中文摘要：

介绍了适用于环上椭圆曲线的加法公式，完善了局部环Z/p^nZ上椭圆曲线密码学的基础理论，构造了环Z/p^nZ上的基于角色的椭圆曲线密码系统．根据环Z/p^nZ的结构特点，简化了其上椭圆曲线的加法完备系统，从而大大提高了环Z/p^nZ上的椭圆曲线计算点加的效率；另外，给出了E（Z/p^nZ）上密码群生成元的选取方法；证明Z/p^nZ上的密码体系与有限域Fp的椭圆曲线密码体系有相同的安全程度；最后在环Z/p^nZ上给出一个基于角色的椭圆曲线密码方案．

英文摘要：

We introduce the addition formula on E （R） where R denotes a ring, complete the theory of elliptic curve cryptography over local ring Z/p^nZ, and propose a role-based cryptosystem on E （ Z/p^nZ）. We analyze the structure of ring Z/p^nZ. On the basis of the relation between Z/p^nZ and Fp, we simplify the complete system of addition laws on E （Z/p^nZ）, which makes addition much more efficient than before. We present a method to select generators of the cryptographic groups. We prove that the security level of the ECC over local ring Z/p^nZ is equal to that over finite field Fp. A role-based cryptosystem is proposed.