Open AccessImproved Scalar Multiplication on Elliptic Curves Defined over F 2 mn
Author(s) -
Lee Dong Hoon,
Chee Seongtaek,
Hwang Sang Cheol,
Ryou JaeCheol
Publication year - 2004
Publication title -
etri journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.295
H-Index - 46
eISSN - 2233-7326
pISSN - 1225-6463
DOI - 10.4218/etrij.04.0103.0073
Subject(s) - scalar multiplication , scalar (mathematics) , polynomial basis , normal basis , mathematics , binary number , elliptic curve , elliptic curve cryptography , multiplication (music) , basis (linear algebra) , polynomial , representation (politics) , elliptic curve point multiplication , discrete mathematics , algorithm , pure mathematics , computer science , combinatorics , arithmetic , mathematical analysis , geometry , public key cryptography , galois theory , encryption , politics , political science , law , operating system
We propose two improved scalar multiplication methods on elliptic curves over F q n where q = 2 m using Frobenius expansion. The scalar multiplication of elliptic curves defined over subfield F q 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.