Step 1: Boot up my old tower PC.
Step 2: Save the photo on the desktop.
Step 3: Shut down the PC. Go make some coffee for when the hacker gets here.
That PC will not load in under 3 minutes; it would be a miracle. There are dozens of applications set to load at startup too; it’s probably infected with malware of multiple kinds, and he will be prompted for many updates.
I would compress it with kzip to obscure its internal format so an automatic scan couldn’t find it, change the file extension to something unhelpful like .cfg or .xkz, and drop it in among the myriad configuration files of a big program like Chrome or Firefox. If Mr. Hacker could manually examine 100,000 files on my computer in three minutes, he would deserve to win.
[edit] How in the world did this lame answer get over 5k upvotes? Don’t you guys have anything better to do?
It’s too bad that the hacker has three minutes instead of, say, one second, because in that case there’s a pretty straightforward solution: I would simply write a program that simultaneously reads and erases the file, meanwhile sending the contents hundreds of thousands of miles away to a non-artificial communications satellite. By the time the messages return to Earth, the hacker’s one second would be up.

But three light-minutes is about 35 million miles, which is unfortunately a lot further out than the moon.
On the other hand, it’s only about two thirds of the way to Mars. And fortunately by virtue of my wild college days, I happen to know some people who operate some communications equipment in that neighborhood.

So I’d use my 28 minutes to call in / beg for a favor, then use the NASA Deep Space Network antennas to send the file over X-band to a robot sufficiently far away from my computer that retrieving a file from it in under three minutes would violate the known laws of physics.

Beat that, crypto nerds.
I’ll ignore the wording and not play around with an earlier clone of the hard disk, with the recent one containing the jpeg being unplugged and just sitting there, nor with an sd card taped next to the motherboard, nor with a printed photo…
I think a lot depends on the assumptions the hacker has about the owner of the system: my grandma looking at cat videos, the teenager renaming a certain folder to pR0n, or a programmer, perhaps initiated in the dark art of information security.
Cause if it is the latter then anything goes, digging out file access times, any kinds of journal the (or even keyloggers) the computer may have, and looking at unlinked files meant to be recovered later from the raw file system data, with no fat entry pointing to it. I mean who’s stupid enough to not cheat in such a situation? If I knew my target, and had the resources, such as a nation state’s, I would compromise it, placing sleepers and loggers and all kinds of shit, way before any challenge arose, and then press a few buttons, instead of doing hacker work in just three minutes.
However, if the hacker thinks it’s grandma’s computer, then having in a webpage’s localStorage a certain key with an xor’d-with-say-helloworld buffer base64′d would not be the first place to look for a jpeg file.
So, littering the jpeg into several valid audible mp3 files (and making sure it is erased from the disk, not just from the file allocation table) could well be considered steganography, since mp3 files will play, maybe with a bleep or a bloop, but will play even if invalid data is added to their stream. It’s just how mp3 file packets are constructed. So a few dozen bytes into several thousand files would be next to impossible to reconstruct without prior knowledge, if some security through obscurity is also mixed in — certainly not in 3 minutes — and no versioning is done on the disks’ contents — think Time Machine in Mac, or why not, git — and the program is not saved. But even then, who knows the order those few bytes need to come together. Honestly, I like the mp3 solution more than writing to unallocated parts of the hard disk. Or maybe create several files with names obtained from the base64 of the jpeg, created in a certain order other than the order they were in the stream.
As an XKCD episode highlights it, if that jpg is that important, it could be more effective to pull a few fingernails, like adults do, than playing around with hacker tools like some virgin in their mother’s basement.
