Cryptology ePrint Archive: Report 2019/173

Shorter Quadratic QA-NIZK Proofs

Vanesa Daza and Alonso González and Zaira Pindado and Carla Rŕfols and Javier Silva

Abstract: Despite recent advances in the area of pairing-friendly Non-Interactive Zero-Knowledge proofs, there have not been many efficiency improvements in constructing arguments of satisfiability of quadratic (and larger degree) equations since the publication of the Groth-Sahai proof system (JoC'12). In this work, we address the problem of aggregating such proofs using techniques derived from the interactive setting and recent constructions of SNARKs. For certain types of quadratic equations, this problem was investigated before by González et al. (ASIACRYPT'15). Compared to their result, we reduce the proof size by approximately 50% and the common reference string from quadratic to linear, at the price of using less standard computational assumptions. A theoretical motivation for our work is to investigate how efficient NIZK proofs based on falsifiable assumptions can be. On the practical side, quadratic equations appear naturally in several cryptographic schemes like shuffle and range arguments.

Category / Keywords: cryptographic protocols / zero knowledge, elliptic curve cryptosystem

Date: received 18 Feb 2019, last revised 29 Mar 2019

Contact author: carla rafols at upf edu,zaira pindado@upf edu

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Version: 20190329:114023 (All versions of this report)

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