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Definition
A pseudorandom function is a deterministic function of a key and an input that is indistinguishable from a truly random function of the input.
Theory
Let s be a security parameter, let K be a key of length s bits, and let f(K, x) be a function on keys K and inputs x. Then f is a pseudorandom function if:
f can be computed in polynomial time in s.
if K is random, then f cannot be distinguished from a random function in polynomial time.
In this context, “distinguishability” refers to the ability of an algorithm to tell whether a function is not truly random. Let g be a truly random function of x with the same output length as f. Suppose a polynomial-time algorithm A is given access to a “oracle” which, on input x, either consistently returns f(K, x), or consistently returns g(x). After some (polynomial) number of accesses to the oracle, the algorithm outputs a guess, b, as to whether the oracle is f or g. Let ε...
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Recommended Reading
Goldreich O, Goldwasser S, Micali S (1986) How to construct random functions. J ACM 33(4):210–217
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Kaliski, B. (2011). Pseudorandom Function. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_427
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DOI: https://doi.org/10.1007/978-1-4419-5906-5_427
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