## 1 Introduction  
Since its first emergence in the 1960s [1], chaos theory has emerged in multiple scientific fields, ranging from physics to biology, medicine, engineering, communications and economics. Chaotic systems are deterministic dynamical systems, modelled by a set of differential or difference equations. Their unique feature is that their solution can be extremely prone to changes in the initial conditions of the system, or to parameter changes. This means that solution trajectories starting from almost identical initial key values will diverge over time, giving rise to completely different behaviors. The above-mentioned feature makes chaotic systems hard to predict. This property, combined with their deterministic nature, makes chaotic systems suitable in security applications that require the use of complex dynamics, like encryption [2, 3, 4], communications [5, 6, 7, 8, 9], random number generators [10] and more [11]. Thus, there is an ongoing interest in creating novel chaotic systems, since their demand in applications is continuous. To design a chaotic system, researchers developed several different approaches. One way is to consider an existing chaotic system, and modify it by adding more terms to the differential/difference equations describing the system, or modifying an existing term, or even adding a new state to the system and changing its order [12, 13, 14]. In such cases, the new system should preferably have a more complex behavior compared to the original one, which is usually indicated by the highest value that the Lyapunov exponent can achieve. Another approach, which is the method used here, is to design a new system by utilizing nonlinear functions that are documented to yield chaotic behavior, like the hyperbolic sine function, the exponential function, the cubic power, or the absolute value; see, for example [15, 16, 17, 18, 19, 20] and the references found therein. Interestingly, when considering chaotic systems, it is preferable if the resulting system has hidden attractors [21]. An attractor is called hidden if its basin of attraction does not intersect with any open neighbourhood of an equilibrium. Systems with hidden attractors have gained attention due to their complex behavior, which makes them suitable for applications. Examples of recent works on such systems are [7, 18, 21, 22, 23, 24, 25, 26]. Based on the above, this work considers a chaotic system with a hidden attractor, having a line equilibrium. The system has two parameters, and is purely nonlinear, having no linear terms. A dynamical analysis on the system is performed by studying its bifurcation diagrams, the Poincare map, and the Lyapunov exponents diagram. Moreover, to showcase the applicability of the system to chaos based encryption applications, the system is applied to two problems. First, the problem of secure communications is considered. Here, the aim is to find a method to combine an information signal, with the values of the states of the chaotic system, resulting in a scrambled signal that carries the masked information in it. Then, this signal can be safely transmitted through a communication channel, and after appropriate signal processing, the original information can be unmasked and safely retrieved at the receiver end [6, 27]. The method used here is the symmetric chaos shift keying (SCSK) modulation, applied in [7, 28]. The present work extends the work of [29] by including an extensive bit-error-rate (BER) performance analysis of the proposed communication scheme. The simulation results show that a combination of the states of the chaotic system with a sine function can yield better performance under a noisy transmission channel. In addition to the above application, the design of a pseudo-random bit generator (PRBG) is considered. In this application, the states of the chaotic system are used to generate a sequence of bits, that possesses properties similar to those of a random sequence. Such bit generators are highly useful, since they can be used to encrypt binary information signals.