Past exam of the computer science course of the University of Oxford / 2015 / Computer security / 3 / b / i / Solution

Perfect secrecy means that observing the ciphertext changes no probability concerning the plaintext. For every distribution of the message $X$, and every $x,c$ with $\mathrm{Pr}(C=c)>0$,Equivalently, for every pair $x,x^{\prime }$ the conditional probability distributions of the ciphertext are identical:The randomness here comes from independent key generation and any encryption randomness. The claim is information theoretic: unlimited computation cannot extract information about $X$ from $C$ beyond what was known beforehand.