以魔方陣為基底的加密資訊隱藏研究

Magic matrix encryption for secure data hiding

黃素瓊(Su-Chiung Huang)

指導教授 ： 范國清

國立中央大學/資訊電機學院/資訊工程學系碩士在職專班/碩士(2008年)

摘要

本論文中，我們應用密碼學的原理，以數學遊戲中的「魔方陣」 (Magic square)，做為進行密碼學中取代(Substitution) 及置換 (Transposition) 等基本運算的根據，並且將金鑰資訊加密技術融入，以達到演算法可公開、僅保護金鑰即能增加密文被破解困難度的需求。方法中所使用的三把分散金鑰，任何一把錯誤的情形下，都將使解出資料錯誤，由錯誤金鑰解出錯誤訊息的實驗結果可知，其與正確訊息間的平均漢明距離約為0.5，這樣的結果與盲目猜測的結果幾乎一致。為使密文能受到更嚴密的保護，並能增強密文的安全性等前提，我們應用資訊隱藏的方法，提出以受金鑰保護的魔方陣置亂矩陣遮罩，將宿主影像與欲隱藏的秘密訊息置亂，並將兩者進行配對(Matching)編碼後產生難以猜測破解的密文序列，並將密文序列嵌入宿主影像中每個像素點的最不重要位元 (LSB)，形成偽裝影像 (Stego image)。這樣的機制，同時具備了資訊隱藏技術所提供秘密通訊不易被察覺的特性，及密碼學技術所提供密文不易被破解的優點，可以大幅提高資料通訊傳遞的安全性。更重要的是，由演算法的描述可以看出，我們所提出的演算法十分簡單，但卻可以藉宿主影像所提供的資料複雜性，達到十分強固的保密需求。

關鍵字

密文 ； 資訊隱藏 ； 魔方陣 ； 密碼學

並列摘要

In this thesis, a novel method is presented to hide secure data for secrete communications by incorporating cryptography and data hiding technologies. In our approach, original data is encrypted by using the order of a magic matrix with secrete keys. There are two fundamental operations, including substitution and permutation, in traditional encryption process. According to the selected host image and magic matrix, mapping table for substation and permutation sequence are generated instead of the fixed permutation rule and substitution table used in traditional encryption algorithms. There are three secrete keys, host image selection key and magic matrix selection key pair, for use in encryption and decryption processes for data transmission. Finally, secure data obtained from previous processes are hided into LSB bit plane of the host image to construct a stego-image.

　　The proposed system consists of two main modules, which are secure data hiding and data extraction modules. In data hiding module, eight steps are performed for data encryption and hiding. They are host image obtaining, magic matrix key obtaining, host mask generation, magic mask generation, mapping table generation, secure mask generation, secure data stream generation, and hiding process. As to the data extraction module, the first five steps are the same as those in the data hiding module excepting steps 6~8 which are secure data stream extraction, secure data stream decoding, and hiding data extraction.

　　Experiments were conducted on various binary images and gray images. The average Hamming distance, i.e., error bit rate, is about 50% between original data and error binary data extracted by any of the secrete keys which is error or the corresponding secure data is lost. The phenomenon reveals that any attacker can not extract correct data when any of the secrete keys is lost. In addition, the information extracted by the attacker using error key will be the same as that obtained by random guess. Experimental results demonstrate the validity and efficiency of our proposed method. Moreover, the advantages of image complexity and variability property are both considered in designing the robust secure data hiding algorithm.

並列關鍵字

Magic matrix ； Cryptography ； Secure data hiding ； Hamming distance

參考文獻

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