Does a linear cryptographic hash function exist?
By linear I mean a function 'f' such that:
where + is mod n for some large constant n
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Yes,the cryptographically strong SWIFFT algorithm (a variant was a condender for the SHA3 standard) is linear such that h(a + b) = h(a) + h(b)
It is an interesting example of a hash that is both cryptographically strong and not psuedorandom. It is also another unexpected use of the much lauded FFT algorithm.
http://en.wikipedia.org/wiki/SWIFFT