Paper 2025/475
HammR: A ZKP Protocol for Fixed Hamming-Weight Restricted-Entry Vectors
, Clemson University, Clemson UniversityAbstract
In this paper, we introduce $\mathsf{HammR}$, a generic Zero-Knowledge Proof (ZKP) protocol demonstrating knowledge of a secret vector that has a fixed Hamming weight with entries taken from a shifted multiplicative group. As special cases, we are able to directly apply this protocol to restricted vectors and to rank-1 vectors, which are vectors with entries that lie in a dimension one subspace of $\mathbb{F}_q$. We show that these proofs can be batched with low computational overhead, and further prove that this general framework is complete, sound, and zero-knowledge, thus truly a genuine ZKP. Finally, we present applications of $\mathsf{HammR}$ to various Syndrome Decoding Problems, including the Regular and Restricted SDPs, as well as other implementations such as lookup instances, proof of proximity, and electronic voting protocols.
Metadata
- Available format(s)
-
PDF
- Category
- Cryptographic protocols
- Publication info
- Preprint.
- Contact author(s)
-
manganm @ clemson edu
fslaugh @ g clemson edu - History
- 2025-03-14: approved
- 2025-03-12: received
- See all versions
- Short URL
- https://ia.cr/2025/475
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2025/475,
author = {Felice Manganiello and Freeman Slaughter},
title = {{HammR}: A {ZKP} Protocol for Fixed Hamming-Weight Restricted-Entry Vectors},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/475},
year = {2025},
url = {https://eprint.iacr.org/2025/475}
}
