Testing randomness: Implementing poker approaches with hands of four numbers
In this paper we discuss the problem of testing randomness motivated by the need to evaluate of the quality of different random number generators which may not generate a true random numbers. Such number generators are used by many practical applications including computer simulations, cryptography, and communications industry, where the quality of the randomness of the generated numbers affects the quality of these applications. In this paper we concentrate with one of the most popular approaches for testing randomness, Poker test. In particular, two versions of Poker test are known: the classical Poker test and the approximated Poker test, where the latter has been motivated by the difficulties involved in implementing the classical approach at the time it is designed. Given a sequence of random numbers to be tested, the basic Poker approach divides this sequence into groups of five numbers, observes which of the possible patterns is matched by each quintuple, computes the occurring probability of each of these patterns, and finally applies Chi-square test to check the randomness of such sequence. In [11], we showed such approach can be implemented with no significant extra running time compared with the approximated approach.
In this paper, motivated by certain practical applications such as cryptography and simulation we implement the classical Poker test (respectively, the corresponding approximated approach) that uses hands of four numbers instead of hands of five numbers. The numerical experiments applied hands of four numbers approach show that the running time is significantly less than those applied hands of five numbers approach.
Keywords: Poker test, randomness, random numbers tests, cryptography, secret keys
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ABOUT THE AUTHORS
Wael M. F. Abdel-Rehim
He received the B.Sc. degree in Mathematics and Scientific Computations from the Faculty of Science, Suez Canal University, Ismailia, Egypt in 2007. After that he worked as a demonstrator at the Faculty of Science in Suez, Suez Canal University, Egypt. His current research interests are in wireless networks, network simulation, Random number testing, and performance evaluation of computer networks.
Ismail A. Ismail
Professor, Dean, College of Computers and informatics, Misr international University, Egypt, received the M.S. and Ph Degrees from the University of Cairo, Egypt, in 1971 and 1976, respectively. His research interests include pattern analysis and machine intelligence, data structures and analysis, genetic algorithms, neural network, and database.
Ehab Morsy
He received the PhD degree in Combinatorial Optimization from Graduate School of Informatics, Kyoto University, Japan, 2009. After that and till now he worked as an assistant professor at Department of Mathematics, Faculty of Science, Suez Canal University, Egypt. He has 12 publications in various international journals and conferences. His current research interests are Design and Analysis of Graph Algorithms, Distributed Computing, and Combinatorial Optimization.
Wael M. F. Abdel-Rehim
He received the B.Sc. degree in Mathematics and Scientific Computations from the Faculty of Science, Suez Canal University, Ismailia, Egypt in 2007. After that he worked as a demonstrator at the Faculty of Science in Suez, Suez Canal University, Egypt. His current research interests are in wireless networks, network simulation, Random number testing, and performance evaluation of computer networks.
Ismail A. Ismail
Professor, Dean, College of Computers and informatics, Misr international University, Egypt, received the M.S. and Ph Degrees from the University of Cairo, Egypt, in 1971 and 1976, respectively. His research interests include pattern analysis and machine intelligence, data structures and analysis, genetic algorithms, neural network, and database.
Ehab Morsy
He received the PhD degree in Combinatorial Optimization from Graduate School of Informatics, Kyoto University, Japan, 2009. After that and till now he worked as an assistant professor at Department of Mathematics, Faculty of Science, Suez Canal University, Egypt. He has 12 publications in various international journals and conferences. His current research interests are Design and Analysis of Graph Algorithms, Distributed Computing, and Combinatorial Optimization.
