Question: 3. Consider a cryptosystem in which P={a,b,c},C={1,2,3,4},K={K1,K2,K3,K4}, suppose the encryption matrix is as follows: If Pr[K1]=41,Pr[K2]=41,Pr[K3]=41,Pr[K4]=41,Pr[a]=41,Pr[b]=41,Pr[c]=21, (1) compute H(C),H(KC) and H(PC); (10 points) (2) try

3. Consider a cryptosystem in which P={a,b,c},C={1,2,3,4},K={K1,K2,K3,K4}, suppose the encryption matrix

3. Consider a cryptosystem in which P={a,b,c},C={1,2,3,4},K={K1,K2,K3,K4}, suppose the encryption matrix is as follows: If Pr[K1]=41,Pr[K2]=41,Pr[K3]=41,Pr[K4]=41,Pr[a]=41,Pr[b]=41,Pr[c]=21, (1) compute H(C),H(KC) and H(PC); (10 points) (2) try to judge whether it has perfect secrecy and tell the reason. (4 points)

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