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Correlation attacks on cascades of clock controlled shift registers

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1163))

Abstract

Recently, short cascades of stop and go registers have been demonstrated to be susceptible to correlation attacks. This paper examines the correlation coefficients which serve as the basis for such attacks and proves that they converge to 0.5 exponentially fast when the number of stages in the cascade is increased. We use two alternative technical approaches, a transformation matrix describing the input/output behaviour of a cascade and a Markov model describing its state transitions, to derive closed expressions for these coefficients for some special cases, and to find an efficient way to compute them explicitely.

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References

  1. Don Coppersmith, Hugo Krawczyk, and Yshay Mansour. The shrinking generator. In Proceedings of Crypto'93, D.R. Stinson (ed), LNCS 773, pages 22–39. Springer Verlag, 1994.

    Google Scholar 

  2. Jovan Dj. Golić and M.J. Mihaljević. A generalized correlation attack on a class of stream ciphers based on the Levenshtein distance. Journal of Cryptology, 3(3):201–12, 1991.

    Google Scholar 

  3. Dieter Gollmann. Pseudo-random properties of cascade connections of clock-controlled shift registers. In Proceedings of Eurocrypt'84, T. Beth, N. Cot, I. Ingemarsson (eds), LNCS 209, pages 93–8. Springer Verlag, 1985.

    Google Scholar 

  4. Dieter Gollmann and William G. Chambers. Clock-controlled shift registers: a review. IEEE JSAC, 7(4):525–33, 1989.

    Google Scholar 

  5. V.B. Johnsen and Kjell Kjeldsen. Loop-free composition of certain finite automata. Information & Control, 22:303–319, 1973.

    Google Scholar 

  6. Kjell Kjeldsen and Einar Andresen. Some randomness properties of cascaded sequences. IEEE Transactions on Information Theory, 26(2):227–232, 1980.

    Article  Google Scholar 

  7. Erwin Kreyszig. Introductory Functional Analysis with Applications. Wiley & Sons, New York, 1978.

    Google Scholar 

  8. Rudolf Lidl and Harald Niederreiter. Introduction to finite fields and their applications. Cambridge University Press, Cambridge, 1986.

    Google Scholar 

  9. Renato Menicocci. Cryptanalysis of a two-stage Gollmann cascade generator. In Proceedings of SPRC'93, W. Wolfowicz (ed), pages 62–69. Rome, 1993.

    Google Scholar 

  10. Renato Menicocci. Short Gollmann cascade generators may be insecure. In Proceedings of the 4th IMA Conference on Cryptography and Coding, P.G.Farrell (ed), pages 281–297. IMA, 1995.

    Google Scholar 

  11. Peter Nyffeler. Binäre Automaten und ihre linearen Rekursionen. Dissertation, Universität Bern, 1975.

    Google Scholar 

  12. Sang-Joon Park, Sang-Jin Lee, and Seung-Cheol Goh. On the security of the Gollmann cascades. In Proceedings of Crypto'95, D. Coppersmith (ed), LNCS 963, pages 148–156. Springer Verlag, 1995.

    Google Scholar 

  13. Ernst S. Selmer. From the memoirs of a Norwegian cryptologist. In Proceedings of Eurocrypt'93, T. Helleseth (ed), LNCS 765, pages 142–50. Springer Verlag, 1994.

    Google Scholar 

  14. Bernard Smeets. A note on sequences generated by clock controlled shift registers. In Proceedings of Eurocrypt'85, F. Pichler (ed), LNCS 219, pages 142–148. Springer Verlag, 1986.

    Google Scholar 

  15. Rainer Vogel. On the linear complexity of cascaded sequences. In Proceedings of Eurocrypt'84, T. Beth, N. Cot, I. Ingemarsson (eds), LNCS 209, pages 99–109. Springer Verlag, 1985.

    Google Scholar 

  16. Miodrag V. Živković. An algorithm for the initial state reconstruction of the clock-controlled shift register. IEEE Transactions on Information Theory, 37(5):1488–1490, 1991.

    Article  Google Scholar 

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Kwangjo Kim Tsutomu Matsumoto

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© 1996 Springer-Verlag

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Geiselmann, W., Gollmann, D. (1996). Correlation attacks on cascades of clock controlled shift registers. In: Kim, K., Matsumoto, T. (eds) Advances in Cryptology — ASIACRYPT '96. ASIACRYPT 1996. Lecture Notes in Computer Science, vol 1163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034860

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  • DOI: https://doi.org/10.1007/BFb0034860

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61872-0

  • Online ISBN: 978-3-540-70707-3

  • eBook Packages: Springer Book Archive

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