论文标题
晶格筛分的新角度筛网
A New Angle on Lattice Sieving for the Number Field Sieve
论文作者
论文摘要
事实证明，在两个或多个维度上的晶格筛分是在整数分解和涉及数字场筛分的离散日志计算方面必不可少的实际辅助工具。本文的主要贡献是表明，在三个维度上的一种不同的晶格枚举方法将提供显着的加速。我们使用晶格的连续最小和最短的向量，而不是过渡向量通过晶格点进行迭代。我们通过$ \ mathbb {f} _ {p^6} $的133位子组中的记录计算来展示新方法，其中$ p^6 $具有423位。我们的整体时间比以前在422位领域的132位子组的记录快近3美元。该方法概括为4或更多的尺寸，克服了对塔架筛网的实施的关键障碍。
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.
