采用递增缩减因子筛选的编码BKW的渐近复杂性
The Asymptotic Complexity of Coded-BKW with Sieving Using Increasing Reduction Factors
摘要：
带误差学习问题（LWE）是后量子密码学的主要候选问题之一。在Asiacrypt 2017上，提出了一种结合Blum-Kalai-Wasserman算法（BKW）和格筛选技术的算法coded-BKW with sieving。在本文中，我们改进了该算法的筛选部分的不同步骤中使用不同的约简因子。在Regev设置中，其中$q = n^2$和$σ= n^{1.5}/(\sqrt{2π}\log_2^2 n)$，渐近复杂度为$2^{0.8917n}$，从而改进了以前最好的$2^{0.8927n}$复杂度。当假设量子计算机或样本数量有限时，我们得到了类似的改进水平。
英文摘要：
The Learning with Errors problem (LWE) is one of the main candidates for post-quantum cryptography. At Asiacrypt 2017, coded-BKW with sieving, an algorithm combining the Blum-Kalai-Wasserman algorithm (BKW) with lattice sieving techniques, was proposed. In this paper, we improve that algorithm by using different reduction factors in different steps of the sieving part of the algorithm. In the Regev setting, where $q = n^2$ and $σ= n^{1.5}/(\sqrt{2π}\log_2^2 n)$, the asymptotic complexity is $2^{0.8917n}$, improving the previously best complexity of $2^{0.8927n}$. When a quantum computer is assumed or the number of samples is limited, we get a similar level of improvement.
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。
