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Suppose Alice knows a secret number $a$, and Bob knows a secret number $b$.

Is there a simple way for Alice and Bob to know who has the lowest number, without Alice & Bob exchanging their numbers ?

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This is Yao's Millionaires' Problem: en.wikipedia.org/wiki/Yao's_Millionaires'_Problem –  Seth Jul 21 at 21:27
    
@Seth : $\;\;\;$ It's at least approximately that problem. $\:$ If ties are supposed to be broken at random, $\hspace{.41 in}$ then this question's problem may be more difficult. $\;\;\;\;\;\;\;$ –  Ricky Demer Jul 21 at 22:00
    
@RickyDemer In that case a tie could be broken with Blum's "coin-flipping by telephone". –  fkraiem Jul 22 at 9:46
    
@fkraiem remember though, you would have to always run the coin-flip (whether there was a tie or not), otherwise you leak whether or not there was a tie. My point is, things can get complicated. –  mikeazo Jul 22 at 12:56
    
@fkraiem : $\;\;\;$ How would that work? $\:$ Any use of that paper that I can think of would leak $\hspace{.83 in}$ which side a tie would have been broken in favor of. $\;\;\;\;\;\;\;$ –  Ricky Demer Jul 22 at 17:20

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