#519 Consider the following protocol for two parties

Consider the following protocol for two parties - Math

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Free Chegg Question

Consider the following protocol for two parties Alice and Bob to flip a fair coin (more complicated versions of this might be used for Internet gambling):

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A.

case1: if Alice is honest then she would encrypt the correct key i.e. {0,1} which ever she got and send it to bob and T i.e.  , now bob receives the same key and he being honest will send correct  and  back to T.

case2: but if alice is dishonest then she would encrypt the incorrect key then send it to bob and T i.e. , now bob receives the same key and he being honest will send correct  and  back to T.

using XOR gate the output is true only if one of the two inputs are false and other is true

in case 1 if alice got 0,1 on the coin flip and bob got 1,0 then T will give receive two different inputs and so the XOR gate will bear the output true which has a probability 1/2 while if alice got 1,0 on the coin flip and bob got 1,0 then T will give receive two similar inputs and so the XOR gate will bear the output false which has a probability 1/2

in case 2 if alice got 0,1 on the coin flip and bob got 1,0 then T will give receive two similar inputs and so the XOR gate will bear the output false which has a probability 1/2 while if alice got 1,0 on the coin flip and bob got 1,0 then T will give receive two different inputs and so the XOR gate will bear the output false which has a probability 1/2.