论文标题
统计解码2.0:将解码减少到LPN
Statistical Decoding 2.0: Reducing Decoding to LPN
论文作者
论文摘要
基于代码的密码学的安全性主要依赖于使用线性代码进行通用解码的硬度。最好的通用解码算法都是由于prange而引起的旧算法的改进:它们以信息集解码器(ISD)的名称而闻名。不久前,提出了一种不属于该家族的通用解码算法:统计解码。这是一种随机算法,需要计算大量中等重量的奇偶校验检查,并在这些方程式上使用某种多数投票来恢复错误。长期以来,该算法被遗忘了,因为与最简单的ISD算法相比,即使它的最佳变体也表现差。 我们通过更通用的方式使用奇偶校验检查方程来重新访问该旧算法。在这里,使用奇偶校验来获取具有秘密的LPN样品,这是误差的一部分,LPN噪声与我们产生的奇偶校验检查的重量有关。然后,通过标准傅立叶技术解决相应的LPN问题。通过正确选择产生这些低重量方程式的方法和LPN问题的大小,我们能够以这种方式胜过明显的信息,以小于$ 0.3 $的代码速率设置解码。它在60美元的$ 60 $年后首次提供,这是一个不属于ISD家族的重要范围的更好的解码算法。
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.