A New Test for Hamming-Weight Dependencies

Abstract

We describe a new statistical test for pseudorandom number generators (PRNGs). Our test can find bias induced by dependencies among the Hamming weights of the outputs of a PRNG, even for PRNGs that pass state-of-the-art tests of the same kind from the literature, and particularly for generators based on F 2 -linear transformations such as the dSFMT [ 22 ], xoroshiro1024+  [ 1 ], and WELL512 [ 19 ].