## 1 Introduction  
Chaos communications exploit the properties displayed by chaotic oscillators to provide security in data transmission at the physical layer [1]. Low-order chaotic systems are bounded in values but aperiodic in nature. These are theoretically composed by an infinite amount of frequencies and, although being deterministic, they present an extreme sensitivity with respect to the initial conditions that makes long term prediction impossible. Despite the sensitivity towards the starting point, chaotic oscillators can be set to synchronize in several modes, provided that adequate coupling mechanisms are implemented [2; 3]. This pseudorandom-evolution and synchrony prospects associate very well with both the standard cryptographic and data transmission requirements [4], thus paving the way for secure, chaos-based, communications. There are broadly two main categories of chaos synchronization schemes: one is based in continuous time models (e.g., dynamical systems), such as ordinary differential equations. The other group corresponds to discrete models such as chaotic maps. To synchronize the first group, one needs to transmit a chaotic signal carrier continuously over time, which is affected by channel effects such as multipath. The discrete group can be set to synchronize with the transmission of a secret key only, but with less cryptographic potential [1]. Visible light communication (VLC) is an emerging free space optical communication method built upon intensity modulation of light-emitting diodes (LEDs). LEDs, fabricated with p-n junction technology, produce light based on the principle of electroluminescence, where photonic emission takes place in response to an electric field. Their fundamental operation allows LEDs to be switched on and off beyond millions of times per second, far too fast for the human eye to realize flickering, enabling binary transmission of information in combination with adequate photodetectors. Accordingly, VLC allows high data rates in the Gb/s region [5; 6]. In fact, most related research has focused on increasing the data rates or implementation of full duplex links (VLC-infrared, VLC-WiFi, and fully VLC). There are many VLC applications including data communications, indoor localization positioning and multi-user access environments [7; 8; 9; 10; 11; 12; 13]. In effect, VLC is a complementary technology to Wi-Fi for fourth and fifth generation (4G/5G) wireless systems. This is particularly useful as Wi-Fi presents difficulties in providing multi-user connectivity. Additionally, LEDs are becoming the first choice as lighting fixtures for indoor environments due to their high energy efficiency, longer life expectancy, fast switching capability, and comparatively low costs. Moreover, advancements in thin film technology allow the fabrication of organic LEDs in large panels, widening its application fields [14]. Their implementation is going beyond indoor lighting as they are being deployed in car lights, streetlights, stand-by pilots, and so on. Consequently, LEDs are potential data transmitters (Txs) in a range of different environments, including car-to-car communications [15], wireless sensor networks, or the Internet of Things (IoT) [16]. In VLC based wireless systems, to avoid blocking and shadowing, hence ensuring 100% link availability, Tx and receiver (Rx) arrays have been adopted to provide diversity, but at the cost of increased multipath induced delay spread that leads to reduced data rates (e.g., [17; 18]). In certain applications, such as indoor or outdoor public spaces, banking, manufacturing, medical, etc., the issue of data security is becoming extremely important. Typical cryptographic techniques used today utilize number theory principles, a branch of mathematics that studies the topology of numbers. While these methods have served well in the last decades, they seem to have their security compromised with the emergence of high-speed computing; capable to process large computation of data sets.