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ID 15380
Eprint ID
15380
FullText URL
Author
Morikawa, Yoshitaka
Abstract
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.
Keywords
finite field
minimal polynomial
irreducible polynomial
higher degree trace
trace
cryptography
Published Date
2001-03-27
Publication Title
Memoirs of the Faculty of Engineering, Okayama University
Publication Title Alternative
岡山大学工学部紀要
Volume
volume35
Issue
issue1-2
Publisher
Faculty of Engineering, Okayama University
Publisher Alternative
岡山大学工学部
Start Page
197
End Page
205
ISSN
0475-0071
NCID
AA10699856
Content Type
Departmental Bulletin Paper
language
英語
File Version
publisher
Refereed
False
Eprints Journal Name
mfe