Paper 2012/303

On The Distribution of Linear Biases: Three Instructive Examples

Mohamed Ahmed Abdelraheem, Martin Aagren, Peter Beelen, and Gregor Leander


Despite the fact that we evidently have very good block ciphers at hand today, some fundamental questions on their security are still unsolved. One such fundamental problem is to precisely assess the security of a given block cipher with respect to linear cryptanalysis. In by far most of the cases we have to make (clearly wrong) assumptions, e.g., assume independent round-keys. Besides being unsatisfactory from a scientific perspective, the lack of fundamental understanding might have an impact on the performance of the ciphers we use. As we do not understand the security sufficiently enough, we often tend to embed a security margin -- from an efficiency perspective nothing else than wasted performance. The aim of this paper is to stimulate research on these foundations of block ciphers. We do this by presenting three examples of ciphers that behave differently to what is normally assumed. Thus, on the one hand these examples serve as counter examples to common beliefs and on the other hand serve as a guideline for future work.

Available format(s)
Secret-key cryptography
Publication info
Published elsewhere. extended abstract to appear at CRYPTO 2012. This is the full version.
Contact author(s)
g leander @ mat dtu dk
2012-06-03: received
Short URL
Creative Commons Attribution


      author = {Mohamed Ahmed Abdelraheem and Martin Aagren and Peter Beelen and Gregor Leander},
      title = {On The Distribution of Linear Biases: Three Instructive Examples},
      howpublished = {Cryptology ePrint Archive, Paper 2012/303},
      year = {2012},
      note = {\url{}},
      url = {}
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