混沌系統對初始值及參數高度敏感，具遍歷性…等，這些特性符合一加密系統的需求。混沌系統已廣泛地應用於加密系統中，Fridrich 型加密系統便是其中一類。Fridrich 加密系統由兩個步驟組成: confusion和diffusion，前者將像素位置作排列，後著則依序改變每一像素的值。

本論文修改 Zhu 等人所提出的一Fridrich 型加密系統，提高其運算並加強安全性。本論文所提出的加密方法將原演算法中的 Arnold cat map 改為 standard map。Standard map 比 Arnold cat map有更大的parameter space。我們保持原來系統的優點-位元排列在confusion階段一樣有diffusion的效果以及像素(0,0)可以被重排到另一個位置。

為了減少加密時間，我們使用查表取代浮點運算操作。我們的方法是利用在 confusion 階段產生的 static 2D lookup table 和在diffusion階段產生的 dynamic 2D lookup table。每一個已經排列的像素值和位置被用來查詢table以獲得一個八位元值和已經排列過的像素值做遮罩。這方法比使用1D chaotic maps的diffusion技巧快。這是因為查表比浮點運算快多了。

本論文所提出的加密系統可以抵擋Fridrich型加密系統可以抵擋的攻擊，而key space為 ，足夠抵擋暴力破解法。本加密系統可將熵值為7.4455的256階灰階影像，提升到熵值7.9993，此數值非常接近理想值8。於效能方面，加密一張 的256階灰階影像平均花費0.096秒，比Fridrich和Zhu的加密系統快了將近0.1秒。在 key 的敏感度測試上，我們對原始影像，使用非常微小變化的key來加密，得到的NPCR值均高達99%以上。本加密系統的安全性與效能高於大部分現有的Fridrich型加密系統，並可安全使用於實際應用。

Chaotic system properties, such as sensitivity to control parameter and initial condition, ergodicity and so on, are essential for secure communication. Many chaos based cryptosystem have been proposed, one of them is the Fridrich-type cryptosystem. The Fridrich encryption scheme is composed of two steps: confusion and diffusion, where the former process permutes the position of pixels with a chaotic map, and the latter process changes the value of each pixel one by one.

We modified the Fridrich-type cryptosystem proposed by Zhu et al. . In our proposed cryptosystem, we exchange the Arnold cat map for the standard map. The standard map has more control parameter space than the Arnold cat map and we keep the superiority of the Zhu’s cryptosystem- the bit-level permutation has the effects of both confusion and diffusion in the confusion stage. The pixel (0, 0) can be permuted to other positions by the modified standard map.

To increase our encryption speed, we replace the floating point arithmetic operations by simple table lookup. Our approach makes use of a static 2D lookup table generated in the confusion stage and a dynamic 2D lookup table created in the diffusion process. The position and the value of each permuted image pixel are used to lookup the tables so as to obtain a new 8-bit value to mask the permuted pixel value. The approach is much faster than other diffusion techniques based on real number 1D chaotic maps. This is because the table lookup and swapping operations are much faster than the floating point arithmetic operations.

Our proposed cryptosystem has ability against attacks of the Fridrich-type cryptosystems and the key space of our proposed cryptosystem is which is big enough to resist all kinds of brute-force attacks. For a 256-gray-scale image, our cryptosystem changes its entropy from 7.4455 to 7.9993 after encrypting. The time for encrypting a 256-gray-scale image is 0.095 seconds. It’s 0.1 second faster than the Fridrich’s and Zhu’s cryptosystem. For key sensitive test, the value of NPCR between two encrypted / decrypted images using slightly different keys is over 99%. Our proposed cryptosystem is more secure and efficient than the current existing Fridrich-type cryptosystems. It is suitable for practical applications.

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