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RolfAndreassen 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.)
The first thing that occurs to me is to decentralise the database, which incidentally is rather a computer-ish concept. Each person designates two or more Keyphrase Holders, with a separate password for each. For low-security situations, they have to give their passphrase to one KH; for maximum security, they have to convince all of them. Ten or a dozen passwords should not be beyond anyone's memorisation capabilities in a world without shiny Internet distractions, and the KH can write them down - this gives you a lot of different DSP-DPs instead of one big one. Any given KH may be suborned or have his database broken into, but by the time you get up to a dozen or so that is unlikely.
Obviously this works best if you don't have to physically drag the KH to the prison cell, or whatever, before you let the innocent one out.
To make this easier to memorize and more secure, you could have there be a much larger number of KHs. Their job is to be KHs; their identities are kept secret even from each other. Each KH has a certain property about the person's password that they learn- e.g. its length, the number of vowels, the number of times the letter "a" appears minus the number of times a letter appears, etc. However, they don't know the password itself; they only know the person's answer to the question. When a person wants to be released, a certain number of KH's, randomly selected, large enough that correct guesses or collaboration is unlikely, and all wearing hoods, are summoned to the person's cell to figure out their identity.
You'd need to ensure that, following an incorrect guess, the same KH isn't used again- or that the innocent person picks a new password. (Propagating password changes would be terrible- it would make sense to have very severe punishments for claiming to be another person. The first time would be standard jail processing- everybody innocent would need to go down a line of KH's and tell them their name and the answer. This also highlights the main weakness of any possible system- the need to have verified who is who when dealing with the initial passwords, since criminals would presumably immediately go to sleep following crimes, or claim to have just woken up.)