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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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Volume 22, Issue 3


Difference of Function on Vector Space over F

Kenichi Arai / Ken Wakabayashi / Hiroyuki Okazaki
Published Online: 2014-03-31 | DOI: https://doi.org/10.2478/forma-2014-0027


In [11], the definitions of forward difference, backward difference, and central difference as difference operations for functions on R were formalized. However, the definitions of forward difference, backward difference, and central difference for functions on vector spaces over F have not been formalized. In cryptology, these definitions are very important in evaluating the security of cryptographic systems [3], [10]. Differential cryptanalysis [4] that undertakes a general purpose attack against block ciphers [13] can be formalized using these definitions. In this article, we formalize the definitions of forward difference, backward difference, and central difference for functions on vector spaces over F. Moreover, we formalize some facts about these definitions.

Keywords : Mizar formalization; difference of function on vector space over F


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About the article

Received: 2014-09-26

Published Online: 2014-03-31

Published in Print: 2014-09-01

Citation Information: Formalized Mathematics, Volume 22, Issue 3, Pages 269–275, ISSN (Online) 1898-9934, DOI: https://doi.org/10.2478/forma-2014-0027.

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© by Kenichi Arai. This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0) BY-SA 3.0

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