發(fā)布時間：2018-07-03 11:28

  本文選題：中國剩余定理 + 分段線性函數(shù)　； 參考：《西南大學》2017年碩士論文

【摘要】：隨著計算智能的快速發(fā)展,圖像所攜帶敏感信息的安全性越來越備受人們的關(guān)注。因此,圖像加密算法也逐漸成為信息安全領(lǐng)域研究的熱點問題。近幾年,利用混沌特性對圖像進行加密的算法也越來越完善。非線性系統(tǒng)參數(shù)取特定的值時,其動力學行為會非常依賴初始值的變化,而且迭代軌道不可精確預測。因此,該特性可以更好的應用到密碼學中的擴散和混亂過程。此外,混沌系統(tǒng)的數(shù)學方程是確定的,只需要保障混沌參數(shù)和初始值的安全性,就可以重構(gòu)出混沌序列�；诨煦绲膱D像保護方法包括兩方面,一方面是利用離散形式的混沌系統(tǒng)來迭代生成混沌序列,來改變圖像像素的布局與替換像素灰度值,從而達到加密的效果;另一方面是基于混沌與門限方案的圖像共享技術(shù),通過多人合作來恢復原始圖像,即使部分圖像份額丟失,仍可重構(gòu)出原始圖像。論文對基于分段線性函數(shù)的圖像編碼與解碼進行了比較深入的探討,研究了基于圖像塊的分段線性函數(shù)的構(gòu)造,并分析了其混沌特性。將基于信息熵的壓縮編碼與中國剩余定理(CRT)結(jié)合,可以有效地減小影子圖尺寸,即改善影子圖的數(shù)據(jù)膨脹問題。論文中將原始圖像分割成若干個小的圖像方塊,統(tǒng)計每個圖像塊中不同的像素值所占比重,經(jīng)過換算轉(zhuǎn)化成概率分布,進而利用概率來構(gòu)造分段線性區(qū)間及其對應的分段線性函數(shù)。然后,利用分段線性函數(shù)及其逆函數(shù)對分塊圖像進行解碼與編碼。由于每個圖像塊最終編碼長度不一定相等,需要對最終所有圖像塊的編碼進行分組處理,保證每組包含相同長度的二進制位。將二進制序列轉(zhuǎn)化成對應的十進制,即待共享的密值。為了提高影子圖對原始圖像像素改變的敏感性,利用混沌序列對密值序列進行置亂處理。當改變塊圖像中像素值時,其對應的熵值亦會改變。如果其未發(fā)生變化,則生成一個小隨機數(shù)疊加到該熵值上。然后,將所有塊圖像中的熵值構(gòu)成一個集合,計算該集合的方差,作為Logistic映射進入混沌狀態(tài)時迭代的起始點,能夠得到不同的迭代軌道。用其對密值序列重新排序,能達到較好的抵抗差分攻擊的效果。最后,利用CRT構(gòu)建門限共享方案,將置亂后的密值序列轉(zhuǎn)化成對應的影子圖,分發(fā)給若干位合法的參與成員。此外,論文中分析了參與成員數(shù)量發(fā)生變化,即授權(quán)子集中包含新增成員。改進算法可以確保原有的參與成員手中的份額不變,通過與新增成員合作仍可以恢復出共享密值。為了保障共享方案的安全性,防止參與成員之間出現(xiàn)欺騙行為。論文設(shè)計了基于非對稱密碼的身份認證方案,只有通過驗證的參與成員,才能利用各自獨立擁有的密值份額,相互合作恢復出共享密值。通過計算機的數(shù)值仿真,并分析影子圖的安全性相關(guān)判定指標,可以發(fā)現(xiàn)實驗結(jié)果均符合理論要求,說明論文中所提出的方案對于密圖共享是安全有效的。
[Abstract]:With the rapid development of computing intelligence, people pay more and more attention to the security of sensitive information carried by images. Therefore, image encryption algorithm has gradually become a hot issue in the field of information security. In recent years, the algorithm of image encryption based on chaos is becoming more and more perfect. When the parameters of the nonlinear system are given a certain value, the dynamic behavior of the nonlinear system depends very much on the change of the initial value, and the iterative orbit can not be predicted accurately. Therefore, this feature can be better applied to the diffusion and confusion of cryptography. In addition, the mathematical equations of chaotic systems are determined, and chaotic sequences can be reconstructed only by ensuring the security of chaotic parameters and initial values. The method of image protection based on chaos includes two aspects. On the one hand, chaotic sequences are generated iteratively by discrete chaotic system to change the layout of image pixels and replace the gray values of pixels so as to achieve the effect of encryption. On the other hand, the image sharing technology based on chaos and threshold scheme is used to restore the original image through multi-person cooperation. Even if part of the image is lost, the original image can still be reconstructed. In this paper, the image coding and decoding based on piecewise linear function are deeply discussed, and the construction of piecewise linear function based on image block is studied, and its chaotic characteristics are analyzed. Combining the compression coding based on information entropy with the Chinese residue Theorem (CRT), the size of shadow graph can be reduced effectively, that is, the problem of data expansion of shadow graph can be improved. In this paper, the original image is divided into several small image blocks, the proportion of different pixel values in each image block is counted, and the probability distribution is transformed by conversion. Then the piecewise linear interval and its corresponding piecewise linear function are constructed by probability. Then, the piecewise linear function and its inverse function are used to decode and encode the block image. Because the final coding length of each image block is not necessarily equal, it is necessary to block the coding of all the final image blocks to ensure that each group contains binary bits of the same length. Converts the binary sequence to the corresponding decimal value, the secret value to be shared. In order to improve the sensitivity of shadow image to the pixel change of the original image, chaotic sequence is used to scramble the dense sequence. When the pixel value in the block image is changed, the corresponding entropy value also changes. If it does not change, a small random number is generated and superimposed on the entropy value. Then the entropy values in all block images are formed into a set and the variance of the set is calculated as the starting point of the iteration when the Logistic map enters the chaotic state different iterative orbits can be obtained. It can be used to reorder the dense sequence, which can resist the differential attack. Finally, the threshold sharing scheme is constructed by using CRT, and the scrambled secret value sequence is transformed into the corresponding shadow graph, which is distributed to a number of legitimate participating members. In addition, the paper analyzes the changes in the number of participating members, that is, the authorized subset contains new members. The improved algorithm can ensure that the original share of the participating members remains unchanged, and can recover the shared secret value by cooperating with the new members. In order to ensure the security of the shared scheme and prevent cheating among the participating members. In this paper, an identity authentication scheme based on asymmetric cryptography is designed. Only by authenticating the participating members, can they recover the shared secret value by using their independent secret value shares. Through the numerical simulation of the computer and the analysis of the security index of the shadow graph, it can be found that the experimental results are all in line with the theoretical requirements. It is shown that the scheme proposed in this paper is safe and effective for the secret graph sharing.
【學位授予單位】：西南大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP309.7

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本文編號：2093487