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

doi:10.1587/transfun.E102.A.1659

Special Section on Information Theory and Its Applications

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

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Keywords: group structure, pseudorandom number generator, NTU sequence

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2019 Volume E102.A Issue 12 Pages 1659-1667

DOI https://doi.org/10.1587/transfun.E102.A.1659

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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.

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