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My idea was, given that a computer could produce some sort of lookup tables on paper, could then a human use those lookup tables to create a system for digital signatures?

This was really an idea for fictional writing. I was trying to figure out whether it could be possible in a society at sort of 1950s technology to create a more secure alternative to handwritten signatures.

E.g. that people could order paper pads produced by a computer as service and use those to sign contracts etc with a number rather than a handwritten signature. Another paper pad which was public should be used for verifying the authenticity of the paper.

Could anything like this be done. We assume that given that processing power availability in such a society is much worse than today, this system does not need to be nearly as secure (require as much computation) as today.

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    $\begingroup$ signatures depend on the messages to be known (because it's their purpose to authenticate a specific message). How should such a system work? $\endgroup$ – SEJPM May 18 '15 at 18:38
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    $\begingroup$ If you transfer the current knowledge back to past then you should also transfer the attacking techniques / crypto analysis. Currently we have fast computers that mainly put the cryptographers at an advantage. If you reverse that then the crypto analysts / attackers may actually be better off. $\endgroup$ – Maarten Bodewes May 18 '15 at 18:38
  • $\begingroup$ @SOJPM You could e.g. use the letters in the source text walk through the text pad in some way, in a manner decided by the private key. Or use some paper based hashing function first. $\endgroup$ – Erik Engheim May 18 '15 at 19:07
  • $\begingroup$ You acutally put an intersting question here: "Use some paper based hash function", now which? I don't know any. I guess most people don't. So I asked this as separate question. I'm 100% sure the standard schemes, based on number theoretic stuff and linear error correcting don't apply because they need heavy processing on the message. Now is the question: Is there some exotic scheme that can be "abused" for this? I'd doubt this because modern-crypto mainly produces (more or less) practical stuff (for today) and at this time people relied on hand-written signatures. $\endgroup$ – SEJPM May 18 '15 at 21:56
  • $\begingroup$ @SOJPM I doubt it is possible, but given that such an approach could allow itself to be a lot less secure than present methods given the lack of processing power at the time, I theorized that there just might be some way of doing this. After all we have some paper based solutions for symmetric encryption. $\endgroup$ – Erik Engheim May 19 '15 at 12:35
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The best answer I can come up with is using some sort of Geometric cryptography. It is based on the difficulty of trisecting an angle using a ruler and compass. So you could hand over people a triplet of some secret angle.

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    $\begingroup$ While you cannot precisely trisect an angle with a ruler and compass, it practice it is not difficult to get arbitrarily close. I don't see that working apart from furious handwaving (of course, in a work of fiction, that handwaving is quite possible) $\endgroup$ – poncho Jun 18 '15 at 14:06

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