对基于二次剩余问题的密码体制进行安全性分析 ,利用 Morrison- Brillhart素因子分解算法 ,设计一种新的有效的攻击方法。在新的攻击方法下 ,上述基于二次剩余问题的密码体制是不安全的。论文最后给出设计安全的、基于二次剩余问题的密码体制的基本原则 This paper analyzes the security of the cryptosystem based on the quadratic residue problem and designs a new effective attack method by Morrison-Brillhart prime factorization algorithm. Under the new attack method, the above mentioned cryptosystem based on the quadratic residual problem is unsafe. Finally, the paper gives the basic principles of designing a secure password system based on the quadratic residual problem