Computing pth roots in extended finite fields of prime characteristic p ≥ 2. Issue 9 (8th April 2016)

• Record Type: Journal Article
• Authors: Repka, M.
• Is Part Of: Electronics letters. Volume 52:Issue 9(2016)
• Page Start: 718
• Page End: 719
• Publication Date: 2016-04-08
• Subjects: Galois fields -- matrix inversion -- polynomials; extended finite fields -- prime characteristics -- pth root computation -- reduction polynomial -- squaring matrix inversion -- irreducible polynomial; Electronics -- Periodicals; 621.381
• DOI: 10.1049/el.2015.4141
• Languages: English
• ISSNs: 0013-5194

Abstract

Abstract : Direct computation of p th roots in extended finite fields of characteristic p ≥ 2 is introduced, wherein the reduction polynomial is irreducible and can be even random. Proposed method works in any case of p ≥ 2 and finite field extension. This method is the most efficient, it is even more efficient than the method, which is widely used, based on inversion of squaring matrix utilised in the case of p = 2. This method is more efficient regarding the computation and storing of the matrix as well as the computation of the roots.