## CryptoDB

### Paper: Updateable Inner Product Argument with Logarithmic Verifier and Applications

Authors: Vanesa Daza Carla Ràfols Alexandros Zacharakis DOI: 10.1007/978-3-030-45374-9_18 Search ePrint Search Google We propose an improvement for the inner product argument of Bootle et al. (EUROCRYPT’16). The new argument replaces the unstructured common reference string (the commitment key) by a structured one. We give two instantiations of this argument, for two different distributions of the CRS. In the designated verifier setting, this structure can be used to reduce verification from linear to logarithmic in the circuit size. The argument can be compiled to the publicly verifiable setting in asymmetric bilinear groups. The new common reference string can easily be updateable. The argument can be directly used to improve verification of Bulletproofs range proofs (IEEE SP’18). On the other hand, to use the improved argument to prove circuit satisfiability with logarithmic verification, we adapt recent techniques from Sonic (ACM CCS’19) to work with the new common reference string. The resulting argument is secure under standard assumptions (in the Random Oracle Model), in contrast with Sonic and recent works that improve its efficiency (Plonk, Marlin, AuroraLight), which, apart from the Random Oracle Model, need either the Algebraic Group Model or Knowledge Type assumptions.
##### BibTeX
@article{pkc-2020-30298,
title={Updateable Inner Product Argument with Logarithmic Verifier and Applications},
booktitle={Public-Key Cryptography – PKC 2020},
series={Public-Key Cryptography – PKC 2020},
publisher={Springer},
volume={12110},
pages={527-557},
doi={10.1007/978-3-030-45374-9_18},
author={Vanesa Daza and Carla Ràfols and Alexandros Zacharakis},
year=2020
}