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Elliptic Curve Scalar Point Multiplication Using Radix-4 Modified Booth's Algorithm  

문상국 (목원대학교 정보전자영상공학부)
Publication Information
Journal of the Korea Institute of Information and Communication Engineering / v.8, no.6, 2004 , pp. 1212-1217 More about this Journal
Abstract
The main back-bone operation in elliptic curve cryptosystems is scalar point multiplication. The most frequently used method implementing the scalar point multiplication, which is performed in the upper level of GF multiplication and GF division, has been the double-and-add algorithm, which is recently challenged by NAF(Non-Adjacent Format) algorithm. In this paper, we propose a more efficient and novel scalar multiplication method than existing double-and-add by applying redundant receding which originates from radix-4 Booth's algorithm. After deriving the novel quad-and-add algorithm, we created a new operation, named point quadruple, and verified with real application calculation to utilize it. Derived numerical expressions were verified using both C programs and HDL (Hardware Description Language) in real applications. Proposed method of elliptic curve scalar point multiplication can be utilized in many elliptic curve security applications for handling efficient and fast calculations.
Keywords
HDL; GF($2^{m}$);
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