Secret sharing:

a. Say that we use Shamir secret sharing with t=3 and n=20 (where n is the total number of shares and t+1 is the minimum number of players to recover the secret). But there is a cheater that will just say a random number (say he got a share x, then he can give a number different from f(x)). How many people (minimum) do you need in order to recover the secret? Explain clearly.

b. We consider a (t+1=2,n=7) shamir secret scheme over Z_{11}. Four players A,B,C,D cooperate to find the secret, but one of them is cheating (so the share he claims to have might not be an actual share). They claim that the shares are: A=(1,4), B=(3,7), C=(5,1), D=(7,2). Who is cheating and what is the secret?

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