On Some Algebraic Structures in the AES Round Function

A. M.  Youssef; S. E.  Tavares

Paper 2002/144

On Some Algebraic Structures in the AES Round Function

A. M. Youssef and S. E. Tavares

Abstract

In this paper, we show that all the coordinate functions of the Advanced Encryption Standard (AES) round function are equivalent under an affi ne transformation of the input to the round function. In other words, let $f_i$ and $f_j$ be any two distinct output coordinates of the AES round function, then there exists a nonsingular matrix $A_{ji}$ over $GF(2)$ such that $f_j(A_{ji} x) + b_{ji}= f_i(x), b_{ji} \in GF(2)$. We also show that such linear relations will always exist if the Rijndael s-b ox is replaced by any bijective monomial over $GF(2^8)$. %We also show that replacing the s-box by any bijective monomial will not change this property.

Metadata

Available format(s): PDF PS
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: AES Rijndael Finite fields Boolean functions
Contact author(s): amr_y @ ee queensu ca
History: 2002-09-20: received
Short URL: https://ia.cr/2002/144
License: CC BY

BibTeX

@misc{cryptoeprint:2002/144,
      author = {A. M.  Youssef and S. E.  Tavares},
      title = {On Some Algebraic Structures in the {AES} Round Function},
      howpublished = {Cryptology {ePrint} Archive, Paper 2002/144},
      year = {2002},
      url = {https://eprint.iacr.org/2002/144}
}