Random oracle

In cryptography, a random oracle is an oracle (a theoretical black box) that responds to every unique query with a (truly) random response chosen uniformly from its output domain. If a query is repeated it responds the same way every time that query is submitted.

Stated differently, a random oracle is a mathematical function chosen uniformly at random, that is, a function mapping each possible query to a (fixed) random response from its output domain.

Random oracles as a mathematical abstraction were firstly used in rigorous cryptographic proofs in the 1993 publication by Mihir Bellare and Phillip Rogaway (1993). They are typically used when the cryptographic hash functions in the method cannot be proven to possess the mathematical properties required by the proof. A system that is proven secure when every hash function is replaced by a random oracle is described as being secure in the random oracle model, as opposed to secure in the standard model of cryptography.

Random oracles are typically used as an ideal replacement for cryptographic hash functions in schemes where strong randomness assumptions are needed of the hash function's output. Such a proof generally shows that a system or a protocol is secure by showing that an attacker must require impossible behavior from the oracle, or solve some mathematical problem believed hard in order to break it.

Not all uses of cryptographic hash functions require random oracles: schemes that require only one or more properties having a definition in the standard model (such as collision resistance, preimage resistance, second preimage resistance, etc.) can often be proven secure in the standard model (e.g., the Cramer–Shoup cryptosystem).

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