Secure Science issues preview of their upcoming block cipher

Ralf-Philipp Weinmann weinmann at
Fri Mar 25 12:23:24 EST 2005

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.


[1] Elad Barkan and Eli Biham:
     In How Many Ways Can You Write Rijndael?
     ASIACRYPT 2002, Springer
     note: also on ePrint as
     if you don't have Springer Link access

[2] Elad Barkan and Eli Biham:
     The Book of Rijndaels

[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 <weinmann at>
TU Darmstadt, FB Informatik, FG Theoretische Informatik
Tel: +49-(0)6151-16-6628

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