A Pseudo-Random Permutation (PRP) is a function that cannot be distinguished (with practical effort) from a permutation selected at random with uniform probability from the family of all permutations on the function's domain.

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Luby-Rackoff theorem confusion

The Luby-Rackoff theorem states that if a round function is a secure pseudorandom function (PRF) then 3 rounds are sufficient to make the block cipher a pseudorandom permutation (PRP). PRPs are ...
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Is the inverse of a secure PRP, also a secure PRP?

If a block cipher is a secure PRP, is it's inverse a secure PRP as well? My intuition says yes but I'm not exactly sure. On a related note, if a block cipher is a secure sPRP, is it's inverse a ...
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What is the most computationally efficient way of generating pseudo-random permutations?

I have an application in which I need to create up to J randomly shuffled-copies of an array of length N. Then I will have millions or even billions of iterations such that, in each iteration, I will ...
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Is AES's parity key-dependent?

Is the parity of the permutation of the set $\{0,1\}^{128}$, defined by AES encryption for a certain fixed key, dependent on this key? DES, and any pure Feistel cipher, has even parity for any key. ...