# Difference of Function on Vector Space over F

Formalized Mathematics (2014)

• Volume: 22, Issue: 3, page 269-275
• ISSN: 1426-2630

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## Abstract

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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.

## How to cite

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Kenichi Arai, Ken Wakabayashi, and Hiroyuki Okazaki. "Difference of Function on Vector Space over F." Formalized Mathematics 22.3 (2014): 269-275. <http://eudml.org/doc/271080>.

@article{KenichiArai2014,
abstract = {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.},
author = {Kenichi Arai, Ken Wakabayashi, Hiroyuki Okazaki},
journal = {Formalized Mathematics},
keywords = {Mizar formalization; difference of function on vector space over F; difference of function on vector space over },
language = {eng},
number = {3},
pages = {269-275},
title = {Difference of Function on Vector Space over F},
url = {http://eudml.org/doc/271080},
volume = {22},
year = {2014},
}

TY - JOUR
AU - Kenichi Arai
AU - Ken Wakabayashi
AU - Hiroyuki Okazaki
TI - Difference of Function on Vector Space over F
JO - Formalized Mathematics
PY - 2014
VL - 22
IS - 3
SP - 269
EP - 275
AB - 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.
LA - eng
KW - Mizar formalization; difference of function on vector space over F; difference of function on vector space over
UR - http://eudml.org/doc/271080
ER -

## References

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