Abstract
We construct practical and efficient zero-knowledge arguments with sublinear communication complexity. The arguments have perfect completeness, perfect special honest verifier zero-knowledge and computational soundness. Our zero-knowledge arguments rely on two-tiered homomorphic commitments for which pairing-based constructions already exist.
As a concrete application of our new zero-knowledge techniques, we look at the case of range proofs. To demonstrate a committed value belongs to a specific N-bit integer interval we only need to communicate \(O(N^{\frac{1}{3}})\) group elements.
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Groth, J. (2011). Efficient Zero-Knowledge Arguments from Two-Tiered Homomorphic Commitments. In: Lee, D.H., Wang, X. (eds) Advances in Cryptology – ASIACRYPT 2011. ASIACRYPT 2011. Lecture Notes in Computer Science, vol 7073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25385-0_23
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