论文标题
在单一的订单中，完全将任何整数都有效地分解为查找算法
On completely factoring any integer efficiently in a single run of an order finding algorithm
论文作者
论文摘要
我们表明，鉴于单个元素的顺序从$ \ mathbb z_n^*$中随机选择，我们可以很高的概率，对于任何整数$ n $，在多项式时间内有效地找到了$ n $的完整分解。这意味着Shor保理算法的量子部分的单个运行通常就足够了。然后，可以在经典的后处理步骤中以微不足道的计算成本来回收$ n $的所有主要因素。此步骤所需的经典算法本质上是由于米勒。
We show that given the order of a single element selected uniformly at random from $\mathbb Z_N^*$, we can with very high probability, and for any integer $N$, efficiently find the complete factorization of $N$ in polynomial time. This implies that a single run of the quantum part of Shor's factoring algorithm is usually sufficient. All prime factors of $N$ can then be recovered with negligible computational cost in a classical post-processing step. The classical algorithm required for this step is essentially due to Miller.
