What is RANDOM ORACLE? What does RANDOM ORACLE mean? RANDOM ORACLE meaning - RANDOM ORACLE definition - RANDOM ORACLE explanation.
Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.
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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).
Random oracles have long been considered in computational complexity theory, and many schemes have been proven secure in the random oracle model, for example Optimal Asymmetric Encryption Padding, RSA-FDH and Probabilistic Signature Scheme. In 1986, Amos Fiat and Adi Shamir showed a major application of random oracles – the removal of interaction from protocols for the creation of signatures.
In 1989, Russell Impagliazzo and Steven Rudich showed the limitation of random oracles – namely that their existence alone is not sufficient for secret-key exchange.
In 1993, Mihir Bellare and Phillip Rogaway were the first to advocate their use in cryptographic constructions. In their definition, the random oracle produces a bit-string of infinite length which can be truncated to the length desired.
According to the Church–Turing thesis, no function computable by a finite algorithm can implement a true random oracle (which by definition requires an infinite description).
In fact, certain artificial signature and encryption schemes are known which are proven secure in the random oracle model, but which are trivially insecure when any real function is substituted for the random oracle. Nonetheless, for any more natural protocol a proof of security in the random oracle model gives very strong evidence of the practical security of the protocol.
In general, if a protocol is proven secure, attacks to that protocol must either be outside what was proven, or break one of the assumptions in the proof; for instance if the proof relies on the hardness of integer factorization, to break this assumption one must discover a fast integer factorization algorithm. Instead, to break the random oracle assumption, one must discover some unknown and undesirable property of the actual hash function; for good hash functions where such properties are believed unlikely, the considered protocol can be considered secure.