Multiplexed encryption using chaotic systems with multiple stochastic-delayed feedbacks

We propose an efficient and fast bit-multiplexed encryption scheme exploiting hyperchaotic regimes of a single nonlinear oscillator with multiple time-delay feedback loops. Each data stream is encrypted by digitally modulating the values of the various time delays and decrypted using chaos synchronization and cross-correlation measurements. We have numerically applied our approach to an optoelectronic chaotic oscillator based on standard semiconductor lasers subjected to multiple feedbacks and have demonstrated successful data transmission and recovery between multiple users at several Gbits/s on a single communication channel.

Figure 1

(Color online) Schematic configuration for multiplexed encryption based on APD and using a nonlinear oscillator with a delayed feedback loop for each of the $N$ users.

Figure 2

(Color online) Graphical representation of the time-delay encryption performed by ${\text{Alice}}_i$ in her specific encryption slot ${\Delta }_i$. She is encrypting two consecutive symbols through the time delays ${\tau }_{i\mid {\Omega }_k}$ and ${\tau }_{i\mid {\Omega }_{k+1}}$.

Figure 3

(Color online) Simultaneous decryption of four messages composed of $M_i=32$ $\left(i=1,\dots ,4\right)$ symbols at 1 Giga symbols/s per user. The equivalent bit rate is 5 Gbits/s per user. The first line gives input messages ${\tau }_i$, the second line the recovery messages ${\widehat{\tau }}_i$, and the third line relative error $e_i$ on each decrypted symbol in percentage. The equivalent aggregate bit rate is 20 Gbits/s.