利用有限體特性改良多橢圓曲線點乘法效能

陳延華 ； 黃雪玲 ； 李昀真

《NCS 2017 全國計算機會議》 2017 (2018/01) Pp. 289-292

https://doi.org/10.29428/9789860544169.201801.0054

摘要

橢圓曲線上的多點乘法運算是橢圓曲線中運算量最高且最複雜的運算。基於橢圓曲線迪菲-赫爾曼金鑰交換（ECDH）方法，論文利用代數以疊代方式減少平方計算的運算量，而混合動態查表方法可以預算曲線上的點值可以重複使用減少運算量。此計算公式實作的實驗結果顯示出整體的運算減少比原本計算多點乘法運算方法(Double-and-add)的效率提升高達40％。本論文整體結合霍納法與查表方式改良ECC 在有限體的計算並提升橢圓曲線點乘法運算，提升整體加解密速率。

關鍵字

霍納法 ； ECDH ； 橢圓曲線密碼 ； 查表

並列摘要

Elliptic curve cryptosystem is an efficient public key cryptosystem, which is suitable for limited memory Constrained devices. The performance of elliptic curve cryptosystem depends on computation that is called point multiplication. In the paper is given an efficiently scheme to elliptic curve cryptography (ECC) for point multiplication operation. Moreover, It has examined that the lookup table method is efficient than the Horner rule method as this improves the speed of the scalar multiplication. It would reduce the encryption and decryption time by 40%. Elliptic curve point multiplication can be made regular, simple and suitable for Elliptic Curve Diffie-Hellman key Exchange (ECDH) software implementations.

並列關鍵字

ECDH ； ECC ； Horner rule ； Lookup Table