论文标题
使用盒子中的4D筛分和FP4中的记录计算的扩展塔号筛网实现
An Implementation of the Extended Tower Number Field Sieve using 4d Sieving in a Box and a Record Computation in Fp4
论文作者
论文摘要
我们报告了扩展塔号筛（ExtNF）的实现，并在中等特征有限字段$ \ mathbb {f} _ {p^4} $ 512位大小的$中记录计算。从经验上讲，我们表明在一个4维盒子（正对直体）中筛选用于在$ \ mathbb {f} _ {p^4} $中收集extnfs的关系的速度要比在4维超级球中筛选的速度要快。我们还提供了一种新的中间下降方法，即“使用随机向量的下降”，没有该方法，我们的ExtNFS计算中的下降阶段将很困难/不可能，并分析其复杂性。
We report on an implementation of the Extended Tower Number Field Sieve (ExTNFS) and record computation in a medium characteristic finite field $\mathbb{F}_{p^4}$ of 512 bits size. Empirically, we show that sieving in a 4-dimensional box (orthotope) for collecting relations for ExTNFS in $\mathbb{F}_{p^4}$ is faster than sieving in a 4-dimensional hypersphere. We also give a new intermediate descent method, `descent using random vectors', without which the descent stage in our ExTNFS computation would have been difficult/impossible, and analyze its complexity.
