Cryptographic methods are disclosed, which allow a prover party, who holds a number of secrets, to demonstrate satisfiable formulas of propositional logic, wherein the atomic propositions are linear relations between the secrets. The demonstration reveals no more information than is contained in the formula itself. Some implementations allow an unlimited number of such demonstrations to be made, without revealing any additional information about the secrets, whereas other implementations ensure that the secrets, or some of the secrets, will be revealed, if a demonstration is performed more than a predetermined number of times. The demonstrations may be zero-knowledge proofs, or signed proofs.
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