On Measuring Randomness

Is it possible to determine what randomness is let alone measure and classify it? Can random number generators be tested and then compared with each other? How can we know if a randomness test is useful? These are questions that are thoroughly studied in this thesis. One of the main goals of this thesis is to explain interesting details that can be found in randomness and to study how pseudorandomness compares to real randomness. Alongside this paper, a program will be created in order to study and measure pseudorandom number generators and randomness tests. The program will allow the combination of random number generators and randomness tests in order to study any hidden similarities of different generators and tests. The classification of randomness and randomness tests will also be studied. The first chapter reviews the more philosophical discussions concerning randomness and its types. The second chapter is slightly more practical, as it explains in which ways randomness can be measured and defines what a good pseudorandom number generator should look like. The second chapter also reviews concepts and terminology which are crucial in order to understand later chapters. The third chapter studies randomness tests and tries to define an ideal randomness test. The fourth chapter explains the software that is created along with this paper to study randomness tests and pseudorandom number generators and the fifth chapter shows the results of experiments done with the software