Proving Knowledge of Syndrome Decoding Problems with Soundness

Felice Manganiello; Freeman Slaughter

Paper 2026/315

Proving Knowledge of Syndrome Decoding Problems with Soundness

Felice Manganiello

, Clemson University

Freeman Slaughter, University of South Florida

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.
Contact author(s): manganm @ clemson edu
fslaughter @ usf edu
History: 2026-02-21: approved; 2026-02-18: received; See all versions
Short URL: https://ia.cr/2026/315
License: CC BY

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}
}