International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Paper: On Some Algebraic Structures in the AES Round Function

Authors:
A.M. Youssef
S.E. Tavares
Download:
URL: http://eprint.iacr.org/2002/144
Search ePrint
Search Google
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.
BibTeX
@misc{eprint-2002-11667,
  title={On Some Algebraic Structures in the AES Round Function},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / AES, Rijndael, Finite fields, Boolean functions},
  url={http://eprint.iacr.org/2002/144},
  note={ amr_y@ee.queensu.ca 11950 received 20 Sep 2002},
  author={A.M. Youssef and S.E. Tavares},
  year=2002
}