What are the implications of XORing ciphertext with plaintext? I was intrigued by this question: Does adding complexity mean a more secure cipher?
And it led me to wonder: What are the implications (if any) of XORing a ciphertext with the original plaintext message? So:

$$C=(E_k(m)\oplus m)$$

My first impression was: "That sounds like a bad idea.", but is it necessarily? Seems like something similar is being used for Propagating Cipher Block Chaining.


  "In PCBC mode, each block of plaintext is XORed with both the previous plaintext block and the previous ciphertext block before being encrypted."
This is not a correct encryption scheme because it cannot be properly decrypted. Consider $E_k$ to be the one-time pad (OTP), the key being all zeroes. Then, for any message, you have: 

$$C = E_{0^{|m|}}(m) \oplus m = (m \oplus 0^{|m|}) \oplus m = m \oplus m = 0^{|m|}$$ 

Or consider encrypting some random string $r$, then you have:

$$C = E_k(r) \oplus r$$

Which is basically the OTP. How would you expect to decrypt that?

The PCBC mode also does not output this construct as part of the ciphertext but feeds it as input to the block cipher encryption XORed with a plaintext block.