Steps towards Cryptanalysis of Chaotic Active/Passive Decomposition Encryption Schemes Using Average Dynamics Estimation

We analyze the security of encryption schemes based on chaos synchronization and active/passive decomposition. The security is quantified by the number of transmitted samples that has to be acquired in order to reconstruct the transmitted message with an accuracy that may compromise the transmitted information. The dynamics is estimated as the average of dynamics of the observed data within a small neighborhood of the time delay embedding phase space. We examine the factors that affect the choice of embedding dimension and neighborhood size by the unauthorized receiver. We show that the security can be enhanced by mixing a large randomly modulated message component with a smaller chaotic component while keeping the message modulation fine grained. This result is in contrast to the common approach to ensure security by adding a small message component to a larger chaotic component. Further, we show that even when a low dimensional chaotic map is used, then the unauthorized receiver is required to use a reconstruction embedding dimension that can be made large by using chaotic dynamics with large conditional negative Lyapunov exponent. This result allows one to avoid the common restriction to use only high dimensional chaotic dynamics to maintain security. We also suggest guidelines for the design of efficient active passive/passive decomposition schemes in order to maintain low transmission power, fast synchronization, and yet preserve security. We demonstrate our analysis using a relatively simple encryption scheme based on a one-dimensional chaotic tent map.