On Pseudo Random Bit Generators via Two-Dimensional Hybrid Cellular Automata

All cryptography schemes are based on producing keys such that they are not predictable. Hence, the key that is random is used in a cryptosystem and producing such keys is one of the main problems in cryptography [1]. Thus, several methods have been proposed in order to accomplish this problem that is to generate pseudo random numbers (PRN) or bits. Generating PRN by using cellular automata (CAs for brevity) is one of these methods. In spite of very good randomness properties of nonlinear CAs [2] ([3]), linear CAs provide a huge convenience due to its algebraic structure. However, it is a well-known fact that linear CA is not good at generating PRNG. Indeed, evolving a nonlinear cellular automaton (singular, CA) requires nding the value of a function with multiple variables for each cell, however with a linear CA since it is a linear transformation, all cells can be evolved at a reasonable time owing to the transition matrix. Without giving up of linearity structure together with its weakness, it is reasonable to use linear hybrid CAs and while applying it instead of choosing blocks we choose a particular cell for this purpose. By this means, we avoid expensiveness of time consuming comparing to nonlinear CA. The key that is generated through this method or any other in general to be in random it has to pass some basic statistical tests: the frequency test, the serial test, the poker test, the run test, and the autocorrelation test [4]. In [5], by using two-dimensional linear hybrid cellular automata (2D) LHCA, generating pseudo random bit sequences has been attempted and the generated bit sequences have been tested whether they are pseudo random or not. Although some very speci c examples were given, any classi cation of the rules was not proposed. Here in this work, we study with respect to another boundary condition which is so-called adiabatic. Moreover, we intend to classify the rules in order to predict which ones or how many of them are suitable to generate pseudo random bit sequences.