A **pseudorandom function family** (PRF family) is a fundamental concept in cryptography and computer science, particularly in the field of secure communication and data protection. Here's a breakdown of the concept: ### Definition - A pseudorandom function family is a collection of functions—typically indexed by a secret key—such that, given a random key from that family, the function behaves like a truly random function to any efficient adversary (e.g., a polynomial time algorithm).
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A pseudorandom function family is a collection indexed by a key , with an efficient evaluation algorithm. For a random key, an adversary receiving answers to chosen queries should be unable to distinguish from a uniformly random function on the same finite domain and range, within a declared resource bound.
Both experiments answer repeated queries consistently. Fresh queries to the random function receive independent uniform values; queries to use one fixed key throughout. The adversary may choose its next query using previous answers.
For a one-bit output, an all-zero family is easily distinguished: two different queries return with probability one there and probability for a random function. State key length, query bound, running time and distinguishing advantage when using the definition quantitatively.[ref]
How to Construct Random Functions by Oded Goldreich, Shafi Goldwasser and Silvio Micali. function ensembles and oracle indistinguishability definition