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Jan 13, 2017 at 17:38 history edited fgrieu CC BY-SA 3.0
Update
May 18, 2016 at 13:13 comment added fgrieu $\approx0.7825\sqrt s$ is indeed the expected (that is, mean) maximum cycle length of an iterated random mapping over a set of size $s$. It is far off for some mappings (e.g. maximum cycle length is $1$ for the identity mapping, and $s$ for increment modulo $s$). That's why I wrote This however is not a proof; but it remain a valid argument, and one that is extremely common in cryptography.
May 18, 2016 at 1:12 comment added Paul Uszak Can 0.7825√s be so general to iterated sets? I'm not a mathematician, but surely the algorithm determines the period, especially if it's "driven" by some incremented counter. If you simply stuck an "IF" statement into the algorithm as well, altering flow, wouldn't that destroy any form of linear assessment of the period? MOD functions aren't far off "IF"s.
Jan 17, 2016 at 2:08 vote accept Iam Nick
Jan 15, 2016 at 18:34 history edited fgrieu CC BY-SA 3.0
Give an element towards the third point
Jan 15, 2016 at 18:25 history answered fgrieu CC BY-SA 3.0