A Study on a New Pseudorandom Number Generator with Deterministic Maze Construction

In this paper, we propose a new pseudorandom number generator (PRNG), which uses a new deterministic maze construction for our maze-based PRNG [1]. We evaluate some relations between a size and a number of shapes for the mazes generated by our maze construction. Then, we also estimate a number of shapes and the maximum duplicate number of mazes by the size of the maze. By using the asymptotic equations of these estimated values, we can derive the minimum required maze size for the required number of sequences in which most or all sequences are different.