Question about the mathematical properties of hashes

Posted by levand on Stack Overflow See other posts from Stack Overflow or by levand
Published on 2010-04-17T14:06:36Z Indexed on 2010/04/17 14:13 UTC
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cryptography

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hash

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math

Take a commonly used binary hash function - for example, SHA-256. As the name implies, it outputs a 256 bit value.

Let A be the set of all possible 256 bit binary values. A is extremely large, but finite.

Let B be the set of all possible binary values. B is infinite.

Let C be the set of values obtained by running SHA-256 on every member of B. Obviously this can't be done in practice, but I'm guessing we can still do mathematical analysis of it.

My Question: By necessity, C ? A. But does C = A?

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