## 2 Background and Related Work
### Coupled Chaotic Map Lattices  
Coupled chaotic map lattices were first introduced in the mid 1980s through a series of closely released publications [9]. The underlying lattice can exist in infinite dimensions. So, the mappings in coupled chaotic map lattices generally demonstrate chaotic behavior both in time and space [11]. A coupled chaotic map lattice is a dynamical system with discrete time, discrete space, and the continuous state variables. The system evolves through discrete time by mapping onto vector sequences.  
The most common coupled chaotic map lattice models were introduced by [PERSON] in 1983, where the recurrence equation is as follows [9]:  
\[x_{t+1}^{n}=(1-\varepsilon)f(x_{t}^{n})+\frac{\varepsilon}{2}[f(x_{t}^{n+1})+ f(x_{t}^{n-1})],\;n=1,\;2,\;\ldots,\;N \tag{3}\]where \(x_{t}^{n}\in R\) and \(f(\,)\) are the real chaotic mapping, \(t\) is the time index, \(n=1,2,3,\dots\,N\), is the map index, \(N\) is the size of system, and \(\epsilon\) is a coupling constant between 0 and 1.  
[PERSON] and et al. proposed a coupled chaotic tent map lattice system with uniform distribution [11]. In this paper, the system with uniform distribution inherited the coupled diffusion and parallel iteration mechanism of coupled map lattices. The authors modified the original coupled chaotic tent map lattices model. They removed the diffusion coefficient \(\epsilon\) and added the constant term \(k_{i}\), \(k_{i}=\sin(i)\) (\(i\) is radian). In [11], the proposed model has a good uniform distribution property, but their proposed scheme removed the diffusion coefficient \(\epsilon\). It may not be a typical coupled map lattice.  
[PERSON] and et al. proposed a stream cipher based on the discretization of a coupled map lattice [12]. In this paper, it discretizes the coupled map lattice and combines binary computations of chaos and some algebraic operations to enhance its security. The algorithm provides the output with good randomness properties. The output keystreams are tested by the NIST SP 800-22 test suite. The statistical tests and security analysis show that the binary sequences have good pseudorandom characteristics. However, their proposed scheme has complex computations and more numerical conversions, which will increase the load of the system and memory.  
[PERSON] and [PERSON] proposed a new stream cipher based on a coupled map lattice map [10]. In this paper, the system is based on the two outputs of the hyperchaotic map and modifies the chaotic map outputs as new output sequences. The algorithm provides the output with good randomness properties. In [10], the statistical tests and security analysis show that the binary sequences have good pseudorandom characteristics. However, the computation of high-dimensional equations is complex.  
[PERSON] and et al. proposed a new self-synchronizing stream cipher based on a one-way coupled chaotic map lattice [25]. In this paper, the proposed algorithm combines floating-point computations of chaos and some algebraic operations to enhance its security. The authors use the original one-way coupled map lattices for the driving system. In [25], the proposed scheme has high bit confusion and diffusion rates. However, the operation needs constantly heavy transformations between the binary sequence and real number. It increases the system load.