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Re:Zero Knowledge Proofs: The Secret Santa Protocol by capcah on Monday November 30, 2015 @11:39AM (#10650240)
This is not a Zero Knowledge Protocol because the other party has the same information as you do.

Furthermore, this algorithm is equivalent to a DH key exchange between A and B followed by a HMAC(key,M), with the advantage that message size is not limited to the group size.