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On Differential Properties of Pseudo-Hadamard Transform and Related Mappings (Extended Abstract)

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Progress in Cryptology — INDOCRYPT 2002 (INDOCRYPT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2551))

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Abstract

In FSE 2001, Lipmaa and Moriai proposed efficient log-time algorithms for computing some functions that are related to the differential probability of modular addition. They posed it as an open question whether their algorithms can be generalized to more complex functions. In this paper, we will give a fundamentally different proof of their main result by using a more scalable linear-algebraic approach. Our proof technique enables us to easily derive differential probabilities of some other related mappings like the subtraction and the Pseudo-Hadamard Transform. Finally, we show how to apply the derived formulas to analyse partial round mapping of Twofish.

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References

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Author information

Authors and Affiliations

  1. Laboratory for Theoretical Computer Science Department of Computer Science and Engineering, Helsinki University of Technology, P.O.Box 5400, FI-02015, Espoo, Finland

    Helger Lipmaa

Authors
  1. Helger Lipmaa
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Editor information

Editors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Alfred Menezes

  2. Applied Statistics Unit, Indian Statistical Institute, 203, B.T. Road, 700108, Kolkata, India

    Palash Sarkar

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© 2002 Springer-Verlag Berlin Heidelberg

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Lipmaa, H. (2002). On Differential Properties of Pseudo-Hadamard Transform and Related Mappings (Extended Abstract). In: Menezes, A., Sarkar, P. (eds) Progress in Cryptology — INDOCRYPT 2002. INDOCRYPT 2002. Lecture Notes in Computer Science, vol 2551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36231-2_5

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  • DOI: https://doi.org/10.1007/3-540-36231-2_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00263-5

  • Online ISBN: 978-3-540-36231-9

  • eBook Packages: Springer Book Archive

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