A New Test for Hamming-Weight Dependencies

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 in particular for generators based on $\mathbf F_2$-linear transformations such as the dSFMT, xoroshiro1024+, and WELL512.

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