摘要
对多方认证密钥协商协议中求解一般椭圆曲线上ECDLP问题的点乘优化算法和Pollardrho协议攻击算法进行仿真,验证了点乘优化算法可降低运算复杂度,提升了有效性。随阶数的增大,Pollard-rho算法计算量增大。不同阶数的椭圆曲线密钥大小对Pollard-rho算法迭代次数影响具有一定的相似性,于是提出了一个针对协议的不安全密钥舍弃原则。根据Pollard-rho算法复杂度,估算不同密钥长度下的破解时间,验证了椭圆曲线密码体制的安全性,证明了协议的可靠性,给出了协议应采用160 bit长度密钥的依据。
The point multiplication optimization algorithm and the attack algorithm of Pollard-rho protocol for solving ECDLP problem on general elliptic curve in multi-party authenticated key agreement protocol are simulated.The simulation results indicate that the point multiplication optimization algorithm could reduce the computational complexity and improve the effectiveness.With the increase of order,the computation of Pollard-rho algorithm increases,and the influence of different order elliptic curve key sizes on the iteration times of Pollard-rho algorithm is similar.A principle of insecure key abandonment for the protocol is proposed.According to the complexity of Pollard-rho algorithm,the breaking time under different key lengths is estimated,the security of elliptic curve cryptosystem verified,the reliability of the protocol proved,and the basis for the protocol should use a 160-bit length key also given.
作者
郭士增
GUO Shi-zeng(Harbin Institute of Technology,Harbin Heilongjiang 150001,China)
出处
《通信技术》
2019年第11期2738-2743,共6页
Communications Technology
基金
黑龙江省自然科学基金“基于认知的大规模MIM0技术研究”(No.F2015001)~~
