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6

Let me try to answer your second question, and hopefully shed some light on the first one in doing so. When we encrypt a message, it's because we want to keep something about that message secret. But what is it that we actually want to protect? Let's say the message we're encrypting is AGENT DOE REPORTS 23 UNITS ON BOARD SHIP TO BASE ALPHA, DEPARTED ON ...

3

The proof for the perfect secrecy property of the one time pad is quite simple. It makes use of basic probabilities and it says that: $$Pr[M=m|C=c]=Pr[M=m]$$ for a probability distribution M$\{0,1\}^n$ for the message space and a probability space C for the ciphertext space. Proof: Pr[C=c]=\sum{Pr[C=c|M=m']\cdot Pr[M=m']} =\sum{Pr[K=m'\oplus c]}\cdot ...

3

Since the keys are fixed from beginning (the sub-protocols input are ciphertexts), isn't it possible to give the secret key to the (non-uniform) distinguisher as an extra advice (the only restrictions for the advice is that its bitlength is polynomial in the security parameter), and thus allowing the distinguisher to decrypt? This is up to your security ...

3

The ideal encryption scheme $E$ would be one that, for every ciphertext $C=E(K, M)$, if the key remains secret for the adversary, the probability of identifying $M$ is negligible. Since that is not possible in practice, the second most reasonable approach is to define constraints strong enough to satisfy some definition of security. The $IND-$ notation ...

2

(Note: This answer is based on $k$ being generated by applying a pseudorandom function to a unique message-ID – counter – each time.) It depends how many times you want to encrypt with it. If you want it as a complicated OTP, then it's secure. In order to see this, just ignore the $x$ parts and note that $s_1m \bmod p$ and $s_2m \bmod p$ are to independent ...

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The author does not define hybrid PKE schemes. What is their definition? A hybrid public-key encryption scheme is a scheme that uses public-key encryption along with symmetric encryption to gain speed advantages for long messages. The usual instantiation is to simply encrypt a key for the symmetric scheme and prepend the resulting cipher text. The ...

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