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We introduce a public key encryption scheme that is based on additive mixing of a message with chaotic nonlinear dynamics. A high-dimensional dissipative nonlinear dynamical system is distributed between transmitter and receiver. The transmitter dynamics is public (known to all) and the receiver dynamics is private (known only to the authorized receiver). Bidirectional signals that couple transmitter and receiver are transmitted over a public channel. Once the chaotic dynamics which is initialized with a random state converges to the attractor, a message is mixed with the chaotic dynamics at the transmitter. The authorized receiver who knows the entire dynamics can use a simple algorithm to decode the message. An unauthorized receiver does not know the receiver dynamics and needs to use computationally unfeasible algorithms in order to decode the message. Security is maintained by altering the private receiver dynamics during transmission. We show that using additive mixing modulation is more efficient than the attractor position modulation distributed dynamics encryption scheme. We demonstrate the concept of this new scheme by simulating a simple coupled map lattice. Index Terms--Chaos, nonlinear dynamics, public key encryption.

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 he 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. [ABSTRACT FROM AUTHOR]

Presents an approach to communication with chaotic signals, which demonstrates good performance in the presence of channel distortions. How the binary information is modulated onto the pulse chain; Basic design principles for the chaotic-pulse generator and its synchronization; Discussion on the possibilities of multiuser communication using chaotic-pulse-position modulation.