A class of Gaussian normal bases and their dual bases. (17th November 2017)

• Record Type: Journal Article
• Authors: Sharma, P. L.; Devi, Kiran
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 20:Number 8(2017)
• Page Start: 1741
• Page End: 1755
• Publication Date: 2017-11-17
• Subjects: 12E20 -- 12E30 -- 11T99; Optimal normal basis -- Complexity -- Dual basis -- Finite field; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2017.1303941
• Languages: English
• ISSNs: 0972-0529

Abstract

Abstract: Optimal normal bases of 𝔽3 n are desirable in pairing based cryptography for the fast implementation of arithmetic in the ternary finite fields. But for the finite fields 𝔽3 n optimal normal bases are not possible for every n . Therefore the low complexity normal bases are desirable in such cases. There are low complexity Gaussian normal bases which are obtained from Gauss periods. We discuss the existence of Gaussian normal bases and their dual bases for a specific class of the finite fields with characteristic 3.