The Reducibility of a Special Binary Pentanomial. (2nd September 2014)

• Record Type: Journal Article
• Authors: Kim, Ryul; Kim, Yun Mi
• Other Names: Fleischmann Peter Academic Editor.
• Is Part Of: Algebra. Volume 2014(2014)
• Publication Date: 2014-09-02
• Subjects: Algebra -- Periodicals; Algebra; Electronic journals; Periodicals; 512.005
• DOI: 10.1155/2014/482837
• Languages: English
• ISSNs: 2314-4106

Abstract

Abstract : Swan's theorem determines the parity of the number of irreducible factors of a binary trinomial. In this work, we study the parity of the number of irreducible factors for a special binary pentanomial with even degree x m + x n 1 + x n 2 + x n 3 + 1, where 0 < n 3 < n 2 < n 1 ≤ m / 2, and exactly one of n 1, n 2, and n 3 is odd. This kind of irreducible pentanomials can be used for a fast implementation of trace and square root computations in finite fields of characteristic 2.