Practical Next Bit Test for Evaluating Pseudorandom Sequences


Department of Mathematical Sciences,Sharif University of Technology


Abstract. The Next Bit Test brie
y states that a sequence is random if and only if, given any i
bits of the sequence, it is not possible to predict the next bit of the sequence with a probability of success
signi cantly greater than 1=2. In 1996, Sadeghiyan and Mohajeri proposed a so-called new universal test
for bit strings", based on the theoretical next bit test. In this paper, we study di erent aspects of this test
and show its weakness. Then, we improve it both theoretically and practically for better classi cation of
the sequences. As a result, a Practical Next Bit (PNB) test is introduced in two Global and Local versions
and a histogram, which gives an impression of the global evaluation of the underlying sequence. Testing
samples of nonrandom sequences, using both the PNB test and the NIST Statistical Test Suite, indicates
the superiority of the PNB test power over that of the NIST.