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Currently I am writing my last assignment about secret sharing. But I don't get clearly about adversary. I know this seems so basic understanding in secret sharing. But I couldn't get references that clearly definite adversary. Moreover, what is passive attack and active attack ? What's the differences ?

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Formally, an adversary is simply a (probabilistic) algorithm, which we usually assume to run in polynomial time in $n$, the security parameter. From a more intuitive point of view, an adversary is the model of an attacker on the real life, since every attacker follows an strategy that boils down to an algorithm.

Now, at a high level, a passive attack is an attack where the adversary simply "sees" the information (encrypted data, signatures, etc.) and try to find the secret data from the information gathered. By contrast, in an active attack, the adversary has the ability to "interact" somehow (for instance, by encrypting messages of his choice or even decrypting messages of his choice).

Of course, each one of these notions has its formalization (e.g. Computational indistinguishability, CPA-security, CCA-security).

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    $\begingroup$ It might help to say that informally, the adversary is the bad guy. In secret sharing s/he might have a variety of goals, like guessing the secret, or preventing reconstruction of the right secret. The formal adversary in the question is a model of the informal one, and the tools s/he might use. $\endgroup$ – fgrieu Mar 31 '17 at 10:24

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