[Resource Topic] 2002/144: On Some Algebraic Structures in the AES Round Function

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On Some Algebraic Structures in the AES Round Function

Authors: A. M. Youssef, S. E. Tavares


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.

ePrint: https://eprint.iacr.org/2002/144

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