Abstract
In this paper, we propose a new pseudorandom number generator (AST) using an Artin-Schreier tower, which is a modified version of the twisted generalized feedback shift register (TGFSR). In TGFSR, the period is depending on the order of its multiplied matrix, and it is difficult to get the theoretical upper bound in general. Using the recursive structure of Artin-Schreier towers, we define a matrix with a parameter whose order is expected to be close to fairly near the upper bound. After examining some properties of this matrix, we give an algorithm of a new pseudorandom number generator AST which produce a sequence of numbers with a long period. Finally, we report the results of TestU01 to qualify that it has a good statistical property, although its generation speed is rather slower than TGFSR.
Funding Statement
Research of the second author was partially supported by Grant-in-Aid for Scientific Research, Kiban (C) 20540044, Ministry of Education, Science and Culture. Research of the third author was partially supported by Grant-in-Aid for Young Scientist (B) 22740017, Ministry of Education, Science and Culture.
Acknowledgements
We would like to express our sincere gratitudes to a number of people who gave useful advice as well as encouragements. Those include Professors Makoto Matsumoto and Hiroshi Haramoto. Thanks are also due to the referee for many valuable comments and suggestions.
Citation
Huiling Song. Hiroyuki Ito. Yukinori Kitadai. "A pseudorandom number generator using an Artin-Schreier tower." SUT J. Math. 47 (1) 73 - 90, January 2011. https://doi.org/10.55937/sut/1314883257
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