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tim comments on Harry Potter and the Methods of Rationality discussion thread, March 2015, chapter 116 - Less Wrong
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Prediction 1: Hermione will soon harrow Azkaban. Why wouldn't she? She's all but immortal, now.
Prediction 2: Time-travel and memory-charm shenanigans incoming. Evidence:
Harry weirdly ignored the missing recognition code on LV's forged message.
Cedric considered in Harry's plans, and his Time-Turner mentioned, then seemingly forgotten.
Death-Eaters all dead, but no faces observed.
Flamel asserted dead, but we didn't see it, and LV explicitly didn't kill him personally.
Dumbledore thinks in stories, yet we're supposed to believe he's surprised when the villain reveals he's captured the hero and his equipment (Harry and the Cloak), just like villains always catch heroes and take their stuff near the end (see: Frodo Baggins, Luke Skywalker).
Hermione has been asleep the whole time, neither giving nor receiving information.
Questions:
did Harry tell Cedric to do certain things before Harry left? Did Harry tell Cedric to Obliviate Harry afterward so Harry could play his part convincingly? What did Harry most likely tell Cedric to do?
who will do the Time-Turning, Hermione, Cedric, or Harry?
who will be saved? Obvious candidates include Flamel, Dumbledore, Lucius Malfoy, maybe all the anonymous Death-Eaters.
if you were Hermione and had a Time-Turner and the Stone and the Cloak and six hours to save everybody but Voldemort, Quirrell and Macnair, how would you do it? (Do you need the help of someone who can Obliviate well? Do you need partial Transfiguration?)
This is not how (Harry's) recognition code works. It is used to identify exact(ish) copies of himself because he is the only one - barring magical mental shenanigans - that can immediately recognize it. Writing it down on a piece of paper and then giving that piece of paper to someone else would defeat the purpose entirely.
The cryptographic solution to this problem is to publicize related codes derived in such a way that the possessor of the secret code can recognize the derivation, but bystanders can't use them to rederive the secret code.
It's probably a bit much to expect Harry to use that in its strong form -- most of the relevant math was known in 1991, but it only rose to prominence with the Internet, and it's quite laborious by hand -- but there's probably a similar ad-hoc scheme he can use that'd provide reasonably strong authentication against a bunch of cryptographically naive wizards.
How much security could one expect from a mental PRNG? Simple, RNGs go back many decades so Harry could use it easily if he knew of them and thought of the application, mathematically breakable but only with knowledge of the algorithms & more samples than Harry realistically ever needs...
Does it need to be pure mental ? In some cases yes, but if he has time to carefully write himself a note, he probably has time to roll dices or write number on pieces of paper, fold them, mix them, and draw one at random. Or take a random book and look at a random letter of a random page (using some correction algorithm to deal with the difference of letter frequency).
For all practical uses x'=(x*8+1) mod 49 is a simple PRNG that can be executed mentally easily. If you seed it with the next best number you see it gives suitably random numbers for every-day purposes (and when no dice are available). Note that this is taken from TAoCP by Knuth. I use it for fair choices and mental story telling.
It's not hard to generate random numbers in your head in real life. Generate 5 or 6 "random" numbers from 0 to X-1, add them, and take the result mod X.
I don't like things which use apparatuses because they introduce a dependency (and since this scheme is for use in extreme/unusual circumstances, it's especially likely that Harry would not have leisure time or access to his pouch) and they make part of the process observable, hence, easier to realize the existence of & reverse-engineer.
A fully mental PRNG is doable under all circumstances in under a second and is unobservable except via Legilimency (which if it isn't blocked, means one is screwed anyway since one can just be False-memory-charmed into remembering having done the verification*).
* Kripkenstein would approve!
The fact that he uses prime factorization as his test for "can use you time turner to solve computationally hard problems" is evidence that he did know about prime number based cryptography, not strong evidence, but evidence still, since the prime-based crypto is the most common reason people are interested in having fast ways to factor primes.
The "potato" code, yes.
But knowing that Harry is "be prepared" so much that he prepared a recognition code when he didn't think he would ever use it, and then had been nearly a year with a time-turner, and knowning about Oblivatiate, it's quite surprising that he didn't device a recognition code to recognize a message sent either by a future self to his past self (time-turner) or from his past self to his future self (Obliviate).