Efficient construction of elliptic curves over optimal extension-field (English)

In: Transactions of the Information Processing Society of Japan   ;  41 ,  8  ;  2092-2101  ;  2000
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Recently, D.B. Bailey and C. Paar (1998) proposed the Optimal Extension Field (OEF) which is defined over a base field with a computer's word size. Since the arithmetic in an OEF is relatively faster than that in F(2n), elliptic curves over an OEF would be more attractive when applied to a smart card, a personal computer, etc. However the definition of an OEF is rather strict since it is based on a general condition sufficient for fast arithmetic. The authors extend the definition of an OEF such that it includes more extension fields with efficient arithmetic. Furthermore we construct elliptic curves over an OEF including our extended OEF efficiently by applying the SEA algorithm. Our implementation can count order of elliptic curves over 155-bit extended OEF and 160-bit OEF in 10.1 and 11.6 seconds on average on a Pentium II 400 MHz (Linux-2.2.5), respectively.

Table of contents – Volume 41, Issue 8

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Generating shared RSA parameters for two communicating parties
Barmawi, A.M. / Takada, S. / Doi, N. | 2000
Efficient construction of elliptic curves over optimal extension-field
Futa, Y. / Miyaji, A. | 2000
The secure renewal of cryptosystems in the open network architecture
Yamada, T. / Miyaji, A. / Soshi, M. | 2000
Anonymous communication with elementary cyclic routes
Kitazawa, S. / Nagano, S. / Soshi, M. / Miyaji, A. | 2000
Applying legitimate access database for MLSI-based intrusion detection
Harada, S. / Asaka, M. | 2000
Security analysis on the proactivized system against latent virus attacks
Watanabe, Y. / Imai, H. | 2000
Software-based music delivery platform
Uda, R. / Sunada, A. / Inoue, A. / Shigeno, H. / Matsushita, Y. | 2000
An optimal decision method for establishment of security objectives
Nagai, Y. / Fujiyama, T. / Sasaki, R. | 2000
A macro system with class objects for the Java language
Tatsubori, M. / Chiba, S. / Itano, K. | 2000