I am looking at oracle security. What is a random oracle? Does a random oracle exist? How is the random oracle behavior approximated in the real world?
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What is a random oracle?
Imagine a monkey living in a black box with a book and a dice. You feed some input into the box. The monkey generates some random and uniform output with his dice, writes it down in his book and returns the output to you. If you feed some input into the box that the monkey has already seen, he looks it up in his book and returns the same output to you.
Does a random oracle exist?
No. No implementation of a truly random oracle exist.
How is the random oracle behavior approximated in the real world?
With cryptographic hash functions.
If you want to know more about Random Oracles, I suggest you read the Wikipedia page as well as this nice blog series by Matthew Green.