Cyclic Vector Multiplication Algorithm Based on a Special Class of Gauss Period Normal Basis | Zendy

Kato Hidehiro | Zendy; Nogami Yasuyuki | Zendy; Yoshida Tomoki | Zendy; Morikawa Yoshitaka | Zendy

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Cyclic 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.

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