可验证秘密共享及其应用研究

发布时间：2018-06-22 04:11

本文选题：秘密共享 + 存取结构　；参考：《陕西师范大学》2014年博士论文

【摘要】：秘密共享是密码学中的重要工具。它是构建许多安全协议和分布式计算,如安全多方计算、门限秘密、保密数据挖掘、访问控制、通用不经意传输、拜占庭协议等的基础工具。在现代密码学中占有重要的地位。尽管秘密共享为构建上述安全协议提供了一种解决思路,但应用环境的复杂性给利用秘密共享构建其它安全协议带来了极大的挑战,还有待进一步研究。如在多秘密共享中可能存在分发者欺骗问题,需要进行秘密和子份额的真伪验证。特别是在安全多方计算和隐私保护数据挖掘的应用领域中,多秘密共享方案中多秘密和子份额的有效验证问题是急需解决的问题。针对保密数据挖掘、安全多方计算以及无线网络中密钥管理等应用场景的安全需求,研究了安全多方计算的相关知识,并给出了立体几何问题的安全多方计算协议。结合椭圆曲线的离散对数和因子分解假设以及范德蒙行列式的性质等,从安全性和实用性角度对如何构造高效的可证的秘密共享方案进行了相关研究。另外,判定秘密共享方案优劣的一个重要指标是确定给定的存取结构秘密共享方案的信息率的大小。构建信息率为1的理想秘密共享也是很重要的研究问题。结合非循环超图的最长路径和存取结构的对应关系,对如何构建理想的秘密共享方案也进行了相关研究。文章的主要工作包括以下几个方面： 1.针对理想秘密共享问题,通过构造非循环超图的最长路径,利用向量空间构造法和(t,t)门限体制相结合的思想设计了一个信息率为1的理想秘密共享方案。由于所有存取结构与超图之间存在一一对应的关系。相比图存取结构而言,超图对应的存取结构更为一般化；而且不局限于秩为2的情况。该内容见第3章。 2.根据强t-一致性和可验证的定义,利用范德蒙行列式的性质构建了一个高效强t-一致的可验证秘密共享方案,与Harn和Lin的方案相比,该方案能抵抗并检验出Harn方案中出现的欺诈行为,而且无需选取κ个子多项式。因此,在保证秘密份额满足强亡-一致定义的前提下具有较低的计算复杂度,能更好地满足应用需求。详细内容见第4章。 3.基于椭圆曲线的因子分解困难假设和离散对数困难假设,提出可证的强(n,t,n)秘密共享方案,利用椭圆曲线的点乘运算将多项式和子份额点乘基点加密进行公开验证子秘密和子份额,不但满足强t-一致性而且保证秘密的真实。通过对方案的性能和安全性等方面的分析,证明该方案具有较小的计算复杂度和通信复杂度。该内容见第4章。 4.通过将参与者集合进行划分,每一部分作为一隔间。其中,隔间内部的参与者共享次主密钥,整个参与者集合共享主秘密,构造了一个高效可验证的层次秘密共享方案,利用双变量单向函数实现了可验证性,可防止不诚实欺诈行为。每个参与者只需持有一个较短的秘密份额即可重构长度较大的主秘密,具有较高的信息率。该内容见第5章。 5.在6章中,为了检验可验证秘密共享方案的应用,我们探讨了其在无线传感器网络密钥分发方案和隐私保护数据挖掘方案中的运用。验证表明,这些方案可以用来作为构建高效密钥分配协议和隐私保护数据挖掘协议的基础工具。 6.在7章中,研究了四面体体积的安全多方计算,提出了解决方案,并使用模拟范例证明该方案的保密性。然后基于四面体体积的安全多方计算,解决了：1)一个点与一个平面之间的关系；2)一条线和一个平面之间的关系；3)两个平面之间的关系的三个安全多方计算问题,并给出解决方案。
[Abstract]:Secret sharing is an important tool in cryptography . It is a basic tool for building many security protocols and distributed computing , such as secure multi - party computing , threshold secret , secret data mining , access control , general - purpose inadvertent transmission , Byzting protocol , etc .

According to the security requirements of security data mining , secure multi - party computing and key management in wireless network , this paper studies the relevant knowledge of secure multi - party computing , and gives a secure multi - party computing protocol for three - dimensional geometric problems .

The main work of this article includes the following aspects :

1 . Aiming at the ideal secret sharing problem , by constructing the longest path of the non - cyclic hypergraph , an ideal secret sharing scheme with an information rate of 1 is designed by combining the idea of the vector space structure method and the ( t , t ) threshold system .
and is not limited to the case where the rank is 2 .

2 . According to the definition of strong t - consistency and verifiability , a highly efficient and strong t - consistent verifiable secret sharing scheme is constructed by using the property of van der - meng determinant . Compared with the schemes of Harn and Lin , this scheme can resist and verify the fraud behavior in Harn scheme , and it is not necessary to select the kappa number polynomial . Therefore , it has lower computational complexity under the premise of ensuring the secret share meets the definition of strong death - consistent definition , and can better meet the application requirements . See Chapter 4 for details .

3 . Based on the assumption of the difficult assumption and discrete logarithm difficulty assumption of the elliptic curve , a strong ( n , t , n ) secret sharing scheme is proposed , and the polynomial and the sub - share point are multiplied by the point multiplication operation of the elliptic curve to verify the sub - secret and the sub - share , which not only satisfies the strong t - consistency but also guarantees the truth of the secret . Through the analysis of the performance and the security of the scheme , the scheme proves that the scheme has smaller computing complexity and communication complexity .

4 . By dividing the participants ' collection , each part acts as a compartment . The participants in the compartment share the secondary master key , the whole participant set shares the main secret , constructs an efficient and verifiable hierarchical secret sharing scheme , realizes verifiability by using the bi - variable one - way function , and can prevent dishonest fraud .

5 . In Chapter 6 , in order to verify the application of verifiable secret sharing scheme , we discuss its application in wireless sensor network key distribution scheme and privacy protection data mining scheme . The verification shows that these schemes can be used as the base tool for constructing efficient key distribution protocol and privacy protection data mining protocol .

6 . In Chapter 7 , the security multi - party calculation of the tetrahedra volume is studied , the solution is put forward , and the security of the scheme is proved by using the simulation example . Then , the relation between one point and one plane is solved based on the security multi - party calculation of the tetrahedra volume ;
2 ) the relation between a line and a plane ;
3 ) Three security multi - party computing problems of the relationship between two planes , and the solution is given .
【学位授予单位】：陕西师范大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN918.1

【参考文献】