Paper 2026/1995 Original: eprint.iacr.org/2026/1995 ↗
Symmetric Models for Syndrome Decoding
Abstract
This paper introduces a new polynomial model for the exact variant of the Syndrome Decoding Problem (SDP) in the binary case. The model is based on elementary symmetric polynomials. We estimate the computational complexity of solving the corresponding polynomial system by establishing bounds on the degree of regularity and on the solving degree of the ideal associated to the model. The complexity estimate is lower than for previous polynomial models. We also provide a variant of the model whose complexity depends directly on the specific instance of the SDP and is lower than for the first model. Finally, we discuss how to apply our ap- proach to solve other variants of the SDP.
Metadata
- Available format(s)
PDF- Category
- Attacks and cryptanalysis
- Publication info
- Preprint.
- History
- 2026-09-12: last updated
- 2026-09-12: published
- Short URL
- https://ia.cr/2026/1995
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2026/1995,
author = {Elisa Gorla and Simone Trebiani},
title = {Symmetric Models for Syndrome Decoding},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/1995},
year = {2026},
url = {https://eprint.iacr.org/2026/1995}
}