统计解码2.0：将解码简化为LPN
Statistical Decoding 2.0: Reducing Decoding to LPN
摘要：
基于代码的密码学的安全性主要依赖于线性代码的通用解码的难度。最好的通用解码算法都是由于Prange而对旧算法的改进：它们被称为信息集解码器（ISD）。不久前，提出了一种不属于这个家族的通用解码算法：统计解码。它是一种随机算法，需要计算一个大的中等权重的奇偶校验集，并对这些方程使用某种多数表决来恢复错误。这个算法被遗忘很久了，因为即使是最好的变体，它的表现也不如最简单的ISD算法。我们重新审视这个老算法，使用奇偶校验方程在一个更一般的方式。在这里，奇偶校验用于获得具有秘密的LPN样本，该秘密是误差的一部分，并且LPN噪声与我们产生的奇偶校验的权重有关。相应的LPN问题，然后解决了标准傅立叶技术。通过适当地选择产生这些低权重方程的方法和LPN问题的大小，我们能够以这种方式在小于$0.3$的码率下显著优于信息集解码。它给出了$60$年后的第一次，一个更好的解码算法的一个显着的范围不属于ISD家庭。
英文摘要：
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of information set decoders (ISD). A while ago, a generic decoding algorithm which does not belong to this family was proposed: statistical decoding. It is a randomized algorithm that requires the computation of a large set of parity-checks of moderate weight, and uses some kind of majority voting on these equations to recover the error. This algorithm was long forgotten because even the best variants of it performed poorly when compared to the simplest ISD algorithm. We revisit this old algorithm by using parity-check equations in a more general way. Here the parity-checks are used to get LPN samples with a secret which is part of the error and the LPN noise is related to the weight of the parity-checks we produce. The corresponding LPN problem is then solved by standard Fourier techniques. By properly choosing the method of producing these low weight equations and the size of the LPN problem, we are able to outperform in this way significantly information set decodings at code rates smaller than $0.3$. It gives for the first time after $60$ years, a better decoding algorithm for a significant range which does not belong to the ISD family.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
