Paper 2024/981
Hadamard Product Arguments and Their Applications
Abstract
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
- 2024-06-20: approved
- 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} }