首先，设计基于带符号阶乘展开式的椭圆曲线标量乘和多标量乘算法。

Firstly, based on the signed factorial expansions,. The fast algorithms for scalar multiplication and multi-scalar multiplication on elliptic curves are presented.

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其次，设计基于整数拆分与预计算相结合的椭圆曲线标量乘和多标量乘算法。

Secondly, the fast algorithms for scalar multiplication and multi-scalar multiplication on elliptic curves are designed based on integer splitting and precomputation technique.

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椭圆曲线密码体制最主要的运算就是椭圆曲线上的标量乘和多标量乘，在各种密码协议中起到了核心作用。

The main operations of elliptic curve cryptosystem are scalar multiplication and multi-scalar multiplication for a pair of integers.

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