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An Equivalence-Preserving Transformation of Shift Registers

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Sequences and Their Applications - SETA 2014 (SETA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8865))

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Abstract

The Fibonacci-to-Galois transformation is useful for reducing the propagation delay of feedback shift register-based stream ciphers and hash functions. In this paper, we extend it to handle Galois-to-Galois case as well as feedforward connections. This makes possible transforming Trivium stream cipher and increasing its keystream data rate by 27 % without any penalty in area. The presented transformation might open new possibilities for cryptanalysis of Trivium, since it induces a class of stream ciphers which generate the same set of keystreams as Trivium, but have a different structure.

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Notes

  1. 1.

    An \(n\)-bit NLFSR is uniform if, for all \(i \in \{\tau ,\tau +1,\ldots ,n-1\}\), the largest index of variables of function \(g_i\) in (2) is smaller than or equal to \(\tau \), where \(\tau \) is the maximal index such that, for all \(j \in \{0,1,\ldots ,\tau -1\}\), \(g_j = 0\).

  2. 2.

    We use an \(n\)-bit ring as a simplification of an \(n\)-bit shift register which shows the structure of its feedback/feedforward connections. The gates implementing GF(2) addition (XORs) are omitted and the gates implementing GF(2) multiplication (ANDs) are represented by a dot. Everything unnecessary for structural analysis is removed.

  3. 3.

    Note that in this case the initial states are the same but generally they can be different [22].

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Acknowledgements

This work was supported in part the research grant No 621-2010-4388 from the Swedish Research Council and in part by the research grant No SM12-0005 from the Swedish Foundation for Strategic Research.

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Authors and Affiliations

  1. Royal Institute of Technology (KTH), Electrum 229, 164 40, Kista, Sweden

    Elena Dubrova

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  1. Elena Dubrova
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Correspondence to Elena Dubrova .

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Editors and Affiliations

  1. Otto-von-Guericke University, Magdeburg, Germany

    Kai-Uwe Schmidt

  2. Austrian Academy of Sciences, Linz, Austria

    Arne Winterhof

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Dubrova, E. (2014). An Equivalence-Preserving Transformation of Shift Registers. In: Schmidt, KU., Winterhof, A. (eds) Sequences and Their Applications - SETA 2014. SETA 2014. Lecture Notes in Computer Science(), vol 8865. Springer, Cham. https://doi.org/10.1007/978-3-319-12325-7_16

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  • DOI: https://doi.org/10.1007/978-3-319-12325-7_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12324-0

  • Online ISBN: 978-3-319-12325-7

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