Formalization of the Advanced Encryption Standard. Part I

Kenichi Arai; Hiroyuki Okazaki

Formalized Mathematics (2013)

  • Volume: 21, Issue: 3, page 171-184
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Kenichi Arai, and Hiroyuki Okazaki. "Formalization of the Advanced Encryption Standard. Part I." Formalized Mathematics 21.3 (2013): 171-184. <http://eudml.org/doc/266858>.

@article{KenichiArai2013,
abstract = {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.},
author = {Kenichi Arai, Hiroyuki Okazaki},
journal = {Formalized Mathematics},
keywords = {Mizar formalization; Advanced Encryption Standard (AES) algorithm; cryptology},
language = {eng},
number = {3},
pages = {171-184},
title = {Formalization of the Advanced Encryption Standard. Part I},
url = {http://eudml.org/doc/266858},
volume = {21},
year = {2013},
}

TY - JOUR
AU - Kenichi Arai
AU - Hiroyuki Okazaki
TI - Formalization of the Advanced Encryption Standard. Part I
JO - Formalized Mathematics
PY - 2013
VL - 21
IS - 3
SP - 171
EP - 184
AB - 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.
LA - eng
KW - Mizar formalization; Advanced Encryption Standard (AES) algorithm; cryptology
UR - http://eudml.org/doc/266858
ER -

References

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