Paper 2019/148 Original: eprint.iacr.org/2019/148 ↗
On the efficiency of pairing-based proofs under the d-PKE
Abstract
We investigate the minimal number of group elements and prover running time in a zk-SNARK when using only a symmetric ``linear'' knowledge assumption, like the $d$-Power Knowledge of Exponent assumption, rather than a ``quadratic'' one as implicitly happens in the most efficient known construction by Groth [Groth16]. The proofs of [Groth16] contain only 3 group elements. We present 4 element proofs for quadratic arithmetic programs/rank 1 constraint systems under the $d$-PKE with very similar prover running time to [Groth16]. Central to our construction is a simple lemma for ``batching'' knowledge checks, which allows us to save one proof element.
Metadata
- Available format(s)
PDF- Category
- Cryptographic protocols
- Publication info
- Preprint.
- History
- 2019-03-18: last updated
- 2019-02-20: published
- Short URL
- https://ia.cr/2019/148
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2019/148,
author = {Ariel Gabizon},
title = {On the efficiency of pairing-based proofs under the d-PKE},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/148},
year = {2019},
url = {https://eprint.iacr.org/2019/148}
}