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One-Way Accumulators

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I have read in schneier's "Applied Cryptography" about OWA and an
applicatiion of it is given by taking the example of Cabal Inc. where
each member calculates the hash of the all other persons and gives it to
other person whom he/she is meeting along with his/her own name. The
other person calculates the hash of both and confirms the name given.

The following function is given:

A(Xi, y) = (X(i-1))^y mod n
n = product of primes
X0 must be agreed upon in advance.
The accumulation of y1, y2, y3 ... would be
((X0^y1 mod n)^y2 mod n)^y3 mod n

Here are some of my questions. Kindly provide the answers if you know:

1. Is the security coming from the fact that it is not easy to find a
product of two numbers (a & b) such that (ab mod n) gives the hash?

2. If Alice meets Bob and each of them exchange their hashes then the
secret which provides the authentication is revealed to the other party
which can be used by him/her to impersonate. How is this addressed?

3. Are there any industrial strength OWA algorithms? If so can you point
me the links?

4. Is it appropriate to quote the portions of the text in the news
groups? The above example has the origin from a paper submitted in

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