JaLCDOI 10.18926/15380
フルテキストURL Mem_Fac_Eng_OU_35_197.pdf
著者 Nogami, Yasuyuki| Morikawa, Yoshitaka|
抄録 Modern communication engineerings, such as elliptic curve cryptographies, often requires algebra on finite extension field defined by modulus arithmetic with an irreducible polynomial. This paper provides a new method to detemine the minimal (irreducible) polynomial of a given proper element in finite extension field. In the conventional determination method, as we have to solve the simultaneous equations, the computation is very involved. In this paper, the well known "trace" is extended to higher degree traces. Using the new traces, we yield the coefficient formula of the desired minimal polynomial. The new method becomes very simple without solving the simultaneous equations, and about twice faster than the conventional method in computation speed.
キーワード finite field minimal polynomial irreducible polynomial higher degree trace trace cryptography
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2001-03-27
開始ページ 197
終了ページ 205
ISSN 0475-0071
言語 English
論文のバージョン publisher
NAID 120002307992