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MessageID: <4244490C.9040205@cdc.informatik.tudarmstadt.de> Date: Fri, 25 Mar 2005 18:23:24 +0100 From: RalfPhilipp Weinmann <weinmann@....informatik.tudarmstadt.de> To: Jerrold Leichter <jerrold.leichter@...rts.com> Cc: Adam Shostack <adam@...eport.org>, bugtraq@...urityfocus.com, BugTraq <bugtraq@...urescience.net>, cryptography@...zdowd.com Subject: Re: Secure Science issues preview of their upcoming block cipher Jerrold Leichter wrote: > I can come up with a cipher provably just as secure as AES128 very quickly.... > > (Actually, based on the paper a while back on many alternative ways to > formulate AES  it had a catchy title something like "How Many Ways Can You > Spell AES?", except that I can't find one like that now  one could even > come up with a formulation that is (a) probably as secure as AES128; (b) > actually faster in hardware or simpler to implement or whatever...) You're probably looking for [1] by Barkan and Biham. What they do is replacing the irreducible polynomial and all the constants involved in Rijndael to get what they call "dual ciphers"; basically those ciphers are isomorphic to Rijndael. All in all they get 240 dual ciphers which are listed in [2]. What I found more interesting back then was that they also give square dual and log dual ciphers of Rijndael. I.e. let E be the Rijndael encryption and E' be the encryption function of the square/log dual Rijndael construction. Furthermore let f be a function that either performs bytewise squaring in GF(2^8) or replaces each byte with a logarithmic representation (relative to a generator g. you also need to fix log_g(0) = \infty for this to make sense). Then E'(f(plaintext), f(key)) = f(E(plaintext, key)) holds. The squaring construction then also naturally extends to what they call "higherorder self dual ciphers": meaning you can apply the squaring multiple times. In 2004 Wu, Lu and Laih then demonstrated that using Barkan's and Biham's method can indeed lead to more efficient implementations of AES/Rijndael in hardware. Cheers, Ralf [1] Elad Barkan and Eli Biham: In How Many Ways Can You Write Rijndael? ASIACRYPT 2002, Springer note: also on ePrint as http://eprint.iacr.org/2002/157 if you don't have Springer Link access [2] Elad Barkan and Eli Biham: The Book of Rijndaels http://eprint.iacr.org/2002/158 [3] SheeYau Wu and ShihChuan Lu and Chi Sung Laih: Design of AES Based on Dual Cipher and Composite Field Topics in Cryptology, CTRSA 2004, Springer  RalfP. Weinmann <weinmann@....informatik.tudarmstadt.de> TU Darmstadt, FB Informatik, FG Theoretische Informatik Tel: +49(0)6151166628  The Cryptography Mailing List Unsubscribe by sending "unsubscribe cryptography" to majordomo@...zdowd.com
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