Algebraic group structure of the random number generator: Theoretical analysis of NTU sequence(s)

Authors

Yuta Kodera, Graduate School of Natural Science and Technology Okayama University
Md. Arshad Ali, Okayama University
Takeru Miyazaki, The University of Kitakyushu
Takuya Kusaka, Graduate School of Natural Science and Technology Okayama University
Yasuyuki Nogami, Okayama University
Satoshi Uehara, University of Kitakyushu
Robert Morelos-Zaragoza, San Jose State University

Publication Date

January 2019

Document Type

Article

Publication Title

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volume

E102A

Issue

12

DOI

10.1587/transfun.E102.A.1659

First Page

1659

Last Page

1667

Abstract

An algebraic group is an essential mathematical structure for current communication systems and information security technologies. Further, as a widely used technology underlying such systems, pseudorandom number generators have become an indispensable part of their construction. This paper focuses on a theoretical analysis for a series of pseudorandom sequences generated by a trace function and the Legendre symbol over an odd characteristic field. As a consequence, the authors give a theoretical proof that ensures a set of subsequences forms a group with a specific binary operation.

Keywords

Group structure, NTU sequence, Pseudorandom number generator

Recommended Citation

Yuta Kodera, Md. Arshad Ali, Takeru Miyazaki, Takuya Kusaka, Yasuyuki Nogami, Satoshi Uehara, and Robert Morelos-Zaragoza. "Algebraic group structure of the random number generator: Theoretical analysis of NTU sequence(s)" IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (2019): 1659-1667. https://doi.org/10.1587/transfun.E102.A.1659