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


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
Issue number12
Publication statusPublished - Jan 1 2019



  • 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

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