Linear Groups with an Exposition of the Galois Field Theory, pp. 3–71. Dover, New York (1958), An updated reprint can be found at http://www-math.cudenver.edu/~wcherowi/courses/finflds.html

  4. eSTREAM, the ECRYPT Stream Cipher Project, Call for Primitives, http://www.ecrypt.eu.org/stream/

  5. Fúster-Sabater, A., Caballero-Gil, P.: Strategic Attack on the Shrinking Generator. Theoretical Computer Science 409(3), 530–536 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fúster-Sabater, A., Caballero-Gil, P., Delgado-Mohatar, O.: Deterministic Computation of Pseudorandomness in Sequences of Cryptographic Application. In: Allen, G., Nabrzyski, J., Seidel, E., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2009, Part I. LNCS, vol. 5544, pp. 621–630. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Fúster-Sabater, A.: Generation of Pseudorandom Binary Sequences with Controllable Cryptographic Parameters. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2011, Part I. LNCS, vol. 6782, pp. 563–572. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Golomb, S.W.: Shift Register-Sequences. Aegean Park Press, Laguna Hill (1982)

    Google Scholar 

  9. Gong, G.: Theory and Applications of q-ary Interleaved Sequences. IEEE Trans. Information Theory 41(2), 400–411 (1995)

    Article  MATH  Google Scholar 

  10. Lee, K., O’Sullivan, M.E.: List decoding of Hermitian codes using Gröbner bases. Journal of Symbolic Computation 44(12), 1662–1675 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hu, Y., Xiao, G.: Generalized Self-Shrinking Generator. IEEE Trans. Inform. Theory 50, 714–719 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Key, E.L.: An Analysis of the Structure and Complexity of Nonlinear Binary Sequence Generators. IEEE Trans. Informat. Theory 22(6), 732–736 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications. Cambridge University Press, Cambridge (1986)

    MATH  Google Scholar 

  14. Massey, J.L.: Shift-Register Synthesis and BCH Decoding. IEEE Trans. Informat. Theory 15(1), 122–127 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  15. Meier, W., Staffelbach, O.: The Self-Shrinking Generator. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 205–214. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  16. Menezes, A.J., et al.: Handbook of Applied Cryptography. CRC Press, New York (1997)

    MATH  Google Scholar 

  17. Rivest, R.L.: The RC4 Encryption Algorithm. RSA Data Sec., Inc. (March 1998)

    Google Scholar 

  18. Respondek, J.S.: On the confluent Vandermonde matrix calculation algorithm. Applied Mathematics Letters 24(2), 103–106 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Respondek, J.S.: Numerical recipes for the high efficient inverse of the confluent Vandermonde matrices. Applied Mathematics and Computation 218(5), 2044–2054 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. Robshaw, M., Billet, O. (eds.): New Stream Cipher Designs. LNCS, vol. 4986. Springer, Heidelberg (2008)

    Google Scholar 

  21. Yet Another SSL (YASSL), http://www.yassl.com

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Author information

Authors and Affiliations

  1. Information Security Institute, C.S.I.C., Serrano 144, 28006, Madrid, Spain

    Amparo Fúster-Sabater

Authors
  1. Amparo Fúster-Sabater
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Editor information

Editors and Affiliations

  1. L-I.S.U.T. - D.A.P.I.t. Facoltà Ingegneria, Università degli Studi della Basilicata, Viale dell’Ateneo Lucano, 10, 85100, Potenza, Italy

    Beniamino Murgante

  2. Covenant University, Canaanland OTA, Nigeria

    Sanjay Misra

  3. Partimento di Scienze e Tecnologie per LAgricoltura, le Foreste, la Natura e lEnergia, Università degli Studi della Tuscia, Via S. Camillo de Lellis, snc, 01100, Viterbo, Italy

    Maurizio Carlini

  4. Dipartimento di Scienze dell’Ingegneria Civile e dell’Architecttura, Politecnico di Bari, Via Orabona, 4, 70125, Bari, Italy

    Carmelo M. Torre

  5. International University VNU-HCM, Quarter 6, Linh Trung, Thu Duc, Ho Chi Minh City, Vietnam

    Hong-Quang Nguyen

  6. School of Business Systems, Monash University, 3800, Clayton, VIC, Australia

    David Taniar

  7. Department of Intelligent Informatics, Kyushu Sangyo University, 2-3-1 Matsukadai, 813-8503, Higashi-ku, Fukuoka, Japan

    Bernady O. Apduhan

  8. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Osvaldo Gervasi

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Fúster-Sabater, A. (2013). Aspects of Linearity in Cryptographic Sequence Generators. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2013. ICCSA 2013. Lecture Notes in Computer Science, vol 7975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39640-3_3

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  • DOI: https://doi.org/10.1007/978-3-642-39640-3_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39639-7

  • Online ISBN: 978-3-642-39640-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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