This paper proposes a novel BiFeO₃ memristor-based electronic circuit for the encryption of sensitive medical data. The hardware cryptographic system is tested through the use of neural signals from a patient experiencing a number of focal epileptic seizures. The Cellular Nonlinear Network theoretical framework provides a basis for sophisticated neural signal processing techniques capable to anticipate the emergence of an epileptic seizure in many cases. The application of these techniques to original data successfully reveals changes before the onset of each epileptic seizure. This information may not be extracted from the encoded data, validating the proper functioning of the memristor-based encryption.