# Difference of Function on Vector Space over F

Kenichi Arai; Ken Wakabayashi; Hiroyuki Okazaki

Formalized Mathematics (2014)

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

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topKenichi 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 -

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