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The two primary techniques I'm familiar with is structuring a cryptographic primitive as a sequence of games and the universally composable security framework. Sequence of Games The idea here is to represent a protocol/primitive as a game played between an attacker and a challenger. You define a bad event and show through the game that the event happens ...

The encryption scheme in the experiment you describe does not have to be fixed-length. We simply require that the two messages the adversary sends to its oracle have the same length. The restriction is on the adversary, not on the encryption algorithm. So why do we put this requirement on the adversary? The reason is that in every practical encryption ...

You had your finger on it, you do know something about the encryption of two messages of different length before they are actually encrypted: the length of the corresponding ciphertexts. If the setting in which you're using your encryption scheme allows for a maximum message length then you can always pad to make every ciphertext the same size ...

I can't give an example illustrating why leakage must be non-negligible for the utility of the mechanism, but I can give a proof of why leakage must be non-negligible for the utility of the mechanism. Let $\;\; U \: = \: \left\{\langle D,D'\rangle : D,D' \text{ differ in one element}\right\} \;\;\;$. By the triangle inequality, for all $D$ and $D'$, for ...

If M0, and M1 are any 2 m-bit messages, how is it possible that their encryption be equal b? The definition does not say that their encryption is equal b. It says that the function f outputs b. This function is often called distinguisher (or attacker) and he should not be able to distinguish which message M0 or M1 was encrypted. In other words there ...

Suppose Alice has $x$ and Bob has $y$ in your scenario, and let $\pi =(\pi_A, \pi_B)$ be the protocol machines for Alice & Bob respectively. Here is how you would formally define security of the protocol against a corrupt Alice. Define the following algorithms / random variables: ${\sf Real}(\pi, y,\mathcal{A},1^k)$: Internally simulate an instance ...

Informally,if you intercept a cipher-text from a perfectly secure encryption system, you can find a key that causes that cipher-text to decrypt to any message you want ( of the correct length). So without knowing which key the author actually picked, you never learn anything about the message. This holds even if you try every possible key (because all keys ...