Theoretical computer science is mostly nice and self-contained, except for a few rough edges where it meets real life (unless you’re happy not to meet real life). One of these intersections is where we abstract some real phenomenon into a mathematical concept (another being when we have a result in our mathematical model and then are trying to interpret its meaning in real life).
If you’re learning theoretical cryptography, the very first abstraction that you’ll have to get to grips with is the use of probability. Our definitions, constructions and proofs of security all vitally depend on probabilistic notions. There is a leap of faith in assuming that something we do (like, obtain a bit-string from some circuitry in our computer) is in fact an instance of a random process. How is it that you can look at a string at hand and say that it was generated according to some probability distribution? If you are already comfortable with the quantum mechanical view of the world, this shouldn’t bother you at all. (You thought you were going to learn computer science, and here I’m talking about physics. But rest assured, it’s just going to be math all along, except at these clumsy interfaces of the abstract and the physical.) But if probabilities and distributions are new for you, well then you just have to keep talking about it until it doesn’t sound funny any more. If it helps, think only about the probability of events in the future, and not of what could have happened, or is happening in parallel universes.
Probability is a concept for which one has to develop an intuitive understanding. But, then again, chances are you have already done it. Don’t you look at a coin which fell heads up and think that it could have been tails up, equally probably? Without being bothered about the aerodynamics of your coin, of course. That’s because you understand the notion at an intuitive level. Maybe you never realized how far this can be taken. But really, that’s all there is to it: millions of coin flips. And you know what a coin flip is.
Once you buy into that completely, you can then start worrying about whether it was alright to do so. But that can wait.
Of course, probability and randomness are not special to cryptography. You must have come across this notion in physics, chemistry, biology, computer science (randomized algorithms), information theory, and perhaps in a course on probability in the math department! That’s probably a good excuse for me to not spend a lot of time on probability in a cryptography course. But I’m making up for that here, bringing it up right at the beginning.