New answers tagged pseudo-random-generator
Since Blum-Micali is cryptographically secure, you know that there won't be a short cycle (not one short enough to detect in polynomial time), because a short cycle would violate cryptographic security. Therefore, you don't need to worry about this. It's not worth your time worrying about it: it's very unlikely you'll run into a short cycle. That said, ...
NIST has a lot of information on testing random number generators at http://csrc.nist.gov/groups/ST/toolkit/rng/index.html that might be of value to you.
Your approach makes getting information other than count of cards in possession of each player at least as hard as breaking the PRFness of HMAC. To make it information-theoretically impossible "for all the ... each player", $\;\;$ if different card_values have different lengths then use $\;\;$ SHA256(commonly_agreed_public_salt:card_value) $\;\;$ ...
The answer given by Henrick is good, but I try to give a explanation with more details in security area. When you think about PRF (Pseudo Random Function), you will think that there are three elements with PRF, which is $K, X, Y$. $K$ means the key, $X$ means the message and $Y$ means the output. PRF is a function, when you give this function $K$ and $X$, ...
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