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Analysis of NORX: Investigating Differential and Rotational Properties

  • Jean-Philippe Aumasson
  • Philipp Jovanovic
  • Samuel Neves
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8895)

Abstract

This paper presents a thorough analysis of the AEAD scheme NORX, focussing on differential and rotational properties. We first introduce mathematical models that describe differential propagation with respect to the non-linear operation of NORX. Afterwards, we adapt a framework previously proposed for ARX designs allowing us to automatise the search for differentials and characteristics. We give upper bounds on the differential probability for a small number of steps of the NORX core permutation. For example, in a scenario where an attacker can only modify the nonce during initialisation, we show that characteristics have probabilities of less than \(2^{-60}\) (\(32\)-bit) and \(2^{-53}\) (\(64\)-bit) after only one round. Furthermore, we describe how we found the best characteristics for four rounds, which have probabilities of \(2^{-584}\) (\(32\)-bit) and \(2^{-836}\) (\(64\)-bit), respectively. Finally, we discuss some rotational properties of the core permutation which yield some first, rough bounds and can be used as a basis for future studies.

Keywords

NORX AEAD LRX Differential cryptanalysis Rotational cryptanalysis 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their comprehensive commentaries which helped to improve the quality of this paper.

Supplementary material

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jean-Philippe Aumasson
    • 1
  • Philipp Jovanovic
    • 2
  • Samuel Neves
    • 3
  1. 1.Kudelski SecurityLausanneSwitzerland
  2. 2.University of PassauPassauGermany
  3. 3.University of CoimbraCoimbraPortugal

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