We show that probabilistically checkable proofs can be used to shorten non-interactive zero-knowledge proofs. We obtain publicly verifiable non-interactive zero-knowledge proofs for circuit satisfiability with adaptive and unconditional soundness where the size grows quasi-linearly in the number of gates. The zero-knowledge property relies on the existence of trapdoor permutations, or it can be based on a specific number theoretic assumption related to factoring to get better efficiency. As an example of the latter, we suggest a non-interactive zero-knowledge proof for circuit satisfiability based on the Naccache-Stern cryptosystem consisting of a quasi-linear number of bits. This yields the shortest known non-interactive zero-knowledge proof for circuit satisfiability. © 2010 International Association for Cryptologic Research.
CITATION STYLE
Groth, J. (2010). Short non-interactive zero-knowledge proofs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6477 LNCS, pp. 341–358). Springer Verlag. https://doi.org/10.1007/978-3-642-17373-8_20
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