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.
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.
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.
为了抵抗椭圆曲线密码的边信道攻击，提出了一种新型快速安全的标量乘算法。
To resist the side channel attacks of elliptic curve cryptography, a new fast and secure point multiplication algorithm is proposed.
基于椭圆曲线密码，提出了一种快速标量乘算法。
This paper presents a new fast scalar multiplication algorithm on elliptic curve cryptography.
除子标量乘是超椭圆曲线密码体制中的关键运算。
Divisor scalar multiplication is the key operation in hyperelliptic curve cryptosystem.
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.
接着研究基于最优扩域的椭圆曲线密码实现过程中的几个关键问题，包括参数的生成、基点的选取和标量乘算法。
Several key problems in the implementation of ECC based on OEF are analyzed, which includes validating the parameters, selecting base point and the algorithms for scalar multiplication.
接着研究基于最优扩域的椭圆曲线密码实现过程中的几个关键问题，包括参数的生成、基点的选取和标量乘算法。
Several key problems in the implementation of ECC based on OEF are analyzed, which includes validating the parameters, selecting base point and the algorithms for scalar multiplication.
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