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Algebraic Group Structure of the Random Number Generator: Theoretical Analysis of NTU Sequence(s)
Yuta KODERA Md. Arshad ALI Takeru MIYAZAKI Takuya KUSAKA Yasuyuki NOGAMI Satoshi UEHARA Robert H. MORELOSZARAGOZA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E102A
No.12
pp.16591667 Publication Date: 2019/12/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E102.A.1659
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications) Category: Sequences Keyword: group structure, pseudorandom number generator, NTU sequence,
Full Text: PDF(2MB)>>
Summary:
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.

