Research On Public-key Encryption Scheme Based On Chaotic System

The proposal of public-key encryption scheme, which is also asymmetrical encryption scheme, makes fundamental changes in cryptography. In this scheme, two keys are used, as well as public key and private key. It doesn't need multi-keys in multi-user's communication, which brings facility to key management and saves greatly system resources.Chaos has many basic characteristics, such as ergodicity, continuous power spectrum, and sensitive dependence on initial conditions and so on, which has a broad application prospects in information security and contact with cryptography in many aspects. However, compared with the wide application in symmetric system, the research about chaos in public-key encryption system is still few.In this paper, through studying the traditional public-key algorithm, such as knapsack public-key encryption algorithm and existing public-key algorithms based on Chebyshev Polynomial, then new algorithms based on non-superincreasing knapsack public-key and high density knapsack are proposed. The main research contents and contribution of this paper are as follows:(1) Have study the public-key algorithm based on multiple chaotic systems and existing Chebyshev Polynomial, in order to solve these problems, an improved algorithm is proposed.(2) Have study the construction of non-superincreasing knapsack, on the basis, an encryption algorithm based on chaotic system and non-superincreasing knapsack is proposed and its security is also analyzed.(3) Have study the design of chaotic Hash function sequence and high density knapsack, an algorithm based on a high density compressed knapsack is proposed.Analysis the result of experiment show that multiple chaotic public-key algorithm based on Chebyshev Polynomial avoid the 2-norm attack effectively; The knapsack algorithm based on non-superincreasing sequence has improvement in both time complexity and security; The high density compressed knapsack algorithm also has much improvement in security of encryption, but it is lower comparative, so accelerating the speed of the algorithm will be the key point in the future.