On the Periods of Fibonacci Sequences Mod N

Author

Li Yong-jiang ; Li Chang-Li ; Ge Jian-hua ; Sun Zhi-lin

Author_Institution

State Key Lab. of Integrated Service Networks, Xidian Univ., Xi´an, China

fYear

2010

Firstpage

1

Lastpage

4

Abstract

An upper bound for the smallest period of the Fibonacci module sequence is obtained, which is 6N, and more accurate and convenient than the current results. Since the smallest period of the Fibonacci module sequence is twice of that of two-dimensional Arnold transformation, the upper bound for the smallest module period of Arnold transformation is naturally 3N. It is a great advance compared with the existing best upper bound N²/2 in the literatures. Moreover, many important properties are gained, which provide new thought for study on the period of Arnold transformation and the necessary mathematical reference of image coding and processing.

Keywords

Fibonacci sequences; data encapsulation; image coding; recursive functions; security of data; watermarking; Arnold transformation; Fibonacci module sequence; image coding; image scrambling; information hiding; mod N; Artificial neural networks; Estimation; Image coding; Intserv networks; Manganese; Transforms; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Logistics Engineering and Intelligent Transportation Systems (LEITS), 2010 International Conference on

Conference_Location

Wuhan

Print_ISBN

978-1-4244-8776-9

Electronic_ISBN

978-1-4244-8778-3

Type

conf

DOI

10.1109/LEITS.2010.5664966

Filename

5664966