Is there a difference in terms of security between

  1. An encrypted stream of bits obtained by encrypting a plaintext concatenated with it's signature

    $ C = E_k(plaintext||\sigma)$

    where $E$ is a symmetric or asymmetric encryption function, II is a concatenation operator and


    where $h$ is a secure MAC (the key is assumed to be the same).

  2. A bit stream obtained by concatenating a ciphertext and the signature over the its corresponding plaintext




  3. A stream obtained by encrypting the ciphertext of the plaintext concatenated with the signature over the respective ciphertext




Also, is there any risk due to using the same key for both encrypting and signing? I don't refer to the cases that do not involve recovering the key through other means other than passive or active attacks.

  • $\begingroup$ Are you talking about MACs or asymmetric signatures? If the latter, which algorithm? And which assumptions do you make about the encryption algorithm? $\endgroup$ Nov 11, 2015 at 20:57
  • $\begingroup$ Asymmetric, RSA. The encryption algorithm can be either symmetric or asymmetric The assumptions are ciphertext indistinguishability: en.wikipedia.org/wiki/Ciphertext_indistinguishability $\endgroup$
    – Sebi
    Nov 11, 2015 at 21:05
  • $\begingroup$ And what assumptions do you make about $h^k$? Is it a secure MAC/PRF? If so, you should call it like that, and not call it hash, since without qualification that generally means an unkeyed hash. $\endgroup$ Nov 11, 2015 at 21:09
  • $\begingroup$ But why? The attacker only sees the ciphertext. Any alteration of it will change bits in the signature making it invalid. Yes, $h^k$ is assumed to be a secure MAC. $\endgroup$
    – Sebi
    Nov 11, 2015 at 21:10
  • 1
    $\begingroup$ The duplicate discusses the difference between your three constructions, assuming different keys are used for encryption and MAC. For the same-key question, see Why can't I use the same key for encryption and MAC? on security.se. $\endgroup$ Nov 11, 2015 at 21:15


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