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Say we have door where you have to say a password to pass. If theres someone standing nearby he would hear the password and could also use it. So therefore the doorman gives you a different number everytime you want to enter and you have to calculate the password in your head. E.g. you have to add 12 if the number is even and double it if the number is odd. Are there some good algorithms which are easy to use by most people and save. By save I mean that someone standing nearby would need to hear more than 100 valid combinations to conclude the algorithm.

Edit: I changed the title. I found out that the correct name would be challenge–response authentication.

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1) The scenario you described is symmetric, since you and the doorman have a shared secret. 2) You need authentication, not encryption –  CodesInChaos Mar 25 at 9:03
    
One-way functions are quite hard to calculate in your head alone. If the listener has access to a computer, there is no algorithm he couldn't brute force. But even then, probably there is no such algorithm due to the limits of calculations in the human brain –  tylo Mar 25 at 10:25
    
pdf.aminer.org/000/320/472/… $\;$ –  Ricky Demer Mar 25 at 10:36
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