The aim of this paper is to propose a new secure communications approach, obtained by combining into one scheme chaotic modulation, recursive encryption and chaotic masking. The objective is achieved by designing control laws to synchronize two hyperchaotic Lorenz systems with encrypted states via a backstepping technique. The encryption process relies on a Unified chaotic system, driven by the hyperchaotic Lorenz system, as well as on a recursive encryption algorithm that exploits an n-fold composition of an invertible function. A novel theorem is proved, which assures that the transmitted message is recovered at the receiver side by virtue of the synchronization of the two Lorenz systems via backstepping design. Numerical simulations are carried out using image and text as transmitted signals, with the aim to show the effectiveness of the conceived chaos-based encryption scheme.

本文的目的是提出一种新的安全通信方法，该方法通过将混沌调制，递归加密和混沌屏蔽组合为一个方案而获得。通过设计控制定律以通过反步技术使两个超混沌Lorenz系统与加密状态同步来实现此目的。加密过程依赖于由超混沌Lorenz系统驱动的统一混沌系统以及利用n的递归加密算法。可逆函数的三折构成。证明了一个新颖的定理，该定理通过两个Lorenz系统的同步通过后推设计确保了在接收方恢复发送的消息。使用图像和文本作为传输信号进行了数值模拟，目的是证明所构想的基于混沌的加密方案的有效性。