The main operations of elliptic curve cryptosystem are scalar multiplication and multi-scalar multiplication for a pair of integers.
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。
Firstly, based on the signed factorial expansions,. The fast algorithms for scalar multiplication and multi-scalar multiplication on elliptic curves are presented.
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。
Secondly, the fast algorithms for scalar multiplication and multi-scalar multiplication on elliptic curves are designed based on integer splitting and precomputation technique.
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。
The spectral domain Green's functions of scalar and vector potentials for vertical and horizontal electric as well as magnetic dipoles in multi-layered medium are presented and verified.
本文给出多层媒质中水平和垂直电、磁偶极子的谱域标量位和矢量位格林函数的一般表达式，并验证了其正确性。
In these public key cryptographic algorithms, the kernel operations are modular exponentiation of multi-precision integer and elliptic curve scalar multiplication, which both are computing intensive.
这些公钥密码算法的关键操作为大整数模幂乘操作与椭圆曲线标量乘法操作，均属于计算密集型运算。
In these public key cryptographic algorithms, the kernel operations are modular exponentiation of multi-precision integer and elliptic curve scalar multiplication, which both are computing intensive.
这些公钥密码算法的关键操作为大整数模幂乘操作与椭圆曲线标量乘法操作，均属于计算密集型运算。
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