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Emile comments on Open Thread, September 1-15, 2012 - Less Wrong
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I'm thinking about a fantasy setting that I expect to set stories in in the future, and I have a cryptography problem.
Specifically, there are no computers in this setting (ruling out things like supercomplicated RSA). And all the adults share bodies (generally, one body has two people in it). One's asleep (insensate, not forming memories about what's going on, and not in any sort of control over the body) and one's awake (in control, forming memories, experiencing what's going on) at any given time. There is not necessarily any visible sign when one party falls asleep and the other wakes, although there are fakeable correlates (basically, acting like you just appeared wherever you are). It does not follow a rigid schedule, although there is an approximate maximum period of time someone can stay awake for, and there are (also fakeable) symptoms of tiredness. Persons who share bodies still have distinct legal and social existences, so if one commits a crime, the other is entitled to walk free while awake as long as they come back before sleeping - but how do they prove it?
There are likely to be three levels of security, with one being "asking", the second being a sort of "oh yeah? prove it" ("tell me something only my wife would know / exhibit a skill your cohabitor hasn't mastered / etc."), and the third being... something. Because you don't want to turn loose someone who could be a dangerous criminal just because they were collaborating with a third party to learn information, or broke into the National Database of Secret Person-Distinguishing Passphrases, or didn't disclose all their skills to some central skill registry - but you don't want to lock up innocent people who made bad choices about who to move in with when they were eight, either.
Is there something that doesn't require computers, or human-atypical levels of memorization/computation, or rely critically on a potentially-break-into-able National Database of Secret Person-Distinguishing Passphrases, which will let someone have a permanently private bit of information they can use to verify to arbitrary others who they are? (There is magic, but it is not math-doing magic.)
A few possibilities:
A clockwork Analytical engine / Enigma machine, that does something equivalent to public key verification (though I assume you don't want that kind of machine either).
In each city is a temple of the Sigils, in which are stored the Sigils of people, in public view. The Sigils are like intricate signatures drawn on clay tablets; but they are made on a special clay, Sigil Clay, that dries in about a minute, and changes color depending on the pressure you apply to it, the heat (depending of whether you're touching it with a stylus or with your fingers), and how dry it is. Sigil Priests know hundreds of drawing techniques, and when an alternate pair is created, each person will be taught a few techniques to apply to his drawing, with no overlap between the alternates (so it should be quite hard for someone to reproduce his alternate's Sigil). Being able to draw one's Sigil is generally considered a proof of identity, and since only the Sigil Priests know how to make Sigil Clay, one has little opportunity to practice drawing someone else's Sigil (not to mention that it's of course considered a grave crime).
For the prisonner's case, why not having the "day" persona return to prison to sleep and give a new passphrase short (randomly generated with a special set of dice) to the guard, and when he wakes up and wants to get out, he must give the same passphrase (if he gets it wrong, he is lightly punished and must wait at least 30 minutes before trying again.
This is a weird and interesting premise!
The passphrase idea you describe is probably fine for minimum and even medium security, it's just vulnerable to eavesdropping and message-passing by third parties if the prisoner has friends.