NTTproofs: A Maintainable and Aggregatable Vector Commitment With Fast Openings and Updates

Abstract

In vector commitments, the complex process of generating and updating proofs, along with the large-sized proofs, seriously hinders the practicality of stateless cryptocurrencies. In this work, we present NTTproofs, containing two sub-schemes, a vector commitment (VC) and a mulit-vector commitment (MC). Both sub-schemes are maintainable and aggregatable, and they also enjoy fast openings (i.e., generating all the proofs) as well as efficient proof updates. MC in NTTproofs employs the Fast Number Theoretic Transform (NTT) and sharding technique to significantly improve the time of generating all proofs by up to $0.76 \times $ and $0.32 \times $ , respectively, over Balanceproofs, Matproofs. Moreover, our proposed MC in NTTproofs is efficiently maintainable and requires merely 15.78 milliseconds at $n_{1}=n_{2}=2^{12}$ to update all proofs. Meanwhile, NTTproofs schemes exhibit superior aggregatability, taking 0.003 seconds in VC and 0.05 seconds in MC to aggregate 1024 proofs and reducing the size of an aggregated proof to a constant size of 96 Bytes. Finally, macrobenchmarks indicate that our proposed MC in NTTproofs outperforms the other schemes, but is slightly inferior to that of Balanceproofs.