Randomness of Binary Sequences with Long Period by Combining M-Sequence and Knuth's Quadratic Congruential Sequence

Kohei Kawase; Takeru Miyazaki; Shunsuke Araki; Satoshi Uehara; Yasuyuki Nogami

doi:10.1109/ICCE-China.2018.8448725

Randomness of Binary Sequences with Long Period by Combining M-Sequence and Knuth's Quadratic Congruential Sequence

Kohei Kawase, Takeru Miyazaki, Shunsuke Araki, Satoshi Uehara, Yasuyuki Nogami

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

Cryptography is one of the most important elements on the information security. In this paper, we propose a construction method of a long-period binary sequence with good randomness which plays an important role in cryptography. We generate the sequence by combining two types of binary sequences; one is the m-sequence and the other is a quadratic congruential sequence proposed by Knuth. It is well known that the m-sequence has good statistical properties, and Knuth's method can generate a long period sequence. However, both of these sequences cannot pass the almost NIST statistical tests by stand-alone. We derive a binary sequence combining these two sequences. In addition; we also consider the reasons why the proposed sequence has good randomness properties.

Original language	English
Title of host publication	2018 IEEE International Conference on Consumer Electronics-Taiwan, ICCE-TW 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Print)	9781538663011
DOIs	https://doi.org/10.1109/ICCE-China.2018.8448725
Publication status	Published - Aug 27 2018
Event	5th IEEE International Conference on Consumer Electronics-Taiwan, ICCE-TW 2018 - Taichung, Taiwan, Province of China Duration: May 19 2018 → May 21 2018

Other

Other	5th IEEE International Conference on Consumer Electronics-Taiwan, ICCE-TW 2018
Country	Taiwan, Province of China
City	Taichung
Period	5/19/18 → 5/21/18

ASJC Scopus subject areas

Biomedical Engineering
Electrical and Electronic Engineering
Instrumentation

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Kawase, K., Miyazaki, T., Araki, S., Uehara, S., & Nogami, Y. (2018). Randomness of Binary Sequences with Long Period by Combining M-Sequence and Knuth's Quadratic Congruential Sequence. In 2018 IEEE International Conference on Consumer Electronics-Taiwan, ICCE-TW 2018 [8448725] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICCE-China.2018.8448725

Randomness of Binary Sequences with Long Period by Combining M-Sequence and Knuth's Quadratic Congruential Sequence. / Kawase, Kohei; Miyazaki, Takeru; Araki, Shunsuke; Uehara, Satoshi; Nogami, Yasuyuki.

2018 IEEE International Conference on Consumer Electronics-Taiwan, ICCE-TW 2018. Institute of Electrical and Electronics Engineers Inc., 2018. 8448725.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Kawase, K, Miyazaki, T, Araki, S, Uehara, S & Nogami, Y 2018, Randomness of Binary Sequences with Long Period by Combining M-Sequence and Knuth's Quadratic Congruential Sequence. in 2018 IEEE International Conference on Consumer Electronics-Taiwan, ICCE-TW 2018., 8448725, Institute of Electrical and Electronics Engineers Inc., 5th IEEE International Conference on Consumer Electronics-Taiwan, ICCE-TW 2018, Taichung, Taiwan, Province of China, 5/19/18. https://doi.org/10.1109/ICCE-China.2018.8448725

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AB - Cryptography is one of the most important elements on the information security. In this paper, we propose a construction method of a long-period binary sequence with good randomness which plays an important role in cryptography. We generate the sequence by combining two types of binary sequences; one is the m-sequence and the other is a quadratic congruential sequence proposed by Knuth. It is well known that the m-sequence has good statistical properties, and Knuth's method can generate a long period sequence. However, both of these sequences cannot pass the almost NIST statistical tests by stand-alone. We derive a binary sequence combining these two sequences. In addition; we also consider the reasons why the proposed sequence has good randomness properties.

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