 Solution

ID: 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

Pr (C = c) > 0

Pr (X = x ∣ C = c) = Pr (X = x) .

Equivalently, for every pair

x, x^{'}

the conditional probability distributions of the ciphertext are identical:

Pr (C = c ∣ X = x) = Pr (C = c ∣ X = x^{'}) .

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.

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