Time-Variant Signal Encryption by Dual Random Phase Encoding Setups Applied to Fiber Optics Links

Abstract

Spatial optical techniques have shown great potential in the field of information security to encode high-security images. Among them, the dual random phase encoding method (DRPE) has received much attention, since it was proposed by Réfrégier and Javidi at the middle 1990s. Since then, a number of works in the field were proposed introducing different variations of this technique. On the other hand, the space-time duality refers to the close mathematical analogy that exists between the equations describing the paraxial diffraction of beams in space and the first-order temporal dispersion of optical pulses in dielectric media. It is generally used for extending to the temporal domain well-known properties of spatial optical configurations. In this work it is developed a new approach to the secure data transmission problem in fiber optic links. We propose the encoding of time-varying optical signals, mainly for short-haul applications, with encryption methods that can be considered the time domain counterparts of the DRPE, and two of its more frequent variations: the fractional Fourier transform DRPE and the Fresnel transform encoding. Further, as performance is a very relevant subject in fiber optic links, we will analyze mechanisms to produce time limited, as well as bandwidth limited, encoded signals. To this end, the different signal broadenings produced by each stage of the encoding process in both, time and frequency domains, are analyzed by using the Wigner distribution function formalism, and general expressions for the time width, as well as the bandwidth, at all encryption stages are obtained. The numerical simulations show the good system performances, and a comparison between the different encryption processes is made. Furthermore, the robustness of the proposed methods is analyzed against the variation of typical parameters of the encryption-decryption setup. Finally, the implementation of this proposal with current photonic technology is discussed.