_:n161124605ad34361b39f60f438a67c26xb19
<http://schema.org/description>
"Linear pseudorandom number generators are very popular due to their high\nspeed, to the ease with which generators with a sizable state space can be\ncreated, and to their provable theoretical properties. However, they suffer\nfrom linear artifacts which show as failures in linearity-related statistical\ntests such as the binary-rank and the linear-complexity test. In this paper, we\ngive three new contributions. First, we introduce two new linear\ntransformations that have been handcrafted to have good statistical properties\nand at the same time to be programmable very efficiently on superscalar\nprocessors, or even directly in hardware. Then, we describe a new test for\nHamming-weight dependencies that is able to discover subtle, previously unknown\nbiases in existing generators (in particular, in linear ones). Finally, we\ndescribe a number of scramblers, that is, nonlinear functions applied to the\nstate array that reduce or delete the linear artifacts, and propose\ncombinations of linear transformations and scramblers that give extremely fast\npseudorandom generators of high quality. A novelty in our approach is that we\nuse ideas from the theory of filtered linear-feedback shift register to prove\nsome properties of our scramblers, rather than relying purely on heuristics. In\nthe end, we provide simple, extremely fast generators that use a few hundred\nbits of memory, have provable properties and pass very strong statistical\ntests."
<http://api.deepai.org/profile/sebastiano-vigna>