[foaf-dev] playing with reputations and non secret encryption, suited to the "socialization semantics" of foaf groups in an FOAF+SSL context.

Assume a foaf-group exists, has name URI, and its webserver offers the group's foaf card over FOAF+SSL. The foaf card contains statements for the integers: a, r, and M. a is a public function of the URI (given modulus M), and r is a (self-signed) signature of a. From the math (see ref below) anyone can test that URI => a => r. M is claimed to be unique to the group, being the multiple of two large primes (P & Q) chosen at random by the owner of URI.

Next, anyone with a webid (e.g. w) can claim to be a member of the group by applying the group's modulus M. To do so, w includes (r , Aw and Rw) in her/her foaf card - where Rw is a signature of r. Taking the form of the the base case, anyone can test that r => Aw => Rw, and induce URI => Rw.

Anyone with a webid w2 can claim to be a member of the group AND recognise w as another member of the group. To do so, w2 reads Rw from w's foaf card using FOAF+SSL, and includes in his/her foaf card (Rw, Aw2, Rw2). This is the inductive hyptothesis.

In essence, we have made a reverse hash chain from M to Rw2, where M is assumed to be a public identity function of a (foaf-group) URI. Only the real owner of the URI has P and Q factors of M, unlike all usurpers of M. The FOAF+SSL design assumption holds, such that only the owner of a webid can control the contents of the referenced FOAF card

Anyone may now ask the owner of the group URI (identified by M) to mint a random number t (mod M) and to state then that Rw2 is trustworthy (as of now) for the singular purpose of recognizing  Rw1 as a group member  (or that Rw2 is not trusted as a recognizer of Rw1). The URI's Owner may state Rw2<Rw1>  => true/false, by publishing a counter-signature statement  s for either true or false, where s = f(t, M, Aw2) = (t + Aw2/t) mod M

Party verifies the counter-signed statement using Rw2 (and M). Verification establishes URI is the true owner of M, is a foaf-group that someone claims to belong to, and URI trusts w2 to state that w1 is a group member of said group.

Based on my rather limited understanding of the one way functions in http://cryptome.org/nsa-nse/nsa-nse-04.pdf,  twisted around somewhat to do signing and hash chaining.

CAVEAT: I don't pretend to understand the complexity analysis of the underlying math..., or the algebra being leveraged. More than possible that in changing application function, I've introduced fundamental flaws due to inappropriate ciphering...

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