Estimating the Unknown Parameters of a Chaos-Based S-Box from Time Series

A novel estimate system is proposed to discover the security weaknesses of a chaos based S-Box and a chaos based random number generator (RNG) it contains. Convergence of the estimate system is proved using auto-synchronization. Secret parameter of the target chaos based RNG are recovered where the available information are the structure of the chaos based S-Box and a scalar time series observed from the target chaotic system. Simulation and numerical results verifying the feasibility of the estimate system are given such that, next bit can be predicted while the same output bit sequence of the chaos based RNG used for S-Box generation can be regenerated.