We present a new algorithm for solving the LPN problem. The algorithm has a similar form as some previous methods, but includes a new key step that makes use of approximations of random words to a nearest codeword in a linear code. It outperforms previous methods for many parameter choices. In particular, we can now solve the $$(512,\frac{1}{8})$$(512,18) LPN instance with complexity less than $$2^{80}$$280 operations in expectation, indicating that cryptographic schemes like HB variants and LPN-C should increase their parameter size for 80-bit security.

中文翻译：

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使用覆盖码求解 LPN

我们提出了一种解决 LPN 问题的新算法。该算法与之前的一些方法具有相似的形式，但包括一个新的关键步骤，该步骤利用随机词与线性代码中最近的代码字的近似值。它在许多参数选择方面优于以前的方法。特别是，我们现在可以求解复杂度低于 $$2^{80}$$280 的 $$(512,\frac{1}{8})$$(512,18) LPN 实例，这表明密码学像 HB 变体和 LPN-C 这样的方案应该增加它们的参数大小以实现 80 位安全。