 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-2/12i/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Write the intercepted ciphertext, known plaintext, and desired plaintext without spaces:

C = LRPFOJQLCUD, P = FLYXATXONCE, P^{'} = REMAINXHERE .

Because the pad is additive, Eve applies the malleability of an additive one-time pad and sends

C^{'} = C - P + P^{'} (mod 26) .

Letter-by-letter, using

A = 1, \dots, Z = 26

, this gives

C P P^{'} C^{'} L F R X R L E K P Y M D F X A I O A I W J T N D Q X X Q L O H E C N E T U C R J D E E D

Thus Eve should deliver

XKDIWDQETJD .

Indeed, if

C = P + K

, then

C^{'} = C - P + P^{'} = P^{'} + K

, so Ollie decrypts the desired message.

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