云计算环境下矩阵求逆外包方案的研究

发布时间：2018-04-27 00:38

本文选题：云计算 + 校验矩阵　；参考：《湖北工业大学》2017年硕士论文

【摘要】：云计算作为一种新型计算模式,它为在大容量专业性计算、存储提供了一种新的安全可靠的解决方案。一个计算能力有限的用户可将复杂的计算外包到有足够计算能力的云服务器,云服务器将计算好的结果返回给用户,用户既提高了计算效率又节约计算资源。外包计算的出现为计算资源有限的用户带来了新的解决方案,但同样也存在一些有待解决的关键问题:第一,安全可靠的外包计算必须保证计算结果的可验证性,如果云服务器出现故障或被劫持的情况下返回一个错误的计算结果,用户应该能通过简单的验证来终止外包协议;第二,必须保证数据的隐私安全,主要包括外包数据和计算结果不被泄露,通常外包数据中包含一些敏感信息,这些信息对于用户来说是保密的,云服务器不能通过在计算过程中的推理或其他手段来获取;第三,外包计算要满足用户能容忍的高效性,即外包方案能够极大的减少客户端的计算量。针对大型矩阵求逆问题,我们提出一种可验证安全的矩阵求逆的外包方案,并通过实验仿真证明了方案的可行性和高效性。本文的主要内容如下:(1)校验矩阵构造算法和密钥构造算法。校验矩阵构造算法根据原始矩阵维度随机生成的一个小型可逆矩阵,校验矩阵用于校验云服务器是否严格按照协议执行矩阵求逆运算;密钥构造算法包括是利用密钥空间、随机置换函数和克罗内克函数生成的一个可逆的稀疏矩阵,用于外包矩阵的加密和返回结果的解密,保护用户的数据隐私安全。(2)可验证安全的大型矩阵求逆外包方案。方案将原始矩阵中混入一个校验矩阵,加密后发送给云服务器,云服务器运算后把结果返回给用户,用户解密完成校验,从而判断云服务器是否诚实工作。通过对本方案的形式化证明,对一个概率多项式时间攻击者来说,其破解协议的概率极低,保证了外包方案的安全性。通过实验仿真和数据分析验证了方案的高效性,该方案与相关研究工作相比,用户的计算复杂度更低,减少了外包次数,实用性更高。(3)外包方案的应用推广。根据矩阵求逆的特点,我们利用该外包方案实现了大型线性方程组的安全外包处理,通过提取系数矩阵,实现对方程组的高效求解。在该方案的推广中,我们利用矩阵加密与图像加密的相似点,提出了一种图像加密的方案,通过提取图像的像素矩阵混入校验矩阵,然后利用加密矩阵加密上传服务器保存。
[Abstract]:As a new computing model, cloud computing provides a new secure and reliable solution for large capacity professional computing and storage. A user with limited computing power can outsource complex computing to a cloud server with sufficient computing power. The cloud server returns the calculated results to the user, which not only improves the computing efficiency but also saves computing resources. The emergence of outsourced computing has brought new solutions to users with limited computing resources, but there are also some key problems to be solved: first, secure and reliable outsourced computing must ensure the verifiability of computing results. If a cloud server fails or is hijacked to return an incorrect calculation, the user should be able to terminate the outsourcing protocol through simple verification; second, the privacy of the data must be secured. Mainly including outsourced data and calculation results are not leaked, usually the outsourced data contains some sensitive information, which is confidential to users, cloud server can not be obtained by reasoning or other means in the calculation process; Thirdly, the outsourced computing should satisfy the high efficiency that the user can tolerate, that is, the outsourced solution can greatly reduce the computing cost of the client. In order to solve the problem of large matrix inversion, we propose a verifiable and secure outsourcing scheme for matrix inversion, and the feasibility and efficiency of the scheme are proved by experimental simulation. The main contents of this paper are as follows: 1) check matrix construction algorithm and key construction algorithm. The algorithm of constructing check matrix is a small reversible matrix randomly generated according to the dimension of the original matrix. The check matrix is used to check whether the cloud server performs the inverse operation of matrix strictly according to the protocol, and the key construction algorithm includes the use of key space. A reversible sparse matrix generated by the random permutation function and the Croneker function is used to encrypt the outsourced matrix and decrypt the returned result, and to protect the user's data privacy. In the scheme, a check matrix is mixed into the original matrix, which is encrypted and sent to the cloud server, and the result is returned to the user after the cloud server operation. The user decrypts the check to judge whether the cloud server is honest or not. Through the formal proof of this scheme, for a probabilistic polynomial time attacker, the probability of breaking the protocol is very low, which ensures the security of the outsourced scheme. Experimental simulation and data analysis verify the efficiency of the scheme. Compared with related research work, the proposed scheme has lower computational complexity, reduced the number of outsourcing, and has higher practicability. According to the characteristics of matrix inversion, we use the outsourcing scheme to realize the secure outsourcing of large linear equations. By extracting the coefficient matrix, we can solve the equations efficiently. In the extension of this scheme, we propose an image encryption scheme by using the similarities between matrix encryption and image encryption. We extract the pixel matrix of the image and mix it into the checksum matrix, and then use the encryption matrix to encrypt and upload the server to save it.
【学位授予单位】：湖北工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP309;TP393.09

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