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What are the differences between:

  1. perfect security
  2. information-theoretic security
  3. semantic security
  4. indistinguishability
  5. Are there any other definitions which are closely related?

Do these security definitions depend on the attack? For example, OTP is perfectly secure against passive attack, and what about an active attack?

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1 and 2 are the same. 4 doesn't speak about a cryptosystem but about probability distribution : for example mu et chi are indistinguishable.

The other (weaker) definitions you can use are

5a Statistical security -> It means that you authorized some negligeable bad events, in which ones the adversary wins the game

5b Computational security -> It means that your security proof is based on a computational problem considered as hard.

These definition doesn't imply a specific attacker, and each time you use this definition, you have to precise the power of the attacker you consider.

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  • 4
    $\begingroup$ This isn't correct. Semantic security and information-theoretic security are quite different. Semantic security implies computational security which is the opposite of information-theoretic security. Also, semantic security only guarantees IND-CPA, not IND-CCA (which is what 5 is talking about). Even 1 and 2 are not the same. While perfect secrecy always implies information-theoretic security, it doesn't work the other way around. A Carter-Wergman MAC provides true information-theoretic security, but perfect secrecy doesn't apply to it. $\endgroup$ – forest Jul 22 at 19:21
  • $\begingroup$ You are right, I edit the post $\endgroup$ – Ievgeni Jul 23 at 7:42

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