hashes on restricted domains: random functions or permutations?

[Travis H.]

So I was reading about the OTP system (based on S/Key) described in RFC 2289.
It basically hashes a secret several times (with salt to individualize
it) and stores
the value that the correct password will hash to.

Now my question is, if we restrict ourselves to, say, 160-bit inputs, is SHA-1
a permutation, or do collisions exist?  If there are collisions, then iterating
the hash could lead to fewer possible values each time, potentially converging
on a set of inputs that form a permutation and are closed under composition.

Is that correct?  What are the expected sizes of such sets?
Is it worth worrying about?
-- 
"The obvious mathematical breakthrough would be the development of an
easy way to factor large prime numbers.'' [sic] -- Bill Gates  -><-
<URL:http://www.subspacefield.org/~travis/>
GPG fingerprint: 9D3F 395A DAC5 5CCC 9066  151D 0A6B 4098 0C55 1484

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