Query about hash function capability
Victor Duchovni
Victor.Duchovni at MorganStanley.com
Thu Aug 4 10:03:01 EDT 2005
On Thu, Aug 04, 2005 at 12:55:51PM +1000, Arash Partow wrote:
> Hi all,
>
> My question relates to hash functions in general and not specifically
> cryptographic hashes. I was wondering if there exists a group of hash
> function(s) that will return an identical result for sequentially
> similar yet rotate/shift wise dissimilar input:
>
> ie: input1 : abcdefg -> h(abcdefg) = 123
> input2 : gabcdef -> h(gabcdef) = 123
> input3 : fgabcde -> h(fgabcde) = 123
>
Sure, just pick the lexicographically first cycle and hash
that. This is an invariant of all cyclic permutations of the
string.
epermut -> h(epermut)
ermutep -> h(epermut)
muteper -> h(epermut)
permute -> h(epermut)
rmutepe -> h(epermut)
tepermu -> h(epermut)
uteperm -> h(epermut)
More generally given any automorphism group on the input strings, hashing
the lexicographically smallest member of the orbit of an input string
under the group gives a hash that is invariant under the group operation.
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