本文選題：云計(jì)算 + 校驗(yàn)矩陣�。� 參考：《湖北工業(yè)大學(xué)》2017年碩士論文

【摘要】：云計(jì)算作為一種新型計(jì)算模式,它為在大容量專業(yè)性計(jì)算、存儲(chǔ)提供了一種新的安全可靠的解決方案。一個(gè)計(jì)算能力有限的用戶可將復(fù)雜的計(jì)算外包到有足夠計(jì)算能力的云服務(wù)器,云服務(wù)器將計(jì)算好的結(jié)果返回給用戶,用戶既提高了計(jì)算效率又節(jié)約計(jì)算資源。外包計(jì)算的出現(xiàn)為計(jì)算資源有限的用戶帶來(lái)了新的解決方案,但同樣也存在一些有待解決的關(guān)鍵問(wèn)題:第一,安全可靠的外包計(jì)算必須保證計(jì)算結(jié)果的可驗(yàn)證性,如果云服務(wù)器出現(xiàn)故障或被劫持的情況下返回一個(gè)錯(cuò)誤的計(jì)算結(jié)果,用戶應(yīng)該能通過(guò)簡(jiǎn)單的驗(yàn)證來(lái)終止外包協(xié)議;第二,必須保證數(shù)據(jù)的隱私安全,主要包括外包數(shù)據(jù)和計(jì)算結(jié)果不被泄露,通常外包數(shù)據(jù)中包含一些敏感信息,這些信息對(duì)于用戶來(lái)說(shuō)是保密的,云服務(wù)器不能通過(guò)在計(jì)算過(guò)程中的推理或其他手段來(lái)獲取;第三,外包計(jì)算要滿足用戶能容忍的高效性,即外包方案能夠極大的減少客戶端的計(jì)算量。針對(duì)大型矩陣求逆問(wèn)題,我們提出一種可驗(yàn)證安全的矩陣求逆的外包方案,并通過(guò)實(shí)驗(yàn)仿真證明了方案的可行性和高效性。本文的主要內(nèi)容如下:(1)校驗(yàn)矩陣構(gòu)造算法和密鑰構(gòu)造算法。校驗(yàn)矩陣構(gòu)造算法根據(jù)原始矩陣維度隨機(jī)生成的一個(gè)小型可逆矩陣,校驗(yàn)矩陣用于校驗(yàn)云服務(wù)器是否嚴(yán)格按照協(xié)議執(zhí)行矩陣求逆運(yùn)算;密鑰構(gòu)造算法包括是利用密鑰空間、隨機(jī)置換函數(shù)和克羅內(nèi)克函數(shù)生成的一個(gè)可逆的稀疏矩陣,用于外包矩陣的加密和返回結(jié)果的解密,保護(hù)用戶的數(shù)據(jù)隱私安全。(2)可驗(yàn)證安全的大型矩陣求逆外包方案。方案將原始矩陣中混入一個(gè)校驗(yàn)矩陣,加密后發(fā)送給云服務(wù)器,云服務(wù)器運(yùn)算后把結(jié)果返回給用戶,用戶解密完成校驗(yàn),從而判斷云服務(wù)器是否誠(chéng)實(shí)工作。通過(guò)對(duì)本方案的形式化證明,對(duì)一個(gè)概率多項(xiàng)式時(shí)間攻擊者來(lái)說(shuō),其破解協(xié)議的概率極低,保證了外包方案的安全性。通過(guò)實(shí)驗(yàn)仿真和數(shù)據(jù)分析驗(yàn)證了方案的高效性,該方案與相關(guān)研究工作相比,用戶的計(jì)算復(fù)雜度更低,減少了外包次數(shù),實(shí)用性更高。(3)外包方案的應(yīng)用推廣。根據(jù)矩陣求逆的特點(diǎn),我們利用該外包方案實(shí)現(xiàn)了大型線性方程組的安全外包處理,通過(guò)提取系數(shù)矩陣,實(shí)現(xiàn)對(duì)方程組的高效求解。在該方案的推廣中,我們利用矩陣加密與圖像加密的相似點(diǎn),提出了一種圖像加密的方案,通過(guò)提取圖像的像素矩陣混入校驗(yàn)矩陣,然后利用加密矩陣加密上傳服務(wù)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.
【學(xué)位授予單位】：湖北工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP309;TP393.09

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