Regev recently introduced a quantum factoring algorithm that may be perceived as a $d$-dimensional variation of Shor's factoring algorithm. In this work, we extend Regev's factoring algorithm to an algorithm for computing discrete logarithms in a natural way. Furthermore, we discuss natural extensions of Regev's factoring algorithm to order finding, and to factoring completely via order finding.

翻译：Regev近期提出了一种量子因子分解算法，可视为Shor因子分解算法的$d$维变体。本研究将Regev的因子分解算法以自然的方式扩展为计算离散对数的算法。此外，我们讨论了Regev因子分解算法在序求解方面的自然扩展，以及通过序求解实现完全因子分解的方法。