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If, as can be reasonably inferred from the question, a fresh random $k$ is chosen on each invocation of $G$, then $G$ is not a pseudorandom generator because it is not deterministic. (A pseudorandom generator by definition is a deterministic algorithm.) If $k$ is fixed, then more information would be needed. For example, is $k$ always the same, or is a ...


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To give this question its deserved answer, I’ll repeat what Ricky Demer noted in his comment: $$G(x \oplus 1^s) = F(k,x \oplus 1^s) \oplus F(k,x \oplus 1^s \oplus 1^s) \\ \downarrow \\ F(k,x \oplus 1^s) \oplus F(k,x \oplus 1^s \oplus 1^s) = F(k,x \oplus 1^s) \oplus F(k,x \oplus 0^s) \\ \downarrow \\ F(k,x \oplus 1^s) \oplus F(k,x \oplus 0^s) = F(k,x ...


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There is quite a bit of confusion in your question. First, differentiate between the real and ideal models. The adversary in the ideal model sends the adversary's input and gets its output (and can also sometimes determine if the honest party gets output, depending on the model). We often call the ideal adversary a "simulator" since this is how we build the ...


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The objective of the simulator is to make the simulated world (often called the ideal world) indistinguishable from the real world (running the actual protocol). See my write-up on the UC framework here for more detail. In the proof setup, the entity attempting to distinguish between the two worlds is often assumed to provide the inputs to the parties. That ...


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$SIM_s$ can do that, but it doesn't need to. $\:$ The distinguisher chooses the parties' inputs.


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Before answering the actual question, I will offer some general advice. It is important to pay attention, both in class and to the textbook you are reading. If learning how to solve such exercises is a key goal of the course, such solutions have very probably been discussed at length in class. Moreover, your textbook also has proof examples, and in this ...


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The relevant part of Neven et al is this: What this means for practice is that one should not instantiate the hash function with a Merkle-Damgård iteration of an $n$-bit compression function. Instead, one should probably simply truncate the output of a $2n$-bit hash function to $n$ bits. (Such a method would in our situation be reminiscent of Lucks’ ...


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"simulator": That's a definition of security in a model that is related to but weaker than the universal composability framework (thanks to Yehuda Lindell for making that clear and you can look at the paper in his comment). You could also look up the wiki link and I think there are also several question on this site. As @Yehuda Lindell mentions in a ...


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There are a very large number of books that have never been scanned, and most of those which have are full of garbage characters and/or are usually scanned into pdf as images, which makes them unusable. If I used an unusual book, transcribed it in text, and wrote a program which took each letter of each word and put them into a numbered database, and then ...


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The simplest example I know of is actually for a pathological case. Namely, it is presented in Chapter 2 of the book of Hazay and Lindell as an example of a two-party MPC protocol which is secure against a malicious adversary but not against a semi-honest one (in the classical sense, for this reason they prefer the notion of augmented semi-honest ...


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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 ...



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