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. MORELOS-ZARAGOZA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A   No.12   pp.1659-1667
Publication Date: 2019/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.1659
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Sequences
group structure,  pseudorandom number generator,  NTU sequence,  

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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.