GGH修改版及其密码分析

发布时间：2018-03-27 18:49

本文选题：多线性映射　切入点：GGH映射　出处：《西安电子科技大学》2015年硕士论文

【摘要】：公钥密码领域中占据重要位置的Diffie-Hellmen双方密钥协商的提出给密码研究带来了新方向。随后在2000年引入了双线性对的二次函数特性后,才实现了三方密钥协商。但是由于双线性映射本身的局限性,不能用于实现任意多方密钥协商。因此将非交互的两方密钥交换扩展到多方密钥协商仍然是一个公开问题。2003年Boneh和Sliverberg提出了多线性映射的概念,同时给出了多线性映射的理想化定义和许多有趣的应用,其中就包括多方Diffie-Hellmen密钥交换和非常高效的广播加密。但是作为双线性映射一般化的多线性映射的实现还只是空想。直到2013年Grag,Gentry和Halevi提出了多线性映射的第一种可行的候选方案,一种基于理想格构造的近似多线性映射方案(简称GGH映射方案)。他们还利用它构造了多方密钥交换方案,这是密码学上的一个新突破。然而2015年Hu和Jia针对GGH映射构造的多方密钥交换和基于三精确覆盖问题的证据加密两种应用提出了一种有效的攻击方法。本文主要做了以下几方面的工作:1.为了测试GGH结构的简单变型是否能够抵抗Hu和Jia的攻击,本文将其他参数保留,通过修改原方案中容易被Hu和Jia的攻击方法利用的编码和译码参数:(a).将1的1级编码修改成了任意元素的1级编码;(b).修改了译码参数的定义;(c).将公开参数、零级编码和零测试参数从一维变成三维,提出了一种有别于GGH映射的修改版;2.为了对GGH修改版进行密码学分析,与原方案一样,利用修改版的GGH映射也构造了多线性映射的经典的密码应用——多方密钥协商方案;3.以基于该GGH映射的修改版构造的具体的K+1方密钥交换方案为例,利用Hu和Jia的攻击方法对其进行了详细的密码学分析,证明在3K是多项式级别大小的假设条件下,该方案可以被攻破。从而验证了Hu和Jia的攻击的有效性,得出这样的结果:GGH映射很难通过简单的修改来抵抗Hu和Jia的攻击。
[Abstract]:In the field of public key cryptography, the key agreement between the two sides of Diffie-Hellmen, which occupies an important position, has brought a new direction to the research of cryptography. Then, after introducing the quadratic function of bilinear pair in 2000, But due to the limitation of bilinear mapping itself, Therefore, it is still a public problem to extend the non-interactive two-party key exchange to multi-party key agreement. In 2003, Boneh and Sliverberg proposed the concept of multilinear mapping. At the same time, the idealized definition of multilinear mapping and many interesting applications are given. This includes multi-party Diffie-Hellmen key exchange and very efficient broadcast encryption. But the implementation of multilinear mapping as bilinear mapping generalization is still a fantasy. Until 2013, Grag Gentry and Halevi proposed the first feasible candidate scheme for multilinear mapping. An approximate multilinear mapping scheme based on ideal lattice (GGH mapping scheme for short). They also use it to construct a multi-party key exchange scheme. This is a new breakthrough in cryptography. However, in 2015 Hu and Jia proposed an effective attack method for the applications of multi-party key exchange constructed by GGH mapping and evidence encryption based on three-precision covering problem. In order to test whether the simple variant of GGH structure can resist Hu and Jia attacks, This article preserves the other parameters, By modifying the encoding and decoding parameters that are easily used by Hu and Jia attack methods in the original scheme, the 1-level coding of 1 is modified into the 1-level encoding of any element. The definition of decoding parameters is modified. This paper presents a modified version of zero level coding and zero test parameters from one dimension to three dimensions, which is different from GGH mapping. In order to perform cryptographic analysis of the modified version of GGH, it is the same as the original scheme. Using the modified GGH map, the classical cryptographic application of multilinear mapping, multi-party key agreement scheme, is also constructed. Taking the specific K _ 1 key exchange scheme based on the modified version of the GGH map as an example, The attack methods of Hu and Jia are used to analyze them in detail, and it is proved that the scheme can be broken under the assumption that 3K is polynomial level. The effectiveness of Hu and Jia's attacks is verified. It is very difficult to resist Hu and Jia attacks by simple modification.
【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】：2015
【分类号】：TN918.1

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