整数环上同态加密算法及其应用研究

发布时间：2018-07-22 20:26

【摘要】：随着互联网技术的飞速发展,大数据得到广泛应用,敏感数据的泄露也随之发生,网络安全逐渐受到人们重视。同态加密算法是大数据隐私保护的重要技术之一。同态加密算法可以对密文进行处理,并且将处理后的新密文正确解密,恢复出明文,减少了敏感信息在网络中的曝光频率。同态加密算法在云计算、密文搜索和电子投票等领域都有广泛应用。本文利用Gentry构造同态加密方案的思想,在现有的同类型同态加密方案的基础上,对公钥的生成进行了改进,设计出两种可以缩短公钥尺寸的同态加密方案。首先,针对同态加密算法中公钥膨胀过快的问题,结合Dijk等人和代洪艳等人的方案,对SomeWhat方案中公钥的生成方式进行了改进,构造出处理1bit明文的同态加密方案。公钥元素组xi,0和xi,1的生成方式不再采用同一种方式,可以减小公钥的脆弱性,公钥个数由τ+1变为2(?)τ+1。在计算公钥元素x0时,引入多项式的选取和计算,用f(p)替代p计算出x0,进一步隐藏了私钥信息。使用MATLAB实现了新SomeWhat方案和新BootStrappable方案,将具体数值带入进行推导演算,证明了新方案的正确性和可行性。并与Dijk等人和代洪艳等人的方案对比,证明新方案拥有最短公钥尺寸O(λ3.5)。接着,为了提高计算效率,在上述新方案的基础上,将明文空间从{0,1}扩展到{0,1}l,构造出批量处理明文的同态加密方案。对选取离散子集的方式进行了改进:将一个具有θ个元素的离散子集,变成两个具有(?)θ个元素的离散子集,减少了计算量。对新BootStrappable方案中的解密电路进行计算,证明解密电路运算次数在允许函数定义的范围内。并证明了新方案的正确性、同态性和安全性。将本文构造的方案与CheonJH等人和罗炳聪等人的方案对比,证明新全同态加密方案拥有最短公钥尺寸O(λ3.5)。最后,研究了批量处理明文的同态加密方案在电子投票系统中的应用,在朱正阳等人和王永恒等人的方案上进行改进,构造出能够批量处理选票的电子投票方案,对选票加密和处理选票的过程进行了改进。密文的处理从t次降为1次。除此之外,本章构造的电子投票方案增加了一个解密系统,计票系统负责验证选票,解密系统负责计算密文选票总和以及解密密文选票,提高了系统工作效率。
[Abstract]:With the rapid development of Internet technology, big data has been widely used, sensitive data leakage has occurred, and network security has been paid more and more attention. Homomorphic encryption algorithm is one of the important technologies of big data privacy protection. The homomorphic encryption algorithm can process ciphertext, and decrypt the processed new ciphertext correctly, restore the plaintext, and reduce the exposure frequency of sensitive information in the network. Homomorphic encryption algorithms are widely used in cloud computing, ciphertext search and electronic voting. In this paper, we use the idea of Gentry to construct homomorphic encryption scheme. Based on the existing homomorphic encryption scheme, we improve the generation of public key, and design two homomorphic encryption schemes which can shorten the size of public key. First of all, aiming at the problem of fast expansion of public key in homomorphic encryption algorithm, combining Dijk et al. And Dai Hongyan's scheme, we improve the way of generating public key in some what scheme, and construct a homomorphic encryption scheme to deal with 1bit plaintext. The generation of public key element groups XING0 and XING1 can reduce the vulnerability of public key, and the number of public keys changes from 蟿 1 to 2 (?) 蟿 1. In the calculation of public key element x0, the selection and calculation of polynomials are introduced, and the information of private key is further hidden by using f (p) instead of p to calculate x0. The new Somewhat scheme and the new Boot Strappable scheme are realized by using MATLAB. The concrete values are brought into the derivation and calculus, and the correctness and feasibility of the new scheme are proved. Compared with Dijk et al and Dai Hongyan schemes, it is proved that the new scheme has the shortest public key size O (位 3.5). Then, in order to improve the computational efficiency, based on the new scheme mentioned above, the plaintext space is extended from {0 ~ 1} to {0 ~ (1)} _ l, and a homomorphic encryption scheme for batch processing of plaintext is constructed. The method of selecting discrete subsets is improved: a discrete subset with 胃 elements is changed into two discrete subsets with 胃 elements, which reduces the computational complexity. The decryption circuit in the new Boot Strappable scheme is calculated, and it is proved that the number of decryption circuit is within the scope of the definition of the permitted function. The correctness, homomorphism and security of the new scheme are proved. Comparing the scheme constructed in this paper with that of Cheon JH et al. And Luo Bingcong et al., it is proved that the new fully homomorphic encryption scheme has the shortest public key size O (位 3.5). Finally, the paper studies the application of homomorphic encryption scheme in batch processing of plaintext in electronic voting system, improves the scheme of Zhu Zhengyang and Wang Yong, and constructs an electronic voting scheme which can process votes in batches. The process of encrypting and processing ballot papers has been improved. The processing of ciphertext was reduced from t to 1. In addition, the electronic voting scheme in this chapter adds a decryption system, the counting system is responsible for verifying the ballot papers, the decryption system is responsible for calculating the total number of the ciphertext ballot papers and decrypting the ciphertext ballot papers, which improves the efficiency of the system.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP309.7

【参考文献】