One-time pad and Perfect secrecy

2018-03-22 03:18:19

Consider the following property of one-time symmetric encryption scheme (Enc, Dec, K). For Every message distribution M, every pair of messages $m_{_0}$,$m_{_1}$ belongs to M and every ciphertext c belongs to C, it holds that: (Pr means Probability)

Pr[M=$m_{_0}$ | C=c] = Pr[M=$m_{_1}$ | C=c]

Argue that the above property is not a characterization of perfect secrecy via a counterexample. (Consider the one-time pad and any non-uniform distribution over {0,1}^j )