| Summary: | 碩士 === 東吳大學 === 資訊科學系 === 93 === Point operations often need to be used in the elliptic curve cryptosystem. The number of point operations determines the efficiency of the elliptic curve cryptosystem. Thus, there are many researches for finding out how to speed up the computation of the forms of and , where k, l are scalars, and P, Q are the points over an elliptic curve. In this thesis, we propose the signed digit representation applied to twin scalars to reduce the number of non-zero digits and the joint Hamming weight, and to put non-zero digits in the same column as possible. In this thesis, the joint Hamming density is reduced to about 31% via the implementation of the signed digit representation. In the process of scalars transforming, we pre-construct a look-up table to reduce the cost of repeated computing and then use the direct formulae to reduce the number of operations in squaring, multiplication and inverse operations.
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