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ID 46982
フルテキストURL
著者
Nogami, Yasuyuki Department of Communication Network Engineering Okayama University
Morikawa, Yoshitaka Department of Communication Network Engineering Okayama University
抄録
Public key cryptosystem has many uses, such as to sign digitally, to realize electronic commerce. Especially, RSA public key cryptosystem has been the most widely used, but its key for ensuring sufficient security reaches about 2000 bits long. On the other hand, elliptic curve cryptosystem(ECC) has the same security level with about 7-fold smaller length key. Accordingly, ECC has been received much attention and implemented on various processors even with scarce computation resources. In this paper, we deal with an elliptic curve which is defined over extension field F(p2c) and has a prime order, where p is the characteristic and c is a non negative integer. In order to realize a fast software implementation of ECC adopting such an elliptic curve, a fast implementation method of definition field F(p2c) especially F(p8) is proposed by using a technique called successive extension. First, five fast implementation methods of base field F(p2) are introduced. In each base field implementation, calculation costs of F(p2)-arithmetic operations are evaluated by counting the numbers of F(p)-arithmetic operations. Next, a successive extension method which adopts a polynomial basis and a binomial as the modular polynomial is proposed with comparing to a conventional method. Finally, we choose two prime numbers as the characteristic, and consider several implementations for definition field F(p8) by using five base fields and two successive extension methods. Then, one of these implementations is especially selected and implemented on Toshiba 32-bit micro controller TMP94C251(20MHz) by using C language. By evaluating calculation times with comparing to previous works, we conclude that proposed method can achieve a fast implementation of ECC with a prime order.
発行日
2003-03
出版物タイトル
Memoirs of the Faculty of Engineering, Okayama University
37巻
2号
出版者
Faculty of Engineering, Okayama University
開始ページ
73
終了ページ
87
ISSN
0475-0071
NCID
AA10699856
資料タイプ
紀要論文
言語
English
OAI-PMH Set
岡山大学
論文のバージョン
publisher
査読
無し
Sort Key
9
Eprints Journal Name
mfe