… Does there exist some problem, just one master problem, that tells us whether cryptography is possible? .. the answer is yes.
… The existence of true one-way functions
… Kolmogorov complexity, concerns how hard it is to tell the difference between random strings of numbers and strings that contain some information.
… zero-knowledge proofs (in which one person can convince another that a statement is true without revealing the proof)
… The concept of randomness is, by its nature, tricky to pin down.
… There’s a Dilbert comic strip in which an office tour guide shows Dilbert the accounting department’s “random number generator” — which turns out to be a monster who just keeps repeating the number 9. “Are you sure that’s random?” Dilbert asks. “That’s the problem with randomness,” his guide answers, “you can never be sure.”
… any description shorter than the string itself
135791113151719212325272931333537394143; The first 22 odd numbers
999999999314159265358979323846264338327; Nine 9s then the first 30 digits of pi