协议攻击Pohlig-Hellman和Pollard-rho算法分析

Analysis of Protocol Attacks on Pohlig-Hellman and Pollard-Rho Algorithms

多方认证密钥协商协议在专网-联盟链应用场景中较为常用。针对每个用户的私钥进行攻击破解,是攻击算法的目标。分析研究相应的协议攻击算法,既可以发现提升多方认证密钥协商协议的可靠性方法,也可以验证其安全性能。Pohlig-Hellman和Pollard-rho算法是对阶数为合数与素数的椭圆曲线进行攻击的两种算法。现分别对椭圆曲线加密攻击的Pohlig-Hellman和Pollardrho算法原理与实现过程进行推导和描述,进行两种的算法比较,从时间复杂度、适用情形和实际情况分析了两种算法的攻击效果。

The multi-party authentication key agreement protocol is more commonly used in the private network-alliance chain application scenario. Attacking and cracking the private key of each user is the target of the attack algorithm. Analysis and research of the corresponding protocol attack algorithm can not only improve the reliability method of multi-party authentication key agreement protocol, but also verify its security performance. Pohlig-Hellman and Pollard-rho algorithms are two algorithms for attacking elliptic curves whose order is composite and prime. The principles and implementations of Pohlig-Hellman and Pollard-rho algorithms for attacking elliptic curve cryptographic are deduced and described! respectively, and these two algorithms also compared. Finally, the attack effects of these two algorithms are analyzed from the time complexity, applicability and practice.