中文摘要：

最近，Ranjan利用m组混沌系统及线性变换组合方法提出一种混沌公钥密码，安全分析表明攻击该公钥密码难度为（NP）”，其中N，P分别为密钥空间大小及线性变换复杂度．由于向量任意的线性变换都能映射为向量2-范数简单的幅度变化，据此提出一种仅依赖公钥、初始向量及算法结构的私钥攻击算法．分析与实验结果均表明该多混沌公钥密码无法抵抗此类攻击，并且该分析方法可以有效攻击各种多混沌公钥密码算法．

英文摘要：

A novel public key encryption technique based on multiple chaotic systems has been proposed. This scheme employs m-chaotic systems and a set of linear functions for key exchange over an insecure channel. The security of the proposed algorithm grows as （NP）^m, where N, P are the size of the key and the computational complexity of the linear functions, respectively. In this paper, the fundamental weakness of the cryptosystem is pointed out and a successful attack is described. Given the fact that any complex linear transformations on a vector will make the norm of the vector approximate linear growth, we present an attack that permits recovering the corresponding secret key from the public key and the initial value. Both theoretical and experimental results show that the attacker can access the secret key without any difficulty, The lack of security discourages the use of such algorithm for practical applications.