Characterisations of Extended Resiliency and Extended Immunity of S-Boxes

  • Josef Pieprzyk
  • Xian-Mo Zhang
  • Jovan Dj. Golić
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3935)


New criteria of extended resiliency and extended immunity of vectorial Boolean functions, such as S-boxes for stream or block ciphers, were recently introduced. They are related to a divide-and-conquer approach to algebraic attacks by conditional or unconditional equations. Classical resiliency turns out to be a special case of extended resiliency and as such requires more conditions to be satisfied. In particular, the algebraic degrees of classically resilient S-boxes are restricted to lower values. In this paper, extended immunity and extended resiliency of S-boxes are studied and many characterisations and properties of such S-boxes are established. The new criteria are shown to be necessary and sufficient for resistance against the divide-and-conquer algebraic attacks by conditional or unconditional equations.


Extended Resiliency Extended Immunity Divide-and- Conquer Algebraic Attacks 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Josef Pieprzyk
    • 1
  • Xian-Mo Zhang
    • 1
  • Jovan Dj. Golić
    • 2
  1. 1.Centre for Advanced Computing – Algorithms and Cryptography, Department of ComputingMacquarie UniversitySydneyAustralia
  2. 2.Telecom Italia Lab, Telecom ItaliaTurinItaly

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