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 journalArticle

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 languageEnglish
Pages (from-to)1659-1667
Number of pages9
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE102A
Issue number12
DOIs
Publication statusPublished - Jan 1 2019

Fingerprint

Random number Generator
Algebraic Groups
Theoretical Analysis
Trace Function
Pseudorandom Sequence
Pseudorandom number Generator
Binary operation
Information Security
Legendre
Security of data
Subsequence
Communication Systems
Communication systems
Odd
Series
Form

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

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 journalArticle

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 = "1",
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 -