Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 12I / b / Solution

Write the intercepted ciphertext, known plaintext, and desired plaintext without spaces:Because the pad is additive, Eve applies the malleability of an additive one-time pad and sendsLetter-by-letter, using $A=1,\dots ,Z=26$, this givesThus Eve should deliverIndeed, if $C=P+K$, then $C^{\prime }=C-P+P^{\prime }=P^{\prime }+K$, so Ollie decrypts the desired message.