Author(s)

Md. Arshad Ali^1*, Yuta Kodera¹, Takuya Kusaka¹, Satoshi Uehara², Yasuyuki Nogami¹, Robert H. Morelos-Zaragoza³

¹Graduate School of Natural Science and Technology, Okayama University, Okayama, Japan.
²Faculty of Environmental Engineering, University of Kitakyushu, Fukuoka, Japan.
³Department of Electrical Engineering, San Jose State University, San Jose, CA, USA.

Pseudo-random sequences with long period, low correlation, high linear complexity, and uniform distribution of bit patterns are widely used in the field of information security and cryptography. This paper proposes an approach for generating a pseudo-random multi-value sequence (including a binary sequence) by utilizing a primitive polynomial, trace function, and k-th power residue symbol over the sub extension field. All our previous sequences are defined over the prime field, whereas, proposed sequence in this paper is defined over the sub extension field. Thus, it’s a new and innovative perception to consider the sub extension field during the sequence generation procedure. By considering the sub extension field, two notable outcomes are: proposed sequence holds higher linear complexity and more uniform distribution of bit patterns compared to our previous work which defined over the prime field. Additionally, other important properties of the proposed multi-value sequence such as period, autocorrelation, and cross-correlation are theoretically shown along with some experimental results.

Pseudo-Random Sequence, Trace Function, Power Residue Symbol, Sub Extension Field, Autocorrelation, Cross-Correlation, Linear Complexity, Distribution of Bit Patterns

Ali, M. , Kodera, Y. , Kusaka, T. , Uehara, S. , Nogami, Y. and Morelos-Zaragoza, R. (2019) Multi-Value Sequence Generated over Sub Extension Field and Its Properties. Journal of Information Security, 10, 130-154. doi: 10.4236/jis.2019.103008.