Paper 2002/099

A New Statistical Testing for Symmetric Ciphers and Hash Functions

Eric Filiol


This paper presents a new, powerful statistical testing of symmetric ciphers and hash functions which allowed us to detect biases in both of these systems where previously known tests failed. We first give a complete characterization of the Algebraic Normal Form (ANF) of random Boolean functions by means of the Möbius transform. Then we built a new testing based on the comparison between the structure of the different Boolean functions Algebraic Normal Forms characterizing symmetric ciphers and hash functions and those of purely random Boolean functions. Detailed testing results on several cryptosystems are presented. As a main result we show that AES, DES Snow and Lili-128 fail all or part of the tests and thus present strong biases.

Note: Updated version accepted for presentation to ICICS 2002. Many thanks to Ralph Wernsdorf (Rohde & Schwarz SIT Gmbh)for his help in improving this paper. Detailed statistical results are available on author's webpage.

Available format(s)
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
AESDESBlock CiphersBoolean FunctionsHash FunctionsCryptanalysisStream CiphersStatistical Testing
Contact author(s)
efiliol @ wanadoo fr
2002-10-02: revised
2002-07-24: received
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Creative Commons Attribution


      author = {Eric Filiol},
      title = {A New Statistical Testing for Symmetric Ciphers and Hash Functions},
      howpublished = {Cryptology ePrint Archive, Paper 2002/099},
      year = {2002},
      note = {\url{}},
      url = {}
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