# Can the AES encryption and decryption algorithms be described as a polynomial for a specific key?

AES is a block cipher that consists of non-linear and linear parts to provide the Shannon requirements of confusion and diffusion respectively. The linear parts can for sure be described as a polynomial and more specifically the SiftRows,MixColumnds,AddRoundKey parts but what about the non-linear one?

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The AES sbox is an affine transformation of the inverse if its input, and has a fairly compact algebraic expression –  Richie Frame Sep 12 '13 at 18:37

Yes, they can be described as a multivariate polynomial over $GF(2)$ (or over $GF(2^8)$). See algebraic cryptanalysis. This expression does not seem to help cryptanalyze AES, so far as we know, but it can be done.