I'm not at Blackhat, nor will I be any time soon. Crypto is hard.
I didn't finish this math book, Finite Fields for Computer Scientists and Engineers. My math is pretty shaky. Usually, when I'm trying to figure out something math-y, I have some particular application in mind, something that deals with something concrete. And when I read a book by, for, and about mathematicians, I'm never quite sure which are the concretely useful parts.
I remember that an Abelian group is something math-y that describes most of the stuff I deal with. Like, if you're dealing with the kinds of numbers that you deal with in my computer stuff, Abelian group probably covers that. But Abelian doesn't assume everything about the kinds of stuff I deal with. And you know that these math people want to figure out if the such-and-such property still holds even if you're in some mathematical universe where you can't rely on the existence of a multiplicative inverse or somesuch.
So I tried and failed to slog through this book. I think I might have made it if math people used more words and less notation. In this book, Fi means something important, but I kept forgetting what it was. And it was hard to find the first use of Fi, when they explained it. I think that the meaning was in bold, so that was easy to spot as I riffled pages. So if I already knew what I was searching for, that bold text would have helped me. But since I didn't know the meaning of the thing I was looking for—that's why I was searching for it—that boldface didn't help me. (It's kind of like reading Perl code if you don't know the Perl programming language very well. %$^ probably means something in Perl. Perl programmers laugh at Python programmers because Python would use three words for that, using up a lot of space. But, by golly, if you need to look up what that word means, you can. I've tried googling for %, and it didn't get me very far.)
If I ever learn why prime numbers are especially useful for crypto, it won't be from this book.