The minister D— is the official villain of the piece. Just to point out: "Minister" here isn't religious but political; he's a high-ranking public official of some sort. We can assume that he's supposed to be acting in the service of the royal man and lady. Still, you might have noticed that he has his own agenda—like stealing the queen's private letter and using it to extort her for a year and a half. Not nice at all.
But it's also not that simple. Dupin and D— have had a previous relationship, and previous conflict (122). We don't know the exact nature of their relationship, nor how far back it extends, but we do know that they're figurative—and just possibly literal—brothers. And Dupin and G— both say some pretty interesting things about D—.
So, let's take a close look at this mysterious guy.
"The thief," said G——, "is the Minister D——, who dares all things, those unbecoming as well as those becoming a man. The method of the theft was not less ingenious than bold." (28)
This is quite an introduction. He's bold, ingenious, and—yep—manly. Notice that the passage also suggests that there are at least two sides to his daring. While this story depicts him as villainous, G— suggests that he does occasionally act in a way "becoming [appropriate to] a man."
The second thing we hear about him is this:
"His lynx eye immediately perceives the paper, recognises the handwriting of the address, observes the confusion of the personage addressed, and fathoms her secret." (28)
The lynx is an adorable kitty cat known for its keen eyesight and magnificently furry paws. So, D— is sharp, ferocious, and predatory. You might even say he purrloins the letter. (Rimshot.)
What's more, he uses his intelligence to put together what he sees in a meaningful way. Contrast this to the king, who apparently sees the same things D— does but without putting them together to come up with any kind of meaning.
But he doesn't seem so lynx-like around Dupin. In fact, he seems downright dumb. D—'s Dupin-inspired blindness casts doubts on all of Dupin's arguments. After all, Dupin could have seen the letter and then told G— to sneak in at night at get it.
Think about this: if, as Dupin claims, D— anticipates every aspect of G—'s investigation (105), wouldn't he have anticipated that G— would hire Dupin, too? Since he knows that Dupin wants revenge for whatever D— did to him in Vienna, wouldn't he have suspected Dupin of being there for nefarious purposes? Wouldn't Dupin's green glasses, instead of concealing Dupin's purpose, make old Lynx eyes suspicious?
That's an awful lot of dumb moves for someone who's supposed to be so smart.
In paragraphs ninety-eight through one hundred, Dupin argues that G— can't find the letter because he thinks that D— is a poet, and therefore a fool. Dupin argues that if G— had only realized that D— was both a poet and a mathematician, he wouldn't have thought him a fool. Dupin also argues that it is through the combination of these two abilities that D— is able to deceive G— for so long.
So D—'s major strength as a wizard of deception is that he's both a poet and a mathematician. He's intellectually rigorous—he's written on differential calculus, which, more power to him—but he also writes poetry. (Hopefully not about differential calculus.) This combination makes him logical and sly.
At the same time, these arguments are a little meaningless. The solution to the mystery doesn't have anything to do with poets or mathematicians, or whether or not G— thinks D— is a fool. G— fails because he miscalculates, and Dupin succeeds because G— has already crossed out all the obvious solutions. So is D— really a criminal mastermind—or did he just get lucky?