The encryption and weaknesses of the E.Álvarez cryptosystem are analyzed.A new chaotic cryptosystem based on ergodicity is proposed.The control parameters and initial condition of a chaotic system are selected as the secret key.A bit chain from the chaotic orbit is generated,and the position at which a plaintext block appears in the chain is found.Then record the number of iterations of the chaotic map as the cipher block.Several weaknesses of the E.Álvarez cryptosystem are voided in the new scheme.The security is strengthened.Finally the new cryptosystem is studied experimentally using a logistic map.It is shown that the new cryptosystem satisfies the confusion and diffuse characteristics.Effectiveness of the proposed scheme is demonstrated.

The technique of calculating the largest Lyapunov exponent of the differential equations is expounded, and the method determining the correlation dimension of the system from a time series is introduced. By utilizing the Lyapunov exponent as criterion and transforming the coordinates, the rotation symmetric generalized Lorenz strange attractors are constructed, and the activity characteristics of the strange attractors are analyzed and the correlation dimensions of the strange attractors are calculated.

It expounds the iterative function systms (it is called IFS for short) theory and the deterministic algorithm. A series of the fractal IFS attractors are simulated by utilizing the computer. The changing regularity of the IFS attractors are discussed when the control parameters are changed, and the fractal dimension of some attractors are reached by the theorem about the fractal dimension of the IFS attractor.