Assume you have:
- A truly random one time pad, $P$
- A plain text message, $M$
- Two symmetric ciphers, $C_S$ and $C_W$, where $C_S$ is always more secure than $C_W$
Assume the keys have already been securely exchanged and the attacker intercepts everything Alice transmits.
In theory, can $C_S(P \space \oplus \space M)$ and $C_W(P)$ taken together be less secure $C_S(M)$?
Also, is $C_S(P \space \oplus \space M)$ and $C_W(P)$ always more secure than $C_S(M)$.
In longer form, if I XOR a message with a one time pad and encrypt that with one cipher and encrypt the one time pad with a different cipher, can that be less secure than just using the stronger of the two ciphers? Is it the case that it would always be stronger?