Communication efficient Zeroknowledge Proofs of knowledge
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Abstract
We show that, after a constantround preprocessing stage, it is possible to give any polynomial number of NonInteractive ZeroKnowledge Proofs of Knowledge for any NP language. Our proofsystem is based on the sole assumption that oneway functions and NonInteractive ZeroKnowledge Proof Systems of Language Membership exist.

It is provably secure under general complexity assumptions. Its security is based on the existence of oneway functions and NonInteractive ZeroKnowledge Proof Systems.

It does not require the presence of a trusted center; not even the Bank is required to be trusted by the users.

Each transaction requires only constant rounds of interaction. Actually, most of the transactions requires just one round of interaction.

Each transaction can be performed by only the users that are interested; that is, it is not necessary for all the users to take part in each single transaction to guarantee privacy and security. Moreover, the transcript of each transaction can be used to prove that the transaction has actually taken place and to prove eventual frauds committed.
Keywords
Proof System Random String Reference String NIZK Proof Double SpendingPreview
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