A new construction method for n-dimensional generalized Arnold matrixes and its application in image scrambling
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摘要: 提出了基于具有輸入密鑰的等差數列來構造一類n維廣義Arnold變換矩陣的方法,并給出了構造變換矩陣和逆變換矩陣的計算算法,算法僅與密鑰有關,其時間復雜度相當于n(n+1)/2次乘法運算.在圖像置亂時用該矩陣作為變換矩陣,采取圖像位置空間與色彩空間的多輪乘積型雙置亂,算法具有周期長和算法完全公開等特點,可有效防止多種攻擊,增強了系統的安全性.此外,通過逆變換對置亂圖像進行恢復,無須計算變換矩陣的周期.實驗結果表明,該置亂變換算法效率高,安全性強.Abstract: Based on an arithmetic progression with an input secret key, a method is proposed to construct n-dimensional generalized Arnold transformation matrixes.Direct calculation algorithms are also presented for the transformation matrix and the inverse transformation matrix.The algorithms are only relevant to the secret key and their time complexity is equal to n(n+1)/2 times multiplication operation.Using the n-dimensional generalized Arnold transformation matrix as a transform matrix, and adopting double product-like scrambling in the image position space and the hue space, the image scrambling method has long period and is public, and can prevent many attacks and thus greatly enhances the system’s security.Moreover, when the inverse transformation matrix is applied to restore the scrambled image, the period of the transformation matrix is not needed to calculate.Simulation experiments show that the proposed method is effective and very secure
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Key words:
- ima ge encryption /
- matrix transformation /
- scrambling /
- plaintext attack
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