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 | |
| 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
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Cite this
Kodera, Y., Ali, M. A., Miyazaki, T., Kusaka, T., Nogami, Y., Uehara, S., & Morelos-Zaragoza, R. H. (2019). Algebraic group structure of the random number generator: Theoretical analysis of NTU sequence(s). IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E102A(12), 1659-1667. https://doi.org/10.1587/transfun.E102.A.1659