Paper 2026/315 Original: eprint.iacr.org/2026/315 ↗
Proving Knowledge of Syndrome Decoding Problems with Soundness
Abstract
This paper introduces a novel set of code-based protocols to demonstrate algebraic relationships in zero knowledge. Specifically, we present a comprehensive collection of secure arguments of knowledge for verifying additive and multiplicative relationships between syndrome-committed secrets, including matrix products, which enable us to construct a generic arithmetic circuit framework. We leverage these primitives to formulate a rich variety of privacy-oriented primitives, such as a post-quantum range proof, lookup argument, and verifiable shuffle protocols. These contributions provide the necessary ingredients to transition advanced confidential designs, such as cryptocurrencies, into the post-quantum code-based setting.
Metadata
- Available format(s)
PDF- Category
- Cryptographic protocols
- Publication info
- Preprint.
- History
- 2026-02-18: last updated
- 2026-02-18: published
- Short URL
- https://ia.cr/2026/315
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2026/315,
author = {Felice Manganiello and Freeman Slaughter},
title = {Proving Knowledge of Syndrome Decoding Problems with Soundness},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/315},
year = {2026},
url = {https://eprint.iacr.org/2026/315}
}