In this work, an asymmetric cryptography method for information security was developed, inspired by the fact that the human body generates chaotic signals, and these signals can be used to create sequences of random numbers. Encryption circuit was implemented in a Reconfigurable Hardware (FPGA). To encode and decode an image, the chaotic synchronization between two dynamic systems, such as Hopfield neural networks (HNNs), was used to simulate chaotic signals. The notion of Homotopy, an argument of topological nature, was used for the synchronization. The results show efficiency when compared to state of the art, in terms of image correlation, histogram analysis and hardware implementation.