= Solution
Write the intercepted ciphertext, known plaintext, and desired plaintext without spaces:
$$
C=\text{LRPFOJQLCUD},\qquad
P=\text{FLYXATXONCE},\qquad
P'=\text{REMAINXHERE}.
$$
Because the pad is additive, Eve applies the <malleability of an additive one-time pad> and sends
$$
C'=C-P+P'\pmod{26}.
$$
Letter-by-letter, using $A=1,\ldots,Z=26$, this gives
$$
\begin{array}{c|ccccccccccc}
C&L&R&P&F&O&J&Q&L&C&U&D\\
P&F&L&Y&X&A&T&X&O&N&C&E\\
P'&R&E&M&A&I&N&X&H&E&R&E\\ \hline
C'&X&K&D&I&W&D&Q&E&T&J&D
\end{array}
$$
Thus Eve should deliver
$$
\boxed{\text{XKDIWDQETJD}.}
$$
Indeed, if $C=P+K$, then $C'=C-P+P'=P'+K$, so Ollie decrypts the desired message.
Back to article page
