Improved Scalar Multiplication on Elliptic Curves Defined over F2mn

We propose two improved scalar multiplication methods on elliptic curves over Fqn where q = 2m using Frobenius expansion. The scalar multiplication of elliptic curves defined over subfield Fq can be sped up by Frobenius expansion. Previous methods are restricted to the case of a small m. However, wh...

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Bibliographic Details
Published in:ETRI journal 2004-06, Vol.26 (3), p.241-251
Main Authors: Lee, Dong Hoon, Chee, Seongtaek, Hwang, Sang Cheol, Ryou, Jae‐Cheol
Format: Article
Language:English
Subjects:
composite field
Elliptic curve
Frobenius expansion
scalar multiplication
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Summary:We propose two improved scalar multiplication methods on elliptic curves over Fqn where q = 2m using Frobenius expansion. The scalar multiplication of elliptic curves defined over subfield Fq can be sped up by Frobenius expansion. Previous methods are restricted to the case of a small m. However, when m is small, it is hard to find curves having good cryptographic properties. Our methods are suitable for curves defined over medium‐sized fields, that is, 10 ≤ m ≤ 20. These methods are variants of the conventional multiple‐base binary (MBB) method combined with the window method. One of our methods is for a polynomial basis representation with software implementation, and the other is for a normal basis representation with hardware implementation. Our software experiment shows that it is about 10% faster than the MBB method, which also uses Frobenius expansion, and about 20% faster than the Montgomery method, which is the fastest general method in polynomial basis implementation.
ISSN:1225-6463
2233-7326
DOI:10.4218/etrij.04.0103.0073