 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-4/3k/a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Because decryption determines

M

from

(C, K)

H (M ∣ C, K) = 0.

The chain rule and monotonicity give

H (M ∣ C) \leq H (M, K ∣ C) = H (K ∣ C) + H (M ∣ C, K) = H (K ∣ C) .

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