發(fā)布時(shí)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(xué)》2017年碩士論文

【摘要】：隨著計(jì)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(diǎn)問題。近幾年,利用混沌特性對(duì)圖像進(jìn)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(shí),其動(dòng)力學(xué)行為會(huì)非常依賴初始值的變化,而且迭代軌道不可精確預(yù)測(cè)。因此,該特性可以更好的應(yīng)用到密碼學(xué)中的擴(kuò)散和混亂過程。此外,混沌系統(tǒng)的數(shù)學(xué)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。基于混沌的圖像保護(hù)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(dá)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(fù)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(duì)基于分段線性函數(shù)的圖像編碼與解碼進(jìn)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(gè)小的圖像方塊,統(tǒng)計(jì)每個(gè)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(jìn)而利用概率來構(gòu)造分段線性區(qū)間及其對(duì)應(yīng)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(duì)分塊圖像進(jìn)行解碼與編碼。由于每個(gè)圖像塊最終編碼長度不一定相等,需要對(duì)最終所有圖像塊的編碼進(jìn)行分組處理,保證每組包含相同長度的二進(jìn)制位。將二進(jìn)制序列轉(zhuǎn)化成對(duì)應(yīng)的十進(jìn)制,即待共享的密值。為了提高影子圖對(duì)原始圖像像素改變的敏感性,利用混沌序列對(duì)密值序列進(jìn)行置亂處理。當(dāng)改變塊圖像中像素值時(shí),其對(duì)應(yīng)的熵值亦會(huì)改變。如果其未發(fā)生變化,則生成一個(gè)小隨機(jī)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(gè)集合,計(jì)算該集合的方差,作為Logistic映射進(jìn)入混沌狀態(tài)時(shí)迭代的起始點(diǎn),能夠得到不同的迭代軌道。用其對(duì)密值序列重新排序,能達(dá)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(duì)應(yīng)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(jìn)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(fù)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(jì)了基于非對(duì)稱密碼的身份認(rèn)證方案,只有通過驗(yàn)證的參與成員,才能利用各自獨(dú)立擁有的密值份額,相互合作恢復(fù)出共享密值。通過計(jì)算機(jī)的數(shù)值仿真,并分析影子圖的安全性相關(guān)判定指標(biāo),可以發(fā)現(xiàn)實(shí)驗(yàn)結(jié)果均符合理論要求,說明論文中所提出的方案對(duì)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(xué)位授予單位】：西南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP309.7

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本文編號(hào)：2093487