混淆理论在密码协议中的研究与应用

发布时间：2018-02-02 15:28

本文关键词： 平均情况下的虚拟黑盒特性不可区分性混淆盲签名可证明安全理论　出处：《西安电子科技大学》2014年硕士论文　论文类型：学位论文

【摘要】：混淆理论来源于代码混淆,其发展近年来十分迅速。简单来说,混淆器是一个以程序(图灵机或回路)作为输入,并输出具有相同功能性的另一个程序,但这个程序是“不可识别的”。密码学家对是否存在通用混淆、如何构造安全的混淆器等多方面的问题进行了深入的研究,并取得了重大的成果。我们将混淆按安全性的等级进行分类:一类是基于黑盒模拟的混淆,该定义由Hada提出,它要求攻击者由混淆程序得到的任意消息,通过只用黑盒访问来模拟这些消息。这类混淆如果可以实现,能够解决密码学上的很多困难性问题,但现在仍处于研究的瓶颈状态,人们转而研究安全性相对较弱的不可区分性混淆。根据混淆的新发展,本文将混淆重新进行分类并予以阐述。我们首次对加密盲签名的功能构造安全的混淆器,并对其安全性进行了相应的分析。本文的主要研究内容如下:一、对加密盲签名功能提出了一个安全的混淆器,其目的是隐藏交互协议中通信消息,使得交互过程不可知。我们首次用Schnorr的盲签名方案和Boneh的线性加密方案来构造混淆器。我们提出了两个新的定义,在加密盲签名混淆器下的盲性和one-more不可伪造性,并以这两个安全性定义来证明混淆器的安全性。我们在判定线性假设和离散对数困难性问题下,构造不同的敌手进行攻击,证明了混淆器具有盲性、one-more不可伪造性和依赖预言机的平均情况下虚拟黑盒特性。二、研究不可区分性混淆。用Garg的不可区分性混淆将任意的MPC协议转化为CRS模型中的2轮协议。在第一轮当事人委托他们的输入和随机数,在第二轮各方在基础MPC协议中提供他们“下一个消息”函数的混淆。然后各方分别计算混淆的下一个消息函数来获得输出。最后证明了该MPC协议在UC设置中抵抗静态恶意敌手。三、研究点函数的混淆。首先构造密钥要素,使其为具有多比特输出的点函数的混淆器(简称MBPF混淆器)。第一个构造基于选择明文安全的PKE方案,在计算难以逆转的辅助输入的情况下,满足AIND安全性的MBPF混淆器。我们的第二个构造基于有损加密方案,在统计难以逆转的辅助输入的情况下,满足AIND安全性的MBPF混淆器,然后我们说明了MBPF混淆器安全性定义间的关系。四、研究各种基础函数类的混淆,并对混淆中用到的计算复杂性、可证明安全性、随机预言机模型、标准模型进行简要的阐述。将现有的混淆定义及安全性进行分类,结合自己的成果,研究混淆安全性定义之间的关系。
[Abstract]:The theory of confusion comes from code confusion, and its development is very rapid in recent years. In brief, the confounding machine is another program which takes the program (Turing machine or loop) as the input and outputs the same function. But this program is "unrecognizable." Cryptologists have made a thorough study on whether there is a general confusion and how to construct a secure confounding device. We classify the confusion according to the security level: one is the confusion based on black box simulation, which is proposed by Hada, which requires the attacker to obtain arbitrary messages from the obfuscation program. This kind of confusion, if possible, can solve many cryptographic difficulties, but it is still in the bottleneck of research. People turn to the relatively weak security of indistinguishable confusion. According to the new development of confusion, the confusion is reclassified and expounded in this paper. For the first time, we construct a secure obfuscator for the function of cryptographic blind signature. The main contents of this paper are as follows: firstly, a secure obfuscator is proposed to hide the communication messages in the interactive protocol. We use blind signature scheme of Schnorr and linear encryption scheme of Boneh to construct obfuscator for the first time. We propose two new definitions. Blindness and one-more unforgeability under cryptographic blind signature obfuscator, and using these two security definitions to prove the security of the obfuscator, we determine the linear hypothesis and the discrete logarithm problem. By constructing different enemies to attack, it is proved that the obfuscator has blind one-more unforgeability and virtual black box characteristic under the average condition of relying on prophecy. 2. The indiscernibility confusion is studied. The arbitrary MPC protocol is transformed into two rounds of CRS model by using the indiscernibility confusion of Garg. In the first round, the parties entrust their input and random number. In the second round, the parties provide their "next message" in the underlying MPC protocol. Function obfuscation. Then each party calculates the confusion of the next message function to get the output. Finally, it is proved that the MPC protocol resists the static malicious adversary in UC setting. 3. In this paper, the confusion of point functions is studied. Firstly, the key elements are constructed to be the obfuscers of point functions with multi-bit output (MBPF obfuscator). The first is based on the PKE scheme of selective plaintext security. In the case of difficult to reverse the calculation of auxiliary input, the MBPF obfuscator satisfies the security of AIND. Our second construction is based on the lossy encryption scheme, in the case of statistically difficult to reverse the auxiliary input. The MBPF obfuscator satisfying the AIND security, then we explain the relationship between the security definitions of the MBPF obfuscator. Fourthly, we study the confusion of various basic function classes. And the computational complexity used in the confusion, can prove the security, random prophecy model, standard model for a brief description of the existing confusion definition and security classification, combined with their own results. The relationship between confusing security definitions is studied.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.2

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