Do you have access to the memory wiping mechanism prior to getting your memory wiped tomorrow?

If so, wipe your memory, leaving yourself a note: "Think of the most unlikely place where you can hide a message, and leave this envelope there." The envelope contains the information you want to pass on.

Then, before your memory is wiped tomorrow, leave yourself a note: "Think of the most unlikely place where you can hide a message, and open the envelope hidden there."

Hopefully, your two memory-wiped selves should be sufficiently similar that the unlikely places they think of will coincide. At the same time, the fact that there is an envelope in the unlikely place you just thought of should be evidence that it came from you.

Implant something into muscle memory that can be used as an encryption key. (Muscle memory has to be retained, right?)

I'm not sure exactly how to go about this. But for example, I've heard of people who say they don't know their passwords for certain sites, but their fingers know how to type them. So leave a message that says "go to this website, use the DOM editor to change the password box to a text box, and try to log in. Use the password that your fingers know as the key to decrypt this other message".

This particular version probably wouldn't work, but something along those lines might.

Your best bet would be to find some sort of channel for communicating with your future self that your adversary does not have access to. Other posters mentioned several such examples, with channels including:

• keeping your long term memories (assuming that the memories couldn't be tampered with by the adversary)
• Swallowing a message, getting it as a tattoo, etc. (assuming that the adversary can't force you to do that)
• Using some sort of biometric lock (assuming that the adversary can't get a proper sample with causing detectable alternations to your blood chemistry which would be detectable in the sample) My personal addition: tell your friends/neighbors/the news the story. Unless your adversary can make you lie (or take your form or use mind magic or whatnot), these people can act as the channel you need.

If you don't have a channel of that sort, I believe you are out of luck. A formal proof eludes me at this time; I'll post again if I figure out out.

Naively, I'd say to write it as short text and sign it with my public key, but that was under the assumption that my recent memories were being wiped.

If all my memories are being wiped there isn't really a "me" to send the message to in any reasonable sense. Even if it's just all my episodic memories I would see amnesiac!ilzolende as a member of my in-group but not as me.

I suppose I could try to package the message with a blood sample (with a lock on a timer), any sample coercively obtained would have much higher cortisol levels (edit: or show signs of sedatives or something).

Tomorrow, all of your memories are going to be wiped.

If that includes semantic memory, then lose my language ability and won't understand the message.

Even with intact semantic memory it likely leaves me in a state without real identity and in that state it will be easy for anyone decently skilled to convince me of a lot of things. It very unlikely that if you strip me of all my memories I will do a decent job at verification.

Gather a series of pictures. Grade how much you like each one. Put all this in your message. Time lock your message so that Mal can't decrypt them in time to find out which pictures you like. If Mal puts a gun to your head and asks what pictures you like, lie. You'll know a message is from you if it matches your tastes.

As others pointed out, "memory wipe" is a broad category, but assuming that this is about episodic memory:

How about sending yourself a letter via delivery service on a specific date in handwriting + audio-recording? This of course completely ignores any other faked messages that would need to be discarded, but even with only episodic memory loss, I assume I'd be so confused as to be easy game for even the most incompetent scammer.

If this is about formal guarantees, we need to have some more precise ideas about the "memory wipe" and the adversary in question. In the most general case, likely game over.

Tattoo private key on inside of thigh.

I have a plan that may not be foolproof, however I believe it may be the most advantageous plan so far. Knowing that there will be a third party trying to destroy your message and implant a new one you would first have to make a decoy for him to find and destroy or edit. The next step would to cut yourself on your inner thigh to the point that once you wake up it will discomfort you enough to investigate the wound. I unfortunately did not save the link to it but I found a special ink online that will disappear after the first writing and reappear after a 24 hour period. Using the ink, write a note explaining the situation. I think most people would believe the hidden message on your thigh in your own handing writing then what some third party told you or a forged letter they made pretending to be you. If I have any holes in my plan please let me know.

If you know of the existence of such tech before "tomorrow", one way would be to have a secret-name that no one else knew. That is, create a word that means "a secret name referring to me that no one else knows that I use to ID myself" and keep thinking about it every day to put that word into your semantic memory so that the mind-wipe won't touch it.

--edit2: this may be formally impossible, I don't actually know. If anyone can demonstrate this I'd be very appreciative.

The case of Clive Wearing is the most profound memory loss I know of. He has a diary in which he keeps recording "NOW I AM AWAKE FOR THE FIRST TIME" and such as he keeps finidng himself conscious, and then crosses the previous entry because he thinks someone else wrote it. However, he retains knowledge of his wife (See the "hello darling I love you" entry in the diary) and how to play music.

Many of our most important memories (such as Clive Wearing's wife) become intrinsic features of our semantic knowledge. He would have remembered "wife" even independantly of any particular memory he had of her because she would be a fact about his world, in the same sense that he'd remember "chair". That's not to say that those memories can't be removed, but unless somehow targeted semantic dementia will also remove general knowledge about the world and word meanings.

Your character would only have Retrograde amnesia whereas Clive has both types of amnesia simultaneously, so if you wish to insert realism I'd suggest following the citations and reading some of the case studies. I imagine a villain might add capgras or prosopagnosia to the mix to circumvent recognition of loved ones.

I am late to comment and your edits may cover this but I think:

1. The problem is too flexible where "memory wipe" could wipe any possible way for you to know the signal you are looking to trust and
2. "malicious party" can be flexible enough to always win.

Any signal that you were trying to hide in your environment might be detected by a "malicious entity" and interfered with; and any signal that might be hidden inside your brain might be wiped, depending on your definition of each part; it may be impossible to defeat the challenges.

One potential subproblem is how to set a time-release message that was verifiably sent over 24 hours ago and not read since being sent. Embedding a reliable secret in such a message would then authenticate it as yours (if you had such a secret).

My first thought is to post the message publicly, encrypted, with the intention that it be brute-forced. The viability of this depends on the adversary's compute resources compared to yours, and how long you're willing to wait before being able to read the message.

Otherwise you could try to pursue physical means. If you had the resources, maybe you could send something into space and back? Otherwise, what you need is a seal such that you can verify how long it's been sealed. This probably exists, but it comes down to materials science, which I don't know well. Maybe if you suspend the message in water and put it in a freezer, you'll be able to verify that it's been freezing for a certain duration at a certain temperature?

The most relevant piece of information seems to be 'there's an enemy out there trying to mislead you for some reason', so the real question is not 'what to send' but 'how to send it'.

1. Tell everybody you are going to be mind wiped tomorrow, so let's finish our business today.
2. Arrange for yourself to find yourself in disturbing circumstances, so as to be alarmed when you wake up.
3. Arrange for your friends to mock-attack you early on the morning so that you will know there's danger.

The problem is equivalent to this one: An unstoppable force is coming your way. Devise an immovable shield against it.