Open AccessCyclic Vector Multiplication Algorithm Based on a Special Class of Gauss Period Normal Basis
Author(s) -
Kato Hidehiro,
Nogami Yasuyuki,
Yoshida Tomoki,
Morikawa Yoshitaka
Publication year - 2007
Publication title -
etri journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.295
H-Index - 46
eISSN - 2233-7326
pISSN - 1225-6463
DOI - 10.4218/etrij.07.0107.0040
Subject(s) - normal basis , gauss , basis (linear algebra) , multiplication (music) , algorithm , multiplication algorithm , class (philosophy) , mathematics , extension (predicate logic) , period (music) , gauss sum , computer science , discrete mathematics , arithmetic , combinatorics , geometry , artificial intelligence , physics , quantum mechanics , galois theory , binary number , acoustics , programming language
This paper proposes a multiplication algorithm for F p m, which can be efficiently applied to many pairs of characteristic p and extension degree m except for the case that 8p divides m(p–1). It uses a special class of type‐⟨ k, m ⟩ Gauss period normal bases. This algorithm has several advantages: it is easily parallelized; Frobenius mapping is easily carried out since its basis is a normal basis; its calculation cost is clearly given; and it is sufficiently practical and useful when parameters k and m are small.