...文中心 关键词：椭圆曲线标量乘；NAF标量乘法；带标记的二进制表现 [gap=880]Key words： elliptic curve scalar multiplication; NAF scalar multiplication; binary representation with symbols ..
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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.
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