TL;DR: Simulation results prove that this K-L transform method can effectively improve the complexity of key sequence and increase the period of Logistic sequence, which makes up the short periodicity phenomenon of digital chaotic sequence.
Abstract: Chaotic special properties make the chaotic encryption technology to be an important research field of information science and technology. However, as digital chaos is affected by the limited precision of computer, chaos system properties present degradation--short periodicity of output sequence. This paper proposes K-L transform method for Logistic 0/1 sequence, and then analyses time-autocorrelation, complexity, frequency spectrum and time-frequency of the sequence. Simulation results prove that this method can effectively improve the complexity of key sequence. More than that, it also can increase the period of Logistic sequence, which makes up the short periodicity phenomenon of digital chaotic sequence. So this kind of digital chaotic key sequence can be applied safely to encryption system.
TL;DR: It is shown that by encoding the problem into Boolean satisfiability and applying the state of the art SAT solvers, one can obtain a discrepancy 2 sequence of length 1160 and a proof of the Erd?s discrepancy conjecture for C = 2, claiming that no discrepancy2 sequence oflength 1161, or more, exists.