数域筛格筛的一个新角度
A New Angle on Lattice Sieving for the Number Field Sieve
摘要：
在二维或多维格筛已被证明是一个不可或缺的实际援助，在整数分解和离散对数计算涉及数域筛。这篇文章的主要贡献是表明，一个不同的方法在三维格枚举将提供一个显着的加速。我们使用格点的连续最小值和最短向量而不是过渡向量来遍历格点。我们展示了一个记录计算的新方法，在一个133位的子组$\mathbb{F}_{p^6}$，与$p^6$有423位。我们的总体时序几乎比422位字段中的132位子组的先前记录快$3$倍。该方法可推广到4维或更大维度，克服了塔号场筛选实施的关键障碍。
英文摘要：
Lattice sieving in two or more dimensions has proven to be an indispensable practical aid in integer factorization and discrete log computations involving the number field sieve. The main contribution of this article is to show that a different method of lattice enumeration in three dimensions will provide a significant speedup. We use the successive minima and shortest vectors of the lattice instead of transition vectors to iterate through lattice points. We showcase the new method by a record computation in a 133-bit subgroup of $\mathbb{F}_{p^6}$, with $p^6$ having 423 bits. Our overall timing nearly $3$ times faster than the previous record of a 132-bit subgroup in a 422-bit field. The approach generalizes to dimensions 4 or more, overcoming a key obstruction to the implementation of the tower number field sieve.
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。
