Properties of Knuth’s Quadratic Congruential Sequences with Modulus m = 2W p

In this paper, we give some important characteristics of Knuth’s quadratic congruential sequences with a particular modulus as a pseudorandom number generator. For modulus m = 2
^W
p where p is an odd prime, we derive some periodic relations of the sequence by using analysis results shown by Iwasaki and Umeno for their one-stroke polynomial. Accordingly, we have theoretical analysis for randomness of these sequences and evaluate pseudorandom number outputs by these sequences by the NIST statistical tests.