Research Article | OPEN ACCESS
Generalized Linear Orthomorphisms
1Haiqing Han, 1Yanping He and 2Siru Zhu
1Department of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, Hubei, China
2Department of the Basics, AFRA, Wuhan 430019, Hubei, China
Research Journal of Applied Sciences, Engineering and Technology 2013 11:3074-3078
Received: August 11, 2012 | Accepted: September 17, 2012 | Published: April 05, 2013
Abstract
In this study, we generalize the conception of orthomorphisms and obtain a counting formula on the generalized linear orthomorphisms over the Galois field with the arbitrary prime number p as the characteristic. Thus the partial generation algorithm of generalized linear orthomorphisms is achieved. The counting formula of the linear orthomorphisms over the finite field with characteristic 2 is the special case in our results. Furthermore, the generalized linear orthomorphisms generated and discussed in this study can gain the maximum branch number when they are designed as P-permutations.
Keywords:
Block cipher, generalized linear orthomorphism, p-permutation, the branch number,
Competing interests
The authors have no competing interests.
Open Access Policy
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Copyright
The authors have no competing interests.
|
|
![](http://www.maxwellsci.com/images/RJASET-maxw.jpg) |
ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
![Submit Manuscript](../images/sub.jpg) |
Information |
|
|
|
Sales & Services |
|
|
|