One of the most liberating aspects of my conversion to evangelical Christianity was throwing these kinds of mind-benders onto the lap of Scripture. And the answer in this case is an undeniable Yes: God permits cursing evildoers. Be cautious, but it's done by great characters in the Scriptures.
If you want an example, there's a Psalm that's featured in a scene in the epic movie Patton. (Sorry, I'm a classic movie buff.) Patton is praying in the aftermath of being humiliated into apologizing for slapping a cowardly soldier. We hear George C. Scott's voice read the Psalm, with such memorable lines as (paraphrasing), "May those who seek to destroy my soul go into the low parts of the Earth; may they be a portion for foxes; may they fall by the sword ....."
Biblical scholars tell us that the Psalms were written mostly by the great Israelite kings Solomon and David.
37