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I have just started my first D&D 5e campaign, and have encountered a seemingly mind-controlled bandit who keeps writing the same thing over and over on the wall. Our DM wrote out what it looks like (character for character). It's supposed to be in Abyssal, the script of which my character can read.

I deciphered this cryptic writing with frequency analysis, but this used my real-world skills to solve the problem, before we're supposed to find the solution in-game. My character is a level 2 High Elf Wizard, so if given enough time (i.e. during a long rest), I think it would be reasonable for my character, with his vast knowledge of written and spoken languages, to discover the meaning.

Given that I actually solved this in the real world, would it be appropriate for my character to do the same? Can I transfer my real-world skill into the game in this way? And if so, what would be the best way to go about it?

Aside: technically the way this cryptic text was implemented was as a simple substitution cipher. In reality, just because I can read the Latin character set doesn't mean I understand Italian. So maybe it's a bit paradoxical that I was able to understand the message at all, and that it maybe shouldn't transfer to in-game discovery because my character can read Infernal but can't speak Abyssal...

Ask your DM whether it's supposed to be viable to decipher it, or whether you were supposed to find the clues in game.

Given that they used a genuine (even if simple) cipher and a proper script hiding an actual message, it seems likely that they meant for cracking it in real life to be an option. But it might just be that they never expected anyone to bother. (Seems unlikely, though)

Personally, I'd bring it up before the start of the next game and ask whether I was supposed to do that during downtime.

Also personally, as a DM, I'd be thrilled if someone broke a puzzle like this during their time away from the game. DMs don't put in the work for nothing and usually enjoy it when people figure things out.

I'd be careful about metagaming, so I concur that you should bring it to your GM prior to bringing it in character as solved. If nothing else, the GM shouldn't go forward in the game thinking the writing is still mysterious, because then a lot of the mystery could be undermined if he gives clues that require deciphering of the text to understand, and you proceed with knowledge he doesn't know you have.

You already hinted at a solution:

My character is a level 2 High Elf Wizard, so if given enough time
(i.e. during a long rest), I think it would be reasonable for my
character, with his vast knowledge of written and spoken languages, to
discover the meaning.

If you can bring this into roleplay, it is fine, after all you are a wizard who most likely is good in deciphering texts. What is your character's backstory? Does your character have previous experience with this kind of riddles? In any case, good roleplaying requires to play coming up with the solution convincingly, not in an ad hoc manner.