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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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    $\begingroup$ 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. $\endgroup$
    – Chad Brewbaker
    Commented Dec 19, 2012 at 17:43
  • $\begingroup$ Combining a hash with an iterated stream cipher should do the trick. $\endgroup$
    – CodesInChaos
    Commented Dec 23, 2012 at 23:10
  • $\begingroup$ crypto.stackexchange.com/questions/5061/… $\endgroup$
    – Chad Brewbaker
    Commented Dec 26, 2012 at 17:32

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