# Algebra of Polynomially Bounded Sequences and Negligible Functions

Formalized Mathematics (2015)

• Volume: 23, Issue: 4, page 371-378
• ISSN: 1426-2630

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## Abstract

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In this article we formalize negligible functions that play an essential role in cryptology [10], [2]. Generally, a cryptosystem is secure if the probability of succeeding any attacks against the cryptosystem is negligible. First, we formalize the algebra of polynomially bounded sequences [20]. Next, we formalize negligible functions and prove the set of negligible functions is a subset of the algebra of polynomially bounded sequences. Moreover, we then introduce equivalence relation between polynomially bounded sequences, using negligible functions.

## How to cite

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Hiroyuki Okazaki. "Algebra of Polynomially Bounded Sequences and Negligible Functions." Formalized Mathematics 23.4 (2015): 371-378. <http://eudml.org/doc/276933>.

@article{HiroyukiOkazaki2015,
abstract = {In this article we formalize negligible functions that play an essential role in cryptology [10], [2]. Generally, a cryptosystem is secure if the probability of succeeding any attacks against the cryptosystem is negligible. First, we formalize the algebra of polynomially bounded sequences [20]. Next, we formalize negligible functions and prove the set of negligible functions is a subset of the algebra of polynomially bounded sequences. Moreover, we then introduce equivalence relation between polynomially bounded sequences, using negligible functions.},
author = {Hiroyuki Okazaki},
journal = {Formalized Mathematics},
keywords = {polynomially bounded function; negligible functions},
language = {eng},
number = {4},
pages = {371-378},
title = {Algebra of Polynomially Bounded Sequences and Negligible Functions},
url = {http://eudml.org/doc/276933},
volume = {23},
year = {2015},
}

TY - JOUR
AU - Hiroyuki Okazaki
TI - Algebra of Polynomially Bounded Sequences and Negligible Functions
JO - Formalized Mathematics
PY - 2015
VL - 23
IS - 4
SP - 371
EP - 378
AB - In this article we formalize negligible functions that play an essential role in cryptology [10], [2]. Generally, a cryptosystem is secure if the probability of succeeding any attacks against the cryptosystem is negligible. First, we formalize the algebra of polynomially bounded sequences [20]. Next, we formalize negligible functions and prove the set of negligible functions is a subset of the algebra of polynomially bounded sequences. Moreover, we then introduce equivalence relation between polynomially bounded sequences, using negligible functions.
LA - eng
KW - polynomially bounded function; negligible functions
UR - http://eudml.org/doc/276933
ER -

## References

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