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

In: Transactions of the Information Processing Society of Japan   ;  41 ,  8  ;  2092-2101  ;  2000
  • ISSN:
  • Article (Journal)  /  Print

How to get this document?

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

Show all volumes and issues

The tables of contents are generated automatically and are based on the data records of the individual contributions available in the index of the TIB portal. The display of the Tables of Contents may therefore be incomplete.

2068
Generating shared RSA parameters for two communicating parties
Barmawi, A.M. / Takada, S. / Doi, N. | 2000
2092
Efficient construction of elliptic curves over optimal extension-field
Futa, Y. / Miyaji, A. | 2000
2102
The secure renewal of cryptosystems in the open network architecture
Yamada, T. / Miyaji, A. / Soshi, M. | 2000
2148
Anonymous communication with elementary cyclic routes
Kitazawa, S. / Nagano, S. / Soshi, M. / Miyaji, A. | 2000
2208
Applying legitimate access database for MLSI-based intrusion detection
Harada, S. / Asaka, M. | 2000
2228
Security analysis on the proactivized system against latent virus attacks
Watanabe, Y. / Imai, H. | 2000
2237
Software-based music delivery platform
Uda, R. / Sunada, A. / Inoue, A. / Shigeno, H. / Matsushita, Y. | 2000
2264
An optimal decision method for establishment of security objectives
Nagai, Y. / Fujiyama, T. / Sasaki, R. | 2000
2327
A macro system with class objects for the Java language
Tatsubori, M. / Chiba, S. / Itano, K. | 2000
Feedback