It would have been incredibly off-topic to ask this on Math.SE -- you're in the write place.
So here's the most important thing:
Your readers, on the whole, know little to nothing about technical subjects, and will not catch fabrications or errors. The portion of readers who do know will respect you for trying if you do it well enough, and respect you even more if you get anything right.
LaurenIpsum provides in her answer an excellent example of literary sleight-of-hand, but it's easy to miss the point of her answer. While you can sidestep technical terminology using her demonstrated method, you don't do it just because you don't know anything about your subject. You do it because it's not the point of the scene.
Think about great scenes in a range of movies and books involving technical imagery and conversation. What made the scene great? It wasn't the complexity of the terminology. It was the circumstances underlying the scene.
If a character reveals that -- oh my god -- using SHA1 on the password wasn't enough -- they used a rainbow table -- we should have used bcrypt, thus thwarting brute-force attacks! -- that's great. That's really great. Nobody knows what anyone just said. But if the compromised password means citadel security is likewise broken, we have a powerful tool to move the plot forward, and the tension just went up a notch. It went up a notch not because of bcrypt, rainbow tables, and SHA1, but because the enemy is coming, and our defenses are down.
What I'm saying is that technical terminology should embellish a scene and add a sense of authenticity, but it's not necessary, and you can make great scenes without it. The success of your scene should not be dependent upon the professor demonstrating Perelman's proof of the Poincaré conjecture.
BUT, all that being said, authenticity is a lot like salt -- if used sparingly in the right places, it adds flavor. Put in too much, and people turn up their noses. Unless you're a master chef, of course.
So -- the ultimate question -- where do you get authenticity when you know nothing? You do what all fiction writers must do -- hybridize learning and invention.
For example, go learn topological basics. Spend a few days on it. If it's a major character, maybe longer. As much as you can stand. Find good sources that you can learn from easily. Do not go take out college textbooks, that would be foolish.
Instead search youtube for beginner's topology. Rearrange the words and search them elsewhere -- "learn topology" "basics of topology" "fundamental topology" "how to learn topology" "where to start with topology". Find nice beginner-friendly sites that have colorful diagrams with arrows. Search for topology animations. As you learn some basic terms, search those terms and see if you can get more detailed information on them, and through that, learn other terms. You'll quickly start building out a mental map that you can take as far as you wish. If you're a good or experienced writer, you'll know when you've gone far enough. If not, you'll learn as you go, and next time you'll know understanding Perelman's proof of the Poincaré conjecture was way, way, too far.
Usually it only takes basic terms to lend authenticity. You don't need to throw around anything heavy, because even beginner's terms are foreign to those who know nothing. Yet, inversely, beginner's terms are the most important, because they are the most commonly used terms in technical conversations. Just like learning a language-- sure, a fluent English speaker can use words like "defenestrate" and "categorical", but in common conversation, the words you see most are "the" and "a" and "hello" and "please/thank you" and so on, and that's an authentic English conversation, and anybody who sees those words knows it very quickly. Don't make the mistake of thinking the character will sound smarter or more real if he uses more arcane words-- that only makes him more likely to be wrong, and harder to understand.
Once you know enough to fool a fool, fill in the gaps with your imagination, with healthy use of LaurenIpsum's hand-waving method. I mean, I don't really understand cryptography at all, but don't you think that little clip would have fooled someone who knew nothing whatsoever?
Always remember it's only embroidery. The core of the story will not depend on the technical terminology, and ultimately the readers will forget it as soon as they read it -- unless you come up with something catchy, e.g. flux capacitor. And the catchiest terms are almost always the imagined ones.
Last tip-- consult someone who does know!