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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year

SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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Volume 21, Issue 3


Formalization of the Advanced Encryption Standard. Part I

Kenichi Arai / Hiroyuki Okazaki


In this article, we formalize the Advanced Encryption Standard (AES). AES, which is the most widely used symmetric cryptosystem in the world, is a block cipher that was selected by the National Institute of Standards and Technology (NIST) as an official Federal Information Processing Standard for the United States in 2001 [12]. AES is the successor to DES [13], which was formerly the most widely used symmetric cryptosystem in the world. We formalize the AES algorithm according to [12]. We then verify the correctness of the formalized algorithm that the ciphertext encoded by the AES algorithm can be decoded uniquely by the same key. Please note the following points about this formalization: the AES round process is composed of the SubBytes, ShiftRows, MixColumns, and AddRoundKey transformations (see [12]). In this formalization, the SubBytes and MixColumns transformations are given as permutations, because it is necessary to treat the finite field GF(28) for those transformations. The formalization of AES that considers the finite field GF(28) is formalized by the future article.

Keywords: Mizar formalization; Advanced Encryption Standard (AES) algorithm; cryptology

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About the article

Published in Print: 2013-10-01

Citation Information: Formalized Mathematics, Volume 21, Issue 3, Pages 171–184, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/forma-2013-0019.

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