Base-φ Method for Elliptic Curves over OEF

Tetsutaro KOBAYASHI 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E83-A  No.4  pp.679-686
Publication Date: 2000/04/20
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: 
Keyword: 
elliptic curve cryptosystem,  scalar multiplication,  OEF,  finite field,  Frobenius map,  table reference method, 

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Summary: 
A new elliptic curve scalar multiplication algorithm is proposed. The algorithm offers about twice the throughput 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 Fpm is expected to enhance elliptic curve operation efficiency more than Fq (q is a prime) or F2n.