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Historically hashes have been from a large set (say 256 characters) to a smaller set (256 bits).

Also, hash functions that are P-complete have no known parallel algorithm; they must be computed serially which ensures a certain amount of temporal cost in computing them.

Three questions:

1)What is the technical term for hashes that map to a larger set than the domain?

2)Are there any good P-complete hashes?

3)Are there any good P-complete hashes that map to a larger set?

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Encoding the string into a Game of Life grid and playing K rounds is an example of a P-complete hash. There must be a better one out there. –  Chad Brewbaker Dec 19 '12 at 17:43
    
Combining a hash with an iterated stream cipher should do the trick. –  CodesInChaos Dec 23 '12 at 23:10
    
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