| Summary: | 碩士 === 國立成功大學 === 電腦與通信工程研究所 === 97 === 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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