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3

The scheme is secure against chosen-plaintext attacks up to $2^{|R|/2}$ queries. Indeed, given this number of queries, it is likely that every encryption call yields a new value $R$, which has never used as part of the permutation input. However, when this bound is reached, some problems occur. Suppose you encrypt the same message $M$ as many as ...

3

At some level, there is no essential difference. Certainly, there is no difference in the distribution on the random variable $O$ vs $f$. However, there is a potential difference in how the terms are typically used. If we say that $O$ is a random (bijective) oracle, then we are usually implicitly hinting that it is available to everyone: the legitimate ...

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Given: The attacker can call PRP() and the inverse function prp() on any message of his choosing. PRP is a pseudorandom permutation indistinguishable to the attacker from a random permutation. Assuming R and K are "sufficiently large", perfectly random, and never leaked to the attacker -- in particular, during a chosen-ciphertext attack, the decryptor only ...

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