Cryptology ePrint Archive: Report 2002/099
A New Statistical Testing for Symmetric Ciphers and Hash Functions
Abstract: 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 M\"obius 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.
Category / Keywords: secret-key cryptography / AES, DES, Block Ciphers, Boolean Functions, Hash Functions, Cryptanalysis, Stream Ciphers, Statistical Testing
Date: received 23 Jul 2002, last revised 1 Oct 2002
Contact author: efiliol at wanadoo fr
Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | BibTeX Citation
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.
Version: 20021002:064508 (All versions of this report)
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