Random Number Generators Based on Models of Random Access Memory and Confined Gas

Approach to designing pseudo-random number generators (PRNGs) by combining the model of operation of plain random-access memory (PRAM) and the model of behavior of confined gas is investigated, proposed and described in the paper. It can be regarded as a transform, converting the input sequence of numbers, random or ordinary, into a new pseudo-random number output sequence. The proposed method is based on the processes of writing in the numbers into the memory matrix of the PRAM, and subsequently reading out its content along appropriate reading paths across the memory. Categories of writing and reading patterns are systematically considered, as ways of restructuring the two-dimensional content of the PRAM into one-dimensional arrangement. The PRAM is numerically formalized by the number matrix (NM), and also abstracted to its pure geometry, in which the concept of writing-reading paths gets its obvious meaning. The proposed skew (randomized) reading and/or writing of the PRAM content adds a new degree of freedom in generating the output random number sequence. The idea for skew reading and/or writing path came from the trajectory of a molecule of the gas confined in a vessel, which is modeled for a one-molecule case, for simplicity. The proposed method is general and enables the design of PRNGs with different characteristics, for different purposes and applications. Two such designs, the most interesting for practical applications, called basic design and improved design, are proposed and described. The proposed approach also can be used to improve the characteristics of some simpler PRNGs with lower levels of randomness. The description of the method and the way of pseudo-random number generator (PRNG) design are discussed and illustrated in the paper. The quality and randomness of the generated sequences of the proposed PRNG designs were analyzed using NIST tests. The test results show that all proposed designs are of satisfactory quality and pass NIST tests. Some of the test results are given in the paper.