This failure of pseudorandom number generators was analyzed decades ago by Don Knuth in his "Art of Computer Programming". That is why I would insist on using a physical random number generator for anything important, and most particularly for encryption. -- Gene On Sunday, March 10, 2019, 3:32:22 PM PDT, Fred Lunnon <fred.lunnon@gmail.com> wrote: Where higher dimensional geometry is involved, bear in mind that even a well-designed pseudo-random number generator is only independent to some fixed precision. Once dimension x (user-demanded precision) exceeds this quantity, the randomness becomes compromised: heed the awful warning in G. Marsaglia "Random numbers fall mainly in the planes" https://www.ncbi.nlm.nih.gov/pmc/articles/PMC285899/pdf/pnas00123-0038.pdf This effective precision is invariably omitted from a PRNG specification, and must instead be deduced from a detailed inspection of the algorithm. WFL