Symmetric Models for Syndrome Decoding

2026-09-12

AI Summary

本文提出了一种基于初等对称多项式的新型多项式模型，用于解决二元情况下的综合征解码问题，并估计了其计算复杂度。

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 approach to solve other variants of the SDP.

Problem

• Syndrome Decoding Problem
• polynomial model
• computational complexity

Innovation

• elementary symmetric polynomials
• Syndrome Decoding Problem (SDP)
• computational complexity
• degree of regularity
• solving degree