文章基本信息

标题：Scalar Multiplication on Elliptic Curves by Frobenius Expansions
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作者：Cheon, Jung-Hee ; Park, Sang-Joon ; Park, Choon-Sik 等
期刊名称：ETRI Journal
印刷版ISSN：1225-6463
电子版ISSN：2233-7326
出版年度：1999
卷号：21
期号：1
页码：28-27
语种：English
出版社：Electronics and Telecommunications Research Institute
摘要：Koblitz has suggested to use "anomalous" elliptic curves defined over , which are non-supersingular and allow or efficient multiplication of a point by and integer, For these curves, Meier and Staffelbach gave a method to find a polynomial of the Frobenius map corresponding to a given multiplier. Muller generalized their method to arbitrary non-supersingular elliptic curves defined over a small field of characteristic 2. in this paper, we propose an algorithm to speed up scalar multiplication on an elliptic curve defined over a small field. The proposed algorithm uses the same field. The proposed algorithm uses the same technique as Muller's to get an expansion by the Frobenius map, but its expansion length is half of Muller's due to the reduction step (Algorithm 1). Also, it uses a more efficient algorithm (Algorithm 3) to perform multiplication using the Frobenius expansion. Consequently, the proposed algorithm is two times faster than Muller's. Moreover, it can be applied to an elliptic curve defined over a finite field with odd characteristic and does not require any precomputation or additional memory.