Paper 2002/149

About Filliol's Observations on DES, AES and Hash Functions (draft)

Nicolas T. Courtois


Recently Filiol proposed to test cryptographic algorithms by making statistics on the number of low degree terms in the boolean functions. The paper has been published on eprint on 23th of July 2002. In this paper we reproduce some of Filiol's simulations. We did not confirm his results: our results suggest that DES, AES, and major hash functions have no significative bias and their output bits behave just like random boolean functions.

Note: Few hours after the submission of this paper, Filiol updated his paper. His new, updated results show that, there is indeed no bias in the terms of degree <=2 in DES or AES. Thus Filiol confirmed our results. However he still does claim some other biases in DES and AES for different, more complex tests. Who knows...

Available format(s)
Secret-key cryptography
Publication info
Published elsewhere. draft, will probably never be published
block ciphersDESAEShash functionsSHA-1HavalRIPEMDMD4MD5boolean functions
Contact author(s)
courtois @ minrank org
2002-10-02: last of 4 revisions
2002-10-01: received
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Creative Commons Attribution


      author = {Nicolas T.  Courtois},
      title = {About Filliol's Observations on DES, AES and Hash Functions (draft)},
      howpublished = {Cryptology ePrint Archive, Paper 2002/149},
      year = {2002},
      note = {\url{}},
      url = {}
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