Shorter quadratic QA-NIZK proofs

Daza, Vanesa; González, Alonso; Pindado, Zaira; Ràfols, Carla; Silva, Javier

doi:http://dx.doi.org/10.1007/978-3-030-17253-4_11

Shorter quadratic QA-NIZK proofs

Citation

Daza V, González A, Pindado Z, Ràfols C, Silva J. Shorter Quadratic QA-NIZK Proofs. In: Lin D, Sako K, editors. Public-Key Cryptography – PKC 2019. 22nd IACR International Conference on Practice and Theory of Public-Key Cryptography; 2019 Apr 14-7; Beijing, China. Berlin: Springer; 2019. p. 314-343. (LNCS; no. 11442). DOI: 10.1007/978-3-030-17253-4_11

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.