基于三角矩阵全同态加密算法的安全电子投票系统研究与设计

发布时间：2018-12-23 09:03

【摘要】：随着社会的不断发展,民主的不断深入人心,投票的使用范围在不断的扩大,投票活动的数量也在日益增多。纸质选票模式需要耗费大量的资源,除了本身的统计效率低,成本高等缺点外,也无法有效的保障投票的公开可验证性和投票过程中的公正性。因此,传统的投票方式已经不能满足投票活动的实际要求。相对于传统的纸质投票模式,电子投票不仅可以在开展投票活动、选票搜集和选票统计等过程中节约大量的人力物力,提高整个投票活动的效率,同时可以提升投票活动的安全性。全同态加密算法在电子投票中有着广泛的应用,阻碍全同态加密应用于电子投票方案的主要问题是其密钥尺寸和密文规模过大、效率过低。本文利用三角矩阵的特殊性质构造了一个无噪声的非对称全同态加密算法MFHE,它是一种具有较小密文规模和较短密钥尺寸的全同态加密算法,新的加密算法可以通过三角矩阵的特殊性有效的降低计算成本,缩小明文和密文的大小,可以达到缩小密钥尺寸和密文规模,提高方案整体效率的目的。本文的主要研究工作如下:(1)利用三角矩阵的特殊性质,提出了一种基于三角矩阵的全同态加密算法MFHE,描述了新的全同态加密算法的实施流程,并给出了MFHE算法的安全性和同态性的详尽分析证明,最后对三种全同态加密算法的性能进行了对比分析。(2)在三角矩阵全同态加密方案MFHE的基础上,并结合RSA签名技术设计了一个安全电子投票方案。该方案不仅改善了电子投票中运算量大的问题,降低了密文选票统计运算中的噪声,而且提高了电子投票的效率和安全性。(3)在上述提出的安全电子投票方案的基础上,结合B/S架构完成了系统的整体框架设计,并实现了安全电子投票系统。
[Abstract]:With the development of society and democracy, the use of voting is expanding, and the number of voting activities is increasing day by day. Paper ballot model needs to consume a lot of resources. Besides its own shortcomings such as low statistical efficiency and high cost, it can not effectively guarantee the public verifiability of voting and the fairness of voting process. Therefore, the traditional voting method can not meet the actual requirements of voting activities. Compared with the traditional paper voting mode, electronic voting can not only save a lot of manpower and material resources in the process of carrying out voting activities, collecting votes and counting votes, but also improve the efficiency of the whole voting activities. It also improves the security of voting activities. Full homomorphism encryption algorithm is widely used in electronic voting. The main problem that hinders the application of full homomorphism encryption in electronic voting scheme is that its key size and ciphertext size are too large and its efficiency is too low. In this paper, a noiseless asymmetric homomorphism encryption algorithm, MFHE, is constructed by using the special properties of triangular matrices. It is a full homomorphic encryption algorithm with smaller ciphertext size and shorter key size. The new encryption algorithm can effectively reduce the computational cost and the size of plaintext and ciphertext through the particularity of triangular matrix. It can reduce the size of key and ciphertext and improve the overall efficiency of the scheme. The main work of this paper is as follows: (1) by using the special properties of triangular matrix, a full homomorphic encryption algorithm based on triangular matrix, MFHE, is proposed to describe the implementation flow of the new full homomorphic encryption algorithm. The security and homomorphism of the MFHE algorithm are proved in detail. Finally, the performance of the three full homomorphic encryption algorithms is compared and analyzed. (2) on the basis of the full homomorphism encryption scheme MFHE for triangular matrix, Combined with RSA signature technology, a secure electronic voting scheme is designed. This scheme not only improves the problem of large computation in electronic voting, reduces the noise in the statistical operation of ciphertext ballot, but also improves the efficiency and security of electronic voting. (3) on the basis of the proposed secure electronic voting scheme, Combined with B / S architecture, the whole frame of the system is designed, and the secure electronic voting system is implemented.
【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP309.7

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