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

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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1659-1667
Number of pages	9
Journal	IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Volume	E102A
Issue number	12
DOIs	https://doi.org/10.1587/transfun.E102.A.1659
Publication status	Published - Jan 1 2019

Keywords

Group structure
NTU sequence
Pseudorandom number generator

ASJC Scopus subject areas

Signal Processing
Computer Graphics and Computer-Aided Design
Electrical and Electronic Engineering
Applied Mathematics

Access to Document

10.1587/transfun.E102.A.1659

Fingerprint Dive into the research topics of 'Algebraic group structure of the random number generator: Theoretical analysis of NTU sequence(s)'. Together they form a unique fingerprint.

Cite this

Algebraic group structure of the random number generator : Theoretical analysis of NTU sequence(s). / Kodera, Yuta; Ali, Md Arshad; Miyazaki, Takeru; Kusaka, Takuya ; Nogami, Yasuyuki; Uehara, Satoshi; Morelos-Zaragoza, Robert H.

In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E102A, No. 12, 01.01.2019, p. 1659-1667.

Research output: Contribution to journal › Article › peer-review

Kodera, Yuta ; Ali, Md Arshad ; Miyazaki, Takeru ; Kusaka, Takuya ; Nogami, Yasuyuki ; Uehara, Satoshi ; Morelos-Zaragoza, Robert H. / Algebraic group structure of the random number generator : Theoretical analysis of NTU sequence(s). In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences. 2019 ; Vol. E102A, No. 12. pp. 1659-1667.

@article{32b49e75579b4a3f86701bb95a5fe641,

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

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",

author = "Yuta Kodera and Ali, {Md Arshad} and Takeru Miyazaki and Takuya Kusaka and Yasuyuki Nogami and Satoshi Uehara and Morelos-Zaragoza, {Robert H.}",

year = "2019",

month = jan,

day = "1",

doi = "10.1587/transfun.E102.A.1659",

language = "English",

volume = "E102A",

pages = "1659--1667",

journal = "IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences",

issn = "0916-8508",

publisher = "Maruzen Co., Ltd/Maruzen Kabushikikaisha",

number = "12",

}

TY - JOUR

T1 - Algebraic group structure of the random number generator

T2 - Theoretical analysis of NTU sequence(s)

AU - Kodera, Yuta

AU - Ali, Md Arshad

AU - Miyazaki, Takeru

AU - Kusaka, Takuya

AU - Nogami, Yasuyuki

AU - Uehara, Satoshi

AU - Morelos-Zaragoza, Robert H.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Group structure

KW - NTU sequence

KW - Pseudorandom number generator

UR - http://www.scopus.com/inward/record.url?scp=85076421982&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85076421982&partnerID=8YFLogxK

U2 - 10.1587/transfun.E102.A.1659

DO - 10.1587/transfun.E102.A.1659

M3 - Article

AN - SCOPUS:85076421982

VL - E102A

SP - 1659

EP - 1667

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 12

ER -