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A private scheme for distributed, shared secret generation

We present a scheme for shared secret generation by n members that combines the contributions the members in a fashion such that the individual contribution of each member is not exposed to anyone-including the other members. We note that for an external attacker trying to break the n L-bit secrets of the members, the effective search space dimension is nL, meaning that all n keys must be broken simultaneously in order to crack system integrity. We also note that the scheme provides "unconditional secrecy" (Menezes et al., 1997).