Normal bases from 1-dimensional algebraic groups. (November 2020)

• Record Type: Journal Article
• Authors: Ezome, Tony; Sall, Mohamadou
• Is Part Of: Journal of symbolic computation. Volume 101(2020)
• Page Start: 152
• Page End: 169
• Publication Date: 2020-11
• Subjects: Normal basis -- Complexity -- Algebraic group; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.07.002
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: This paper surveys and illustrates a geometric method for constructing normal bases allowing fast finite field arithmetic. Indeed, Couveignes and Lercier presented in February 2008 a process for constructing efficient normal bases of F q n over F q from some degree two functions on an elliptic curve over F q . We apply the Couveignes-Lercier method to all the remaining 1-dimensional algebraic groups. That results in natural normal bases with quasi-linear complexity.