抗自适应性选择密文攻击的公钥加密系统  

A Public-key Cryptosystem Secure against Adaptive Chosen Cipher-text Attack

作　　者：巩林明[1] 李顺东[1] 窦家维[2] 王道顺[3] 

机构地区：[1]陕西师范大学计算机科学学院,西安710062 [2]陕西师范大学数学与信息科学学院,西安710062 [3]清华大学计算机科学与技术系,北京100084

出　　处：《密码学报》2016年第1期42-55,共14页Journal of Cryptologic Research

基　　金：国家自然科学基金(61272435;61373020)

摘　　要：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).It is an important research topic, for RSA-type encryption schemes, to consider how to resist attacks from obtaining the private key, which is related to the problem of factorization. At present, for any RSA-type encryption scheme, extending the length of modulus and optimizing system parameters are the most effective ways to withstanding private key obtaining attacks related to the factoring problem. These are two passive approaches. By studying the existing attacks from private key obtaining related to the factoring problem, we found the key factors in the successful implementation of those attacks. Then we propose an encryption scheme that is secure against adaptive chosen cipher-text attack(CCA2) by integrating multiple systems(RSA, Rabin and Diffie-Hellman). This scheme includes three properties as follows:(1) This scheme can implement encryption effectively, and can avoid attacks that come from private key obtaining related to the factoring problem;(2) The privacy of this scheme's private key d has perfect secrecy;(3) This scheme is proven to be with indistinguishability under adaptive chosen ciphertext attacks in standard model.

关 键 词：私钥获取攻击 抗小指数因子分解攻击 自适应性选择密文攻击下不可区分性 标准模型 信息论安全 

分 类 号：TN918.4[电子电信—通信与信息系统]