I'm a programmer and relatively new to cryptography, so pardon my rookie question. :)
Let's say we have a message, both in plain text and encrypted with a 128-bit key. In theory, it possible to somehow find out the key? And, if yes, what computing time are we talking about?
Thanks!
Yes, it's a question of time needed - using brute force one can try each possible combination of bits and guess the right one. Maximal time would be millions and billions of years, so we can say that it can't cracked easily.
However, each algorithm has certain short circuits (for some algorithms such circuits just have not been found yet) that reduce the time needed. Also modern massive parallel computational techniques (eg. employing GPUs in graphic cards) reduce the time even more. There can be other factors that influence the time needed, such as flaws in algorithm application (eg. use of wrong encryption mode or use of short password and padding it with some character to the key length).
Then there exists Rubber-hose cryptanalysis which usually proves to be more effective, than brute force key guessing.