If an all-null message results in a simple/repeating ciphertext, it means that there exists at least one message whose ciphertext leaks information, and that in

If an all-null message results in a simple/repeating ciphertext, it means that there exists at least one message whose ciphertext leaks information, and that in turns means that there are probably more messages like it, and it's also probable that all messages leak info in varying degrees.