pRF

PRF stands for pseudorandom function. In cryptography, a PRF is a family of efficiently computable functions F_k from a domain X to a codomain Y, parameterized by a secret key k. For a randomly chosen key k, the function F_k should be computationally indistinguishable from a uniformly random function to any probabilistic polynomial-time adversary that can query the oracle F_k on input values of its choice but does not know k. Intuitively, the outputs of F_k appear random to an observer lacking the key, making it suitable for deriving unpredictable values or authenticating data.

PRFs are central to many cryptographic constructions. Two well-known uses are message authentication codes (MACs) and key derivation functions (KDFs). In practice, PRFs are built from various primitives, such as hash functions (for example, HMAC is a PRF based on a cryptographic hash) or block ciphers (a PRP or encryption under a fixed key can be viewed as a PRF). HKDF is a widely used KDF built from a PRF. Compared with PRPs, PRFs need not be invertible; a PRP is a PRF that is also a permutation on the input domain.

Security and variants: PRFs are defined in terms of polynomial-time indistinguishability; there are notions such as weak and strong PRFs depending on the allowed queries. In practice, the PRF assumption is a fundamental building block in modern cryptography, underpinning protocols and standards by enabling secure key material derivation and data authentication without exposing the key itself.