Towards an Encryption Scheme Based on Hybrid Systems
Juan Gonzalo Barajas Ramirez, Ricardo Femat, Ilse Cervantes
On this contribution, a hybrid-time system that evolves switching between two continuoustime
vector fields, one stable and the other unstable, is used to proposed a secure communication
scheme. The proposal is to encrypt information on the trajectories of a hybrid-time system with a
switching rule chosen such that the system presents complex behavior. Mostly, the research on the
applications of nonlinear dynamics to secure communication and encryption has been carried out either
on continuous or discrete-time. However, the majority of the applications are realized on hybrid
environments. A motivation for this study is to investigate the effects of the switched nature of the
hybrid-time system on the implementation, realization and performance of an encryption system. One
significant characteristic of hybrid-time systems is their simplicity of construction that may represent
an advantage in practical implementations. As an initial investigation, the hybrid-time system is used
to construct a symmetric block cipher, where the encryption-decryption process is defined in terms
of an stroboscopic map of the system trajectories. In this way, the plaintext message is directly transformed
into a cyphertext signal that can be transmitted over a public channel and requires from an
authorized receiver the use of the transmitter’s hybrid-time system trajectories to recover the original
message. In order to illustrate the proposed encryption scheme, numerical simulations are presented.