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如何抵抗与因子分解相关的私钥获取攻击,是RSA型加密方案的一个重要研究课题.就RSA型加密方案而言,目前普遍采用的抵抗与因子分解相关的私钥获取攻击的方法是优化系统参数,但该方法是被动的.本文分析了现有的针对RSA型加密系统的与因子分解相关的私钥获取攻击,找出这些攻击能够成功的关键因素.然后将RSA、Rabin两个加密系统与Diffie-Hellman密钥交换协议融合在一起设计了一个能抗自适应性选择密文攻击的加密方案.此方案具有如下三个属性:(1)该方案不仅能高效地实现加密操作,而且还能避免出已经出现的各种与因子分解相关的私钥获取攻击(量子算法除外);(2)该方案的私钥d的私密性具有信息论意义;(3)该方案在标准模型下,对自适应性选择密文攻击具有不可区分语义安全(indistinguishability under chosen-ciphertext attack,IDN-CCA).
How to resist the private key acquisition attack related to factorization is an important research topic of RSA encryption scheme.As for the RSA encryption scheme, the commonly used method to resist the attack of private key related to factorization is to optimize the system Parameter, but the method is passive.This paper analyzes the factor-based private key acquisition attacks on the RSA-type encryption system and finds out the key factors that these attacks can be successful.Then RSA, Rabin two encryption systems In combination with the Diffie-Hellman key exchange protocol, we designed an encryption scheme that is adaptive to selective ciphertext attacks.This scheme has the following three properties: (1) This scheme can not only implement encryption efficiently, (2) the privacy of the private key d of the scheme has the meaning of information theory; (3) Under the standard model, this scheme can solve the problem of private key acquisition attacks Adaptive selective ciphertext attack has indistinguishable semantic security (IDN-CCA).