[Resource Topic] 2018/557: Non-Interactive Zero-Knowledge Proofs for Composite Statements

Welcome to the resource topic for 2018/557

Non-Interactive Zero-Knowledge Proofs for Composite Statements

Authors: Shashank Agrawal, Chaya Ganesh, Payman Mohassel


The two most common ways to design non-interactive zero-knowledge (NIZK) proofs are based on Sigma protocols and QAP-based SNARKs. The former is highly efficient for proving algebraic statements while the latter is superior for arithmetic representations. Motivated by applications such as privacy-preserving credentials and privacy-preserving audits in cryptocurrencies, we study the design of NIZKs for composite statements that compose algebraic and arithmetic statements in arbitrary ways. Specifically, we provide a framework for proving statements that consist of ANDs, ORs and function compositions of a mix of algebraic and arithmetic components. This allows us to explore the full spectrum of trade-offs between proof size, prover cost, and CRS size/generation cost. This leads to proofs for statements of the form: knowledge of x such that SHA(g^x)=y for some public y where the prover’s work is 500 times fewer exponentiations compared to a QAP-based SNARK at the cost of increasing the proof size to 2404 group and field elements. In application to anonymous credentials, our techniques result in 8 times fewer exponentiations for the prover at the cost of increasing the proof size to 298 elements.

ePrint: https://eprint.iacr.org/2018/557

Talk: https://www.youtube.com/watch?v=EruBH3Dzir4

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