A few things come to mind:
- Something based on XOR. I'm imagining an endlessly (and randomly) streaming bridge of tiles that can either be in the left position or the right position (ie the message) and you can only cross the bridge if they all line up. Straight bridge:
You know that the bridge started straight, but has been XOR'd with something to make it all wonky:
and you have to find the right "key" to get the bridge back straight.
- "Cracking a password". They have to build a cracking dictionary based on clues. Each clue adds more patterns to the dictionary, and has a better chance of cracking the password - but add too many patterns and it'll take forever! Or your "password cracking machine" only has 10 pattern slots, or something.
Edit Expanding this idea:
The math behind the number of possibilities for a password is combinatorics, but this can be hidden from the user if you want. I'm imagining that the puzzle starts with nothing known about the password and a display saying "1063 Possibilities" (which is 95^32, ie a 32 char password with all 95 printable ASCII chars). If you find a hint saying "Password is less than 16 characters" then the meter drops to 1031. Adding the hint "Contains his daughter's name "Lizzie" " drops it to 1020. And so on. When you get down to something reasonable, like 105 you get the option to brute-force.
For added fun, you could not quite give them enough hints to get them down to the brute-forceable number, making them guess the last couple hints, and maybe have to try a couple times. (This is very much how password cracking works in real life).
- Diffie Hellman Key Exchange is an interesting concept, and can be explored without any math (see image below). You are in a cell and can pass messages with the prisoner in the cell next to yours, but the guards can see it all. You have to coordinate your
ATTACK AT DAWN without the guards catching on.
That's all I've got for now. I could probably keep going, but I should probably go to bed.