Cryptanalysis of a double scroll based “True” random bit generator

An algebraic cryptanalysis of a “true” random bit generator (RBG) based on a double-scroll attractor is provided. An attack system is proposed to analyze the security weaknesses of the RBG. Convergence of the attack system is proved using synchronization of chaotic systems with unknown parameters called auto-synchronization. All secret parameters of the RBG are recovered from a scalar time series using auto-synchronization where the other information available are the structure of the RBG and output bit sequence obtained from the RBG. Simulation and numerical results verifying the feasibility of the attack system are given. The RBG doesn't fulfill NIST-800-22 statistical test suite, the next bit can be predicted, while the same output bit stream of the RBG can be reproduced.