出版社：Electronics and Telecommunications Research Institute
摘要：We propose two improved scalar multiplication methods on elliptic curves over using Frobenius expansion. The scalar multiplication of elliptic curves defined over subfield 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, . 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.
关键词：Elliptic curve;Scalar multiplication;Frobenius expansion;Composite field
