Fast Elliptic Curve Algorithm Combining Frobenius Map and Table Reference to Adapt to Higher Characteristic
Tetsutaro Kobayashi5 
, Hikaru Morita5, Kunio Kobayashi5 and Fumitaka Hoshino5
| (5) |
NTT Laboratories, Nippon Telegraph and Telephone Corporation, 1-1 Hikari-no-oka, Yokosuka-shi, Kanagawa-ken 239-0847, Japan |
Abstract
A new elliptic curve scalar multiplication algorithm is proposed. The algorithm offers about twice the troughput of some conventional
OEF-base algorithms because it combines the Frobenius map with the table reference method based on base-
φ expansion. Furthermore, since this algorithm suits conventional computational units such as 16, 32 and 64 bits, its base
field
is expected to enhance elliptic curve operation efficiency more than
F
q (
q is a prime) or
.
Keywords Elliptic curve cryptosystem - Scalar multiplication - OEF - Finite field - Frobenius map - Table reference method
References secured to subscribers.