On Wed, Aug 25, 2004 at 10:01:25AM +0100, Dale Amon wrote: > On Wed, Aug 25, 2004 at 06:02:22AM +0200, Almut Behrens wrote: > > Somewhat more seriously: are there generally any defining criteria for > > something one would call a 'hash function', saying that it always must > > map some larger input space to some smaller output space? > > Yes. A hash function is any mapping function > > y = map(x) > > where the space y is smaller than the space x. Hashing (think of > cornbeef hash with things all chopped up into bits) is a technique > to generate fast lookup keys. The discussion here is about > cryptographic hash functions. I believe the primary difference is > that a cryptographic hash is: > > * a uniform mapping. For input space n and output space m, > there are on average n/m strings with the same hash key. > * randomness. Input strings which differ by 1 bit in any > position generate hash keys a random distance apart
Add to that: * An output dependence on both the value and position of *every* input byte. Kind of implied by your second postulate, but worth mentioning explicitly. Especially when people think that a simple sum is cryptographically sound -- any combination of the input letters (or other matching combinations) will produce the same hash value. - Matt
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