In cryptography, a Pseudorandom function (PRF), is a collection of efficiently-computable functions which emulate a random oracle in the following so no efficient algorithm can distinguish (with significant advantage) between a function chosen randomly from the Pseudorandom function family and a random oracle (a function whose outputs are fixed completely at random).

Pseudorandom functions are vital tools in the construction of cryptographic Primitive, especially secure encryption schemes.

Pseudorandom functions are not to be confused with pseudorandom generators (PRGs). The guarantee of a pseudorandom generator is that a single output appears random if the input was chosen at random. On the other hand, the Pseudorandom function guarantees the outputs appear random, regardless of how the corresponding inputs were chosen, as long as the function was drawn at random from the Pseudorandom function family.

What is Important#

For Cryptography the randomness (Entropy) of a Pseudorandom function it is only important to be unpredictable. That no one can predict the next random number.

The philosophical debate on true randomness is a debate for outside of Cryptography.

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