Question

Two different message encrypted by same key with xors how to find the key

Answer 1

A wants to send B a message (A and B know both have a common secret key) and C wants to intercept it (without the knowledge of the key)

Now we assume they have an encryption method that let's you define two distinct messages for two distinct keys that both are encoded in the same cyphertext.

With this method A can send the secret message "it is raining tomorrow" encrypted with the secret key, but A can also include the message "it is not raining tomorrow" with another key.

If C manages to intercept the message and manages to find one or both of the keys, they still don't know anything, as there are two contradicting messages. But since B knows which key was used, they can use the correct message.