Cryptology ePrint Archive: Report 2002/099

A New Statistical Testing for Symmetric Ciphers and Hash Functions

Eric Filiol

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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