以最佳化魔方陣應用於成對像素修改法之資訊隱藏研究

使用魔方陣作為基底的PPM (Pixel pair modification)取代法資訊隱藏技術，改善了LSB原有容量與影像品質無法兼顧的缺點，但此類方法，仍有很大的改善空間，目前PPM相關方法皆未考慮方陣內容的組合，若能夠提出最佳化的魔方陣組合，使得掩護影像像素值變動量為最少，如此藏量不變，又可使藏入效能為最高。由於N×N大小的魔方陣排列組合即有(N×N)! 種，幾近無法有效求解。本論文針對 N×N大小的魔方陣最佳化組合求解問題，發展三種求解演算法，一為啟發式演算法、一為加入菁英政策之基因演算法，以及一個窮舉法，針對上項問題加以研究、求解。論文實驗以3×3大小的魔方陣進行，使用峰值信號雜訊比PSNR(Peak signal-to-noise ration)做為判斷偽裝影像品質之效能基準，並透過窮舉法產生所有組合解的效能，評估本論文研究的方法。研究結果顯示，本論文提出的啟發式演算法可以快速推薦魔方陣組合，推薦的魔方陣與最佳解非常接近，而且推薦效能會落在全部組合解最佳的2~20%以內，本論文第二種求解演算法為加入菁英政策之基因演算法，經實驗，透過平均求解魔方陣組合2592次，即可推薦最佳的魔方陣組合，或者設定終止世代在14至19之間，亦可得到接近最佳解效能。最後，本論文提出的窮舉法，以求解首次魔方陣組合的解為依據，之後以計算組合變動所影響的差異值為方式，快速求解其餘的組合解，若將所有機密訊息嵌入到掩護影像的程序中，僅計自掩護影像取出像素對，搜尋魔方陣、修改像素對並回存至掩護影像，這個過程視為標準崁入流程，本論文提出的窮舉法，在求解第一個組合解與標準崁入流程相較，可降低約68.7%的求解時間，約為3.37秒，而在其餘組和解方面，求解每組組合解僅需標準崁入流程的萬分之7.6，約為0.0082秒，可有效解決窮舉法所帶來時間耗費，快速得到魔方陣最佳解。因此，本論文提出的三種求解演算法，可用來提升以魔方陣為基底的PPM取代法資訊隱藏技術的效能。

關鍵字

魔方陣；資訊隱藏； LSB ； PPM ；啟發式演算法；菁英政策；基因演算法

並列摘要

The magic squares based on pixel pair modification (PPM) for data hiding has the drawbacks of payload on PSNR’s of LSB. The traditional PPM-related methods do not consider the combination of square contents. In this thesis, a heuristic magic square algorithm for PPM is proposed to select the optional magic square combination for data hiding while the quality of the stego-image is maintained without affecting the amount of payload. A Genetic Algorithm with elite strategy is used to generate permutation. Experimental results showed that the heuristic magic algorithm can quickly recommend a suitable combination of magic squares with calculated efficiency in the range of 2% to 20%. The algorithm can enhance PPM based on magic squares and can increase the efficiency of data hiding. The elite strategy of GA is used with the average magic square combination of 2592 times to find the optimal magic square combination, otherwise a generation termination in the range between 14 and 19 to get a close to optimal solution. The improved enumeration proposal in this paper by 68.7% at 3.7 sec can reduce the first optimal solution. The remaining solution required 0.076% thousandth of unimproved enumeration to solve every combined solution at 0.0082 seconds. The time consumption by enumeration can be effectively and quickly reduced to get the best magic square solution. The three algorithms proposed in this thesis can be used to increase the efficiency of data hiding technique.

並列關鍵字

Data hiding ； Pixel pair modification ； Magic square ； Heuristic ； Genetic Algorithm

參考文獻

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以最佳化魔方陣應用於成對像素修改法之資訊隱藏研究

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