Linear complexity of pseudo random binary sequence generated by trace function and Legendre symbol over proper sub extension field

• Published in: 2017 Eighth International Workshop on Signal Design and Its Applications in Communications (IWSDA) pp. 84 - 88
• Main Authors: Arshad, Ali Md, Miyazaki, Takeru, Heguri, Shoji, Nogami, Yasuyuki, Uehara, Satoshi, Morelos-Zaragoza, Robert
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-09-2017
• Subjects: Complexity theory; Electrical engineering; Environmental engineering; Generators; Information security; Legendre symbol; linear complexity; primitive polynomial; pseudo random sequence; Random sequences; trace function
• ISSN: 2150-3699
• DOI: 10.1109/IWSDA.2017.8095741

The authors have proposed an approach for generating a pseudo random binary sequence by using primitive polynomial, trace function, and Legendre symbol over the proper sub extension field. There are many uses of pseudo random binary sequence in security applications. The linear complexity of a sequence is considered as the most important property to be analyzed in these types of applications. In this paper, the authors have restricted the discussion on the linear complexity and linear complexity profile properties of the proposed sequence based on some experimental results. According to the results, the proposed sequence always holds a maximum value of the linear complexity.