Study And Implement On Public-key Encryption Based On Chaos

Development of the information technology and popularization of computer network bring the great facility and the enormous economic benefits to the human society. However, they caused a series of security questions at the same time. The cryptography is the key technology of guaranteeing the information safety. The Birth of Public-key Encryption opens new era of cryptography. It makes public-key separated from private key, reduces the key amount needed in multi-user's communication, saves system resources, and brings facility to key management.Because of the characteristics of chaotic system, there are extensive application prospects in information safety. And a lot of basic characteristics of the Chaos, for instance ergodicity, mixing, determinacy and sensitiveness to initial condition, etc., can be connected with the confusion and diffusion in cryptography. But compared with the wide application in symmetric system, the research about chaos in public-key encryption system is still few.Through studying the traditional public-key algorithm, such as RSA algorithm and its security, we have study some existing public-key algorithms based on Chebyshev Polynomial and Torus Automorphism, and have designed a new public-key algorithm based on Torus Automorphism. The main research contents and contribution of this paper are as follows:(1) Have study the public-key algorithms based on Chebyshev Polynomial and Jacobian Elliptic Chebyshev Rational Maps in reference [25], and the analysis of the security of the two algorithms in reference [29].(2) Have study Torus Automorphism and its property and periods, and the public-key algorithms based on Torus Automorphism in reference [26]. And have designed a new public-key algorithm based on Torus Automorphism, and have analysed its security.(3) Have realized two kinds of algorithms with the large integer operational library in VC, and compare them with traditional RSA algorithm.Analysis and result of the experiment indicate that the public-key algorithm based on Torus Automorphism have security similar to RSA, in another word, the security depends on the difficulty of the factorization of large integer. And they can resist the...