Paper 2024/981
Hadamard Product Arguments and Their Applications
, Hanyang University, Seoul, Republic of Korea, Hanyang University, Seoul, Republic of Korea, Radius, Kookmin University, Seoul, Republic of Korea, Hanyang University, Seoul, Republic of KoreaAbstract
This paper introduces transparent and efficient arguments for Hadamard products between committed vectors from two source groups. For vectors of length $n$, the proofs consist of $\mathcal{O}(\log n)$ target group elements and $\mathcal{O}(1)$ additional elements. The verifier's workload is dominated by $\mathcal{O}(\log n)$ multi-exponentiations in the target group and $\mathcal{O}(1)$ pairings. We prove our security under the standard SXDH assumption. Additionally, we propose an aggregator for Groth16 pairing-based zk-SNARKs and a proof aggregation technique for the general case of the KZG pairing-based polynomial commitment scheme using our Hadamard product arguments. Both applications support logarithmic-sized aggregated proofs without requiring an additional trusted setup, significantly reducing the verifier’s pairing operations to $\mathcal{O}(1)$.
Metadata
- Available format(s)
-
PDF
- Category
- Cryptographic protocols
- Publication info
- Preprint.
- Keywords
- Hadamard product argumentstransparent setupzero-knowledge arguments
- Contact author(s)
-
rsias9049 @ hanyang ac kr
donghwanoh @ hanyang ac kr
hankyungko @ hanyang ac kr
jihyek @ kookmin ac kr
hoh @ hanyang ac kr - History
- 2024-09-13: revised
- 2024-06-18: received
- See all versions
- Short URL
- https://ia.cr/2024/981
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2024/981,
author = {Kyeongtae Lee and Donghwan Oh and Hankyung Ko and Jihye Kim and Hyunok Oh},
title = {Hadamard Product Arguments and Their Applications},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/981},
year = {2024},
url = {https://eprint.iacr.org/2024/981}
}
