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I will take a different take vs previous answers. Let's say we really have only 128 bits of entropy at our disposal does that prevent us from applying a determinstic algorithm on shuffling a deck of cards? From a pure counting perspective surely, a determinstic function on 128 bits of input can not have 52! different possible outputs. But If we use ...


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Is it possible to generate all shuffles with a PRNG that has 64, 128 or 160 bit internal state? No, for restriction of "possible .. with" to a deterministic procedure using the Pseudo RNG output as sole input, and: Bound to output a single shuffled sequence per run. To generate all shuffles, $\lceil\log_2(52!)\rceil=226$ bits of PRNG internal state are ...


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