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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.
The most common example of this technique, known as the random oracle model, [1] [2] involves replacing a cryptographic hash function with a genuinely random function. Another example is the generic group model , [ 3 ] [ 4 ] where the adversary is given access to a randomly chosen encoding of a group , instead of the finite field or elliptic ...
In cryptography, a pseudorandom function family, abbreviated PRF, is a collection of efficiently-computable functions which emulate a random oracle in the following way: no efficient algorithm can distinguish (with significant advantage) between a function chosen randomly from the PRF family and a random oracle (a function whose outputs are fixed completely at random).
Lavarand, also known as the Wall of Entropy, is a hardware random number generator designed by Silicon Graphics that worked by taking pictures of the patterns made by the floating material in lava lamps, extracting random data from the pictures, and using the result to seed a pseudorandom number generator.
The algorithm sends the oracle a number of queries before deciding whether the oracle is a random oracle or simply an instance of the pseudorandom function family. Say also that there is a 50% chance that the oracle is a random oracle and a 50% chance that it is a member of the function family.
Random number generation in kernel space was implemented for the first time for Linux [2] in 1994 by Theodore Ts'o. [6] The implementation used secure hashes rather than ciphers, [clarification needed] to avoid cryptography export restrictions that were in place when the generator was originally designed.
This result was generalized to the quantum-accessible random oracle (QROM) by Don, Fehr, Majenz and Schaffner, [3] and concurrently by Liu and Zhandry. [4] In the case that random oracles do not exist, the Fiat–Shamir heuristic has been proven insecure by Shafi Goldwasser and Yael Tauman Kalai . [ 5 ]
All users of the signature scheme agree on a group of prime order with generator in which the discrete log problem is assumed to be hard. Typically a Schnorr group is used. All users agree on a cryptographic hash function H : { 0 , 1 } ∗ → Z / q Z {\displaystyle H:\{0,1\}^{*}\rightarrow \mathbb {Z} /q\mathbb {Z} } .