隨著科技的快速發展，電腦通訊的安全性變得很重要。因此，密碼學吸引了許多學者的興趣。一般來說，在一個密碼系統裡面，亂數產生器決定了這個系統的效能與安全性。由於亂數產生器的重要性，因此有許多關於影像或是語音的加密方法被提出來。但是因為硬體的限制和即時的傳輸，所以一個低複雜度且高速的亂數產生器非常急切需要。基於這些理由，一個虛擬亂數產生器的設計乃是一項艱困的挑戰。

本論文提出一混沌虛擬亂數產生器，它是基於S. Li 和 X. Wang所提出的亂數產生器所建構而成的。我們採取串連多個混沌系統和參數擾亂的方法來抵擋數位退化，因此它擁有長週期、隨機性、高速且低複雜度的特性。此外，我們也針對Q. Lin所提出的以盲演算法為基礎的加密演算法作了一些改善。我們經由修正原演算法的混合矩陣且增加2維與3維的混沌擾亂來增強此加密系統的安全性。最後，我們將所提出的混沌虛擬亂數產生器應用在改良後的盲演算法的影像加密演算法裡。

本論文所提的混沌虛擬亂數產生器通過了一些標準的統計測試，且表現出很好隨機性。它的週期長度接近2^169；在90000到250000個位元中，位元0和位元1的數量比幾乎相等；它的自相關函數類似 函數且交相關函數幾乎為0；此虛擬亂數產生器也通過了FIPS PUB 140-2測試。而我們所提出的影像加密系統通過了許多安全性分析，它們包括key space的分析、靈敏度的分析、統計上的分析、information entropy的分析和攻擊的分析。它的key space大於2^410，足夠抵擋所有類型的暴力攻擊法；且加密後影像的entropy非常接近理論值8，因此它可以有效的抵擋information entropy攻擊。此外，對一張512×512的影像，系統的加密時間約0.35秒，解密時間約0.15秒，它能夠被一般所接受且加密後影像的大小和原始影像一樣。無疑的，這個加密系統安全而適合實際應用。

By the rapid development of the technology, the security of computer communication becomes an important issue. As a result, cryptography has been attracting more interests and researches to solve this problem. General speaking, the random number generator (RNG) determines the performance and security of a cryptosystem. Due to the importance of the RNG, there are many encryption methods proposed for image and speech. Because of limited hardware and real time transmission, a low complexity and high speed RNG is needed. For these reasons, the design of a PRNG is a challenge.

In this thesis, we proposed a chaotic PRNG. The concept of the proposed PRNG is based on the CCS-PRBG proposed by S. Li and the PRBG proposed by X. Wang. We adopt the methods of cascading multiple chaotic systems and perturbation to avoid digital degradation. The proposed PRNG scheme possesses the following properties: long cycle length, good randomness, high speed and low complexity. Besides, we made some improvement over the BSS (Blind Source Separation) based encryption scheme proposed by Q. Lin. We enhance the security of the encryption by revising the mixing matrix of the algorithm and add the 2D and 3D chaotic permutation to the cryptosystem. Finally, we adopt the chaotic PRNG in the improved BSS-based image encryption algorithm.

The proposed chaotic PRNG passes some standard statistical tests and shows good properties of randomness. The cycle length is nearly 2^169, the 0:1 ration is almost equal to 1 from 90000 bits to 250000 bits, the auto-correlation is also -like, and the cross-correlation is nearly zero. The proposed PRNG also passed FIPS PUB 140-2 test. Our proposed image encryption scheme passed security analyses such as key space analysis, sensitivity analysis, statistical analysis, information entropy analysis and attack analysis. The key space size is over 2^410, it is large enough to resist all kinds of brute-force attacks. The entropy of every encrypted image is very close to the theoretical value of 8, showing the suggested encryption scheme is sufficiently secure against the entropy attack. In addition, the encryption time is about 0.35 sec and the decryption time is about 0.15 sec for a 512×512 image, the speed is acceptable and the size of ciphered image is the same as the plain image. The cryptosystem is no doubt secure and suitable for practical application.

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