Situation: Alice has selected a positive integer $a$, and Bob has selected a positive integer $b$. Alice and Bob want to know whether $a > b$, $a = b$, or $a < b$, but neither wishes to reveal their chosen number to the other party.

How can Alice and Bob make this determination?

  • $\begingroup$ Bidding? This smells of auctions. $\endgroup$ – John Dvorak Nov 14 '13 at 5:22
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    $\begingroup$ Just a pointer to an answer at the moment, the problem is called "Yao's Millionaire's Problem" for which there is a protocol. $\endgroup$ – Luke Mathieson Nov 14 '13 at 5:40
  • $\begingroup$ @LukeMathieson Ah, that's great, thanks! I'd seen this somewhere before and couldn't remember what the problem was called. $\endgroup$ – senshin Nov 14 '13 at 5:42
  • $\begingroup$ @LukeMathieson expand it to an answer ? $\endgroup$ – Subhayan Nov 14 '13 at 14:44

As pointed out by Luke Mathieson in the comments, this problem is called Yao's Millionaire Problem, for which protocols can easily be found by Googling.

  • $\begingroup$ I do not understand the problem well enough at this point to write a good answer for this question. If somebody does write a good answer (or really, any answer), I will unaccept this answer and accept that instead. $\endgroup$ – senshin Nov 18 '13 at 23:59

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