新型公钥加密方案及应用研究

发布时间：2018-01-11 20:44

本文关键词：新型公钥加密方案及应用研究　出处：《陕西师范大学》2016年博士论文　论文类型：学位论文

【摘要】：构造安全的新型加密方案和利用加密方案设计高效的安全协议是网络空间信息安全研究的主要热点。本文的工作主要体现在两个方面:(1)具有新性能公钥加密方案的构造和安全性分析;(2)基于这些新型加密方案的安全协议设计。具体而言,本文创新性工作主要包括以下几个方面:1.采用配对函数编码和编码随机化思想构造了一个可隐藏明文统计特性的新型RSA加密方案。与已知的构造相比,新方案有如下优点:(1)能够隐藏明文的统计特性;(2)安全性基于一个新的RSA变形难题,称为RSA选择异或判定性问题;(3)该方案应用于签密中可以使得各用户间无需额外协商加密模与签密模的大小;(4)在标准模型下对自适应性选择密文攻击是安全的。2.在RSA加密系统的基础上,通过增加少量的有限域上的模指数运算,设计了一个标准模型下对选择明文攻击具有不可区分(indistinguishability under chosen plaintext attack,IND-CPA)安全性且保持同态性的RSA型概率同态加密方案和一个标准模型下对自适应性选择密文攻击具有不可区分安全性的(indistinguishability under adaptive chosen ciphertext attack,IND-CCA2)RSA型概率加密方案。这两个方案在实现密文不可区分时,都不再通过明文填充引入随机因子。通过“编码代换”的技巧使得第一个RSA型概率同态加密方案能对单比特加密,利用此技巧还可以将乘法同态加密方案转变成异或同态、或同态和与同态加密方案。然后基于第一个RSA型概率同态加密方案在半诚实模型下设计了一个两方海明距离保密计算协议,并用模拟范例证明了其安全性。此外,本章还提出一个RSA变形问题(称作RSA判定性问题)。3.首先提出一个能够阻止攻击者利用密文可扩展性的同态代数方法;然后基于该方法并综合运用密钥协商、对称加密和非对称加密的技术,构建了一个能阻止敌手利用密文扩展性实施自适应性选择密文攻击(CCA2)的同态加密方案。4.首先提出一个由加密方计算(或选取)加密底数的Paillier变体同态加密方案,并证明了其在标准模型下对选择明文攻击是语义安全(与IND-CPA安全性等价)的。然后在半诚实模型下,基于该同态加密方案设计了一个能够安全计算过两私有点坐标直线(一个尚未解决的公开问题)的协议。最后,将此协议推广应用到解决可归约为安全计算两私有点坐标差商的所有安全多方几何计算问题,从而解决了目前安全多方几何计算领域中,基于同态加密体制的安全两方计算坐标差商存在信息泄露问题。5.首先构造了一个同态-类解密系统,并简单分析证明了其加密算法具有和Paillier加密一样的安全性。然后基于该系统设计了两个高效的安全两方比较协议:一个适用于比较两个Zn上整数的大小,另一个适应于比较两个分数的大小。这两个协议都是计算安全的,因为这两个协议中通信双方传递的数据是用同态加密系统加密的密文。两协议采用云辅助计算模指数运算的技术,而未采用传统的、耗时多的不经意传输协议作为安全比较的子进程,减少了模指数运算对加密效率的影响,从而提高了安全比较协议的效率。分析表明,我们的安全比较方法较先前的安全比较方法在计算效率上有了提高并且实用。最后对本文的工作进行了总结,并对今后的一些研究方向进行了展望。
[Abstract]:A new encryption scheme to construct security and use of encryption security protocol design and efficient is the main research focus of network information security space. The work of this paper is mainly reflected in two aspects: (1) with the analysis of safety and construction of the new performance of public key encryption schemes; (2) the design of security protocol based on the new encryption scheme specifically, this paper mainly includes the following several aspects: 1. using the pairing function encoding and encoding of random thought to construct a hidden plaintext statistical properties of new RSA encryption scheme. Compared with the known structure, the new scheme has the following advantages: (1) statistical characteristics can hide the plaintext; (2) security a new RSA based on the deformation problem, called XOR decision problems for RSA; (3) the applications in signcryption can make each user without additional negotiation encryption mode and signcryption size (4; ) in the standard model of adaptive chosen ciphertext attack is the basis of secure.2. in RSA encryption system, by adding a small amount of domain finite exponent operations on the design of a standard model for the chosen plaintext attack can not be distinguished (indistinguishability under chosen plaintext attack, IND-CPA) and RSA security probabilistic encryption scheme and homomorphism homomorphism of a standard model of adaptive chosen ciphertext attack is indistinguishable from safety (indistinguishability under adaptive chosen ciphertext attack, IND-CCA2 RSA) encryption scheme. The two probability scheme in ciphertext indistinguishability, are no longer the padding introduced stochastic factors. Through the "encoding substitution" technique makes the first RSA type probabilistic homomorphic encryption scheme for single bit encryption, using this technique can also be multiplication Homomorphic encryption scheme into XOR homomorphism, or homomorphism and homomorphic encryption scheme. Then the first RSA type probabilistic homomorphic encryption scheme in the semi honest model to design a two party secure computation protocol based on Hamming distance, and its security is proved by simulation examples. In addition, this chapter also puts forward the deformation problem of a RSA (referred to as RSA decision problems).3. first proposed a ciphertext can prevent an attacker exploit extensible algebraic method of homomorphism; then based on the method and the integrated use of key agreement, symmetric encryption and asymmetric encryption technology, construct a can prevent adversary with ciphertext expansion since the implementation of the adaptive chosen ciphertext attack (CCA2) the homomorphic encryption scheme proposed by.4. by an encryption calculation (or selection) Paillier variant homomorphic encryption base encryption scheme, and prove the standard model of Ming Wengong On the semantic security (and IND-CPA equivalence). Then in the semi honest model, the homomorphic encryption scheme proposed a secure computing two private point coordinates based on linear (an unsolved open problems) protocol. Finally, the application of this agreement to solve all the security multi geometric for the calculation of two private security reduction coordinates calculation problem of the difference, so as to solve the secure multi-party computation geometry in the field of homomorphic encryption secure two party computation coordinate difference exists the problem of information leakage.5. first constructed a class system based on homomorphic decryption, and simple analysis proved that the encryption algorithm with Paillier encryption security of the same. Then based on the system design two efficient secure two party protocol: a comparison for size in comparison with two Zn integer, another to compare two The size of the fraction. The two protocols are computational secure, because the two sides in the communication protocol of transfer data is encrypted ciphertext using homomorphic encryption system. Two protocol uses cloud computing modular exponentiations auxiliary technology, without using the traditional, time-consuming oblivious transfer protocol as compared to the sub the process reduces the influence of modular exponentiation encryption efficiency, thereby improving the efficiency of protocol security. Comparative analysis shows that our security comparison method compared to the previous safety comparison method in computational efficiency has been improved and practical. Finally, the work of this paper are summarized, and some future research directions are outlook.

【学位授予单位】：陕西师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP309.7

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