关于BKW型算法求解LWE的样本复杂性
On the Sample Complexity of solving LWE using BKW-Style Algorithms
摘要：
带误差学习（LWE）问题在密码学中受到广泛关注，主要是由于它在后量子密码学中的基础性意义。在其求解算法中，Blum-Kalai-Wasserman（BKW）算法最初是为了解决带噪声的学习奇偶校验（LPN）问题而提出的，表现良好，特别是对于某些具有加密重要性的参数设置。BKW算法由两个阶段组成，约简阶段和求解阶段。在这项工作中，我们研究了在解决阶段使用的搜索器的性能。我们表明，快速傅立叶变换（FFT）的FFT从Eurocrypt'15具有相同的样本复杂度的最佳FFT，当作出相同数量的假设。我们还表明，它的性能比理论预测的要好得多，并介绍了它的改进称为修剪FFT算法。最后，我们指出，通过广泛的实验，由于LF 2和样品扩增的样品依赖性是有限的。
英文摘要：
The Learning with Errors (LWE) problem receives much attention in cryptography, mainly due to its fundamental significance in post-quantum cryptography. Among its solving algorithms, the Blum-Kalai-Wasserman (BKW) algorithm, originally proposed for solving the Learning Parity with Noise (LPN) problem, performs well, especially for certain parameter settings with cryptographic importance. The BKW algorithm consists of two phases, the reduction phase and the solving phase. In this work, we study the performance of distinguishers used in the solving phase. We show that the Fast Fourier Transform (FFT) distinguisher from Eurocrypt'15 has the same sample complexity as the optimal distinguisher, when making the same number of hypotheses. We also show that it performs much better than theory predicts and introduce an improvement of it called the pruned FFT distinguisher. Finally, we indicate, via extensive experiments, that the sample dependency due to both LF2 and sample amplification is limited.
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