Paper 2002/157

In How Many Ways Can You Write Rijndael?

Elad Barkan and Eli Biham


In this paper we ask the question what happens if we replace all the constants in Rijndael, including the replacement of the irreducible polynomial, the coefficients of the MixColumn operation, the affine transformation in the S box, etc. We show that such replacements can create new dual ciphers, which are equivalent to the original in all aspects. We present several such dual ciphers of Rijndael, such as the square of Rijndael, and dual ciphers with the irreducible polynomial replaced by primitive polynomials. We also describe another family of dual ciphers consisting of the logarithms of Rijndael. We then discuss self-dual ciphers, and extend our results to other ciphers.

Note: An earlier version of this paper appears in Asiacrypt 2002. See also ''The Book of Rijndaels''.

Available format(s)
Secret-key cryptography
Publication info
Published elsewhere. Asiacrypt 2002.
AESGalois FieldDual CipherSelf DualLogarithm
Contact author(s)
barkan @ cs technion ac il
2002-10-16: received
Short URL
Creative Commons Attribution


      author = {Elad Barkan and Eli Biham},
      title = {In How Many Ways Can You Write Rijndael?},
      howpublished = {Cryptology ePrint Archive, Paper 2002/157},
      year = {2002},
      note = {\url{}},
      url = {}
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