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Aumann and Lindell defined covert adversaries in 2009 which is informally adversaries which have a epsilon-deterrence to cheat. Some authors (for ex. John R. Wallrabenstein) have defined similar adversaries and called it rational adversaries who act "rationally". I have not seen a simulation-based definition of rational adversaries.

So, in essence, are covert and rational adversaries same? Can they be used interchangeably?

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As the previous answer says, they are certainly NOT the same. However, there is certainly a connection between them. Specifically, the covert model just says that there is a deterrent parameter $\epsilon$ and the guarantee is that if the adversary tries to cheat then it will be caught with probability at least $\epsilon$. The question that arises is how should $\epsilon$ be set in real life.

Here, rationality can be utilized. Specifically, if you are given the adversary's utility when it succeeds in cheating undetected, its (presumably lower) utility when it doesn't cheat, and its (presumably even lower) utility when it is detected cheating, then you can compute the value of $\epsilon$ that will guarantee that the rational choice is to behave honestly. I'll leave the details of how to compute this to you (it's not difficult).

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  • $\begingroup$ This connection makes sense. However, it seems to me it does not always hold. Suppose there is some way to cheat without detection but resulting in worse utility for the adversary than being honest. This does not seem to be a problem in the rational framework but the protocol would not be secure against covert adversaries in the regular sense. Or am I missing something? $\endgroup$ – Guut Boy Jul 2 '15 at 7:33
  • $\begingroup$ I fully agree and this is what I said; they are NOT the same but ARE related. $\endgroup$ – Yehuda Lindell Jul 2 '15 at 17:44
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No they are different. A covert adversary is essentially just a relaxation of a regular malicious adversary.

Rational cryptography, on other the hand, is a different way of analyzing a cryptographic scheme using game theory. Here the parties of a protocol are seen as rational in a game theoretic sense acting according to some utility.

I am not very well experienced with rational crypto. But as understand it, roughly speaking, the difference is that a covert adversary only cares to break the protocol in any way without getting caught. A rational adversary we can trust to act rationally according to his utility. I.e., he will not try to break the protocol in a way that is to his disadvantage.

Even simpler put you can think of a rational adversary as being clever and a covert as being stupid but careful not to get caught.

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