I am zero training in cryptography, but I would think that if in
addition to
FP(as ++ bs) = FP(bs) `plusFPFlipped` FP(as)
(I think the flipped plusFP def is more intuitive)
there also existed a minusFP for all f and x such that
FP(bs) = FP(as ++ bs) `minusFP` FP(as)
then that might facilitate common subexpression refactorization in the
merging of two hashes of memoized expressions.
One example of such an minusFP (not recommended) is (foldr xor 0):
That xor is its own inverse is no advantage. But xor is associative and
(xor 0) is an identity, so FP([] ++ as) = FP(as ++ []) = FP(as) as
expected. There must be more robust such monoidal functors out there.
Refactorization could be limited to respect substructure boundaries
reflected in the serialization.
Dan Weston
Simon Peyton-Jones wrote:
Interesting! The associativity property is the kind of thing I was after.
Except that I don't really care if FP(as ++ bs) = FP(as) `plusFP` FP(bs). I
only care that the latter is robust in the sense of having low probabilty of
collision. So the Rabin scheme does more than I really need (which is probably
fine).
On page 1 he draws a distinction between fingerprinting and hashing, which
relates to my last wish. Does one need a different technique for the two, or
is it enough to reduce the number of bits in the Rabin scheme, and thereby get
a hashing scheme?
Strangely the paper gives no comparison with other fingerprinting schemes.
Simon
| -----Original Message-----
| From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Lauri Alanko
| Sent: 11 October 2007 11:27
| To: haskell
| Subject: Re: [Haskell] Fingerprints and hashing
|
| If compositionality is important, at least Rabin's fingerprints are
| worth considering: http://citeseer.ist.psu.edu/broder93some.html
|
| They have the neat property that the fingerprint of a concatenation of
| strings can be cheaply computed from the fingerprints of the
| constituents. I think this effectively means that the plusFP operation
| can be made associative, which might offer optimization opportunities.
|
| I remember implementing it some seven years ago when prototyping for a
| C implementation. The code is lost, though. I can give it a shot
| again, if this is considered a reasonable algorithm.
|
|
| Lauri
| _______________________________________________
| Haskell mailing list
| Haskell@haskell.org
| http://www.haskell.org/mailman/listinfo/haskell
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