On the Hardness of the Lee Syndrome Decoding Problem

Lee度量下伴随式译码问题的零知识证明

A Zero-Knowledge Proof for the Syndrome Decoding Problem in the Lee Metric

针对Lee度量下的伴随式译码问题（代码密码学的NP完全问题变体），本文提出了一种知识的零知识证明，为构建更高效的代码密码系统提供支持。

Information Set Decoding for Lee-Metric Codes using Restricted Balls

The Lee metric syndrome decoding problem is an NP-hard problem and several generic decoders have been proposed. The observation that such decoders come with a larger cost than their Hamming metric counterparts make the Lee metric a promising alternative for classical code-based cryptography. Unlike in the Hamming metric, an error vector that is chosen uniform at random of a given Lee weight is expected to have only few entries with large Lee weight. Using this expected distribution of entries, we are able to drastically decrease the cost of generic decoders in the Lee metric, by reducing the o…

Generalizing Syndrome Decoding problem to the totally Non-negative Grassmannian

The syndrome decoding problem has been proposed as a computational hardness assumption for code based cryptosystem that are safe against quantum computing. The problem has been reduced to finding the codeword with the smallest non-zero columns that would satisfy a linear check equation. Variants of Information set decoding algorithms has been developed as cryptanalytic tools to solve the problem. In this paper, we study and generalize the solution to codes associated with the totally non-negative Grassmannian in the Grassmann metric. This is achieved by reducing it to an instance of finding a …

Combinatorial Solution of the Syndrome Decoding Problem using Copula on Grassmann graph

Computational hardness assumption from the syndrome decoding problem has been useful in designing the security of code based cryptosystem that are safe against quantum computing. Due to complexities in solution using high degree linearized polynomial equations modeled from subspaces, we proposed exploiting the dependency between subspaces in a Grassmann graph constructed from Boundary measurement maps by using copula functions. We also used copula functions to estimate the marginal distribution in these subspaces. Thereafter, the Maximum likelihood based estimation approach was used to search …

秩码的译码困难性与最小距离问题

On the hardness of the decoding and the minimum distance problems for rank codes

本文给出了秩码的秩伴随式译码问题和秩最小距离问题的随机约化。我们的结果是基于嵌入从线性码配备了汉明距离线性码的扩展域配备了秩度量。我们证明了，如果前面的两个问题的秩度量是在ZPP = RP $\cap$ coRP，那么我们将有NP=ZPP。我们也给出了各自的近似问题的秩度量的复杂性结果。

基于拟阿贝尔译码困难性的相关伪随机性

Correlated Pseudorandomness from the Hardness of Quasi-Abelian Decoding

本文提出拟阿贝尔校正子译码问题QA-SD，并据此构造任意q>2域上支持OLE的可编程PCG，突破大域与可分裂Ring-LPN限制，得到首个高效N方静默通用算术电路安全计算协议。