| Summary: | 碩士 === 東吳大學 === 資訊管理學系 === 100 === In elliptic curve cryptosystems, the scalar will be first recoded in base 2 usually, and then the pre-computed points will be reused for improving operational performance. This thesis proposes modified left-to-right recoding algorithms for mutual opposite forms with generalized width-w, and specified width-2, 3, and 4, respectively. Those algorithms only require simple conversion rules to achieve the non-zero density reduction. The modified wMOF and the original wMOF have the same average non-zero density and the number of pre-computed points. The recoding time of modified wMOF with width-2, 3, and 4 respectively achieves at least 16%, 21%, 29% time reduction, supported by simulation results. Therefore, the proposed algorithms can effectively improve recoding performance. The time reduction increases with increasing the window size.
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