Random oracle: Difference between revisions

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In [[cryptography]], a '''random oracle''' is an [[oracle machine|oracle]] (a theoretical [[black box (systems)|black box]]) that responds to every query with a (truly) [[random]] response chosen [[uniform distribution (mathematics)|uniformly]] from its output ___domain, except that for any specific query, it responds the same way every time it receives that query. Put another way, a random oracle is a [[mathematical function]] mapping every possible query to a random response from its output ___domain.

Random oracles are a mathematical abstraction used in cryptographic proofs; they are typically used when no known implementable function provides the mathematical properties required by the proof. A system that is proven secure using such a proof is described as being secure in the ''random oracle model'', as opposed to secure in the ''[[standard_model(cryptography)|standard model'']]. In practice, random oracles are typically used to model [[cryptographic hash function]]s 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 the protocol. Not all uses of cryptographic hash functions require random oracles: schemes which require only the property of [[collision resistance]] can be proven secure in the standard model (e.g., the [[Cramer-Shoup cryptosystem]]).

In the more precise definition formalized by Bellare/Rogaway (1993), the random oracle produces a bit-string of infinite length which can be truncated to the length desired. When a random oracle is used within a security proof, it is made available to all players, including the adversary or adversaries. A single oracle may be treated as multiple oracles by pre-pending a fixed bit-string to the beginning of each query (e.g., queries formatted as "1|x" or "0|x" can be considered as calls to two separate random oracles, similarly "00|x", "01|x", "10|x" and "11|x" can be used to represent calls to four separate random oracles).