# 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

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topKenichi 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 -

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