# 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 AES-128 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 AES-128; (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 "higher-order 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] Shee-Yau Wu and Shih-Chuan Lu and Chi Sung Laih:
Design of AES Based on Dual Cipher and Composite Field
Topics in Cryptology, CT-RSA 2004, Springer

--
Ralf-P. Weinmann <[EMAIL PROTECTED]>
TU Darmstadt, FB Informatik, FG Theoretische Informatik
Tel: +49-(0)6151-16-6628

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