One Chaotic Ciphers' Security Analysis Under Finite Precision And Its Application

Some inner properties of chaos, such as randomness, unpredictable orbits and initial variables sensitivity, accord deeply with requirements of cryptography. Between chaos and cryptograph a new cross-disciplinary field called chaotic-cryptograph generates. But because of finite precision, when digital chaos realizes in computer, its dynamic properties descends badly.We first introduce the natural relation between chaos and cryptography, and then give a comprehensive survey about many chaotic ciphers'design scheme and security analysis. Our emphasis is the influence of finite precision to chaotic ciphers and remedies to enhance security of chaotic ciphers. Based on the survey we give an initial investigation about logistic map's dynamic properties degradation under finite precision.This thesis analyzes one chaotic cipher proposed by Yen-Guo in details and finds it is insecure to chosen plain text attack. Also, some remedies are given to improve its security. Based on the modified Logistic map we propose a pseudo-random number generator (PRNG). Theoretical and experimental results show this PRNG has good cryptographic properties. Using this PRNG we design and implement a novel chaotic stream cipher, which shows good security under experimental tests.