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1

fkraiem's answer is basically correct, but it only says that $G$ does not match the "syntax" of a PRG. But this is not entirely satisfactory for understanding what's really wrong with $G$ as a PRG. In addition, $G$ may not be pseudorandom. For example, it could be the case that $F_{00\cdots 0}(x) = 0$ for every $x$, i.e., the all-zeros key is a "weak" key ...


1

Because the key-, input- and output-length of $F$ are equal, if the length of the seed $x$ is $n$, there are $2^n$ keys and so $G$ must compute $F$ $2^n$ times and output a string of length $n\cdot 2^n$. Hence, $G$ runs in time exponential in $n$, which means it can't be a pseudorandom generator because a pseudorandom generator is a deterministic ...


3

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 ...


2

In secret sharing, one person typically wants to share a secret. Only that one person knows that secret, so they are the dealer. In MPC, which VIFF implements protocols for, you actually have multiple parties, each with a secret input(s). So, each of these parties is the dealer for their individual secret input(s). In this sense, there is no central dealer ...


1

Just use a small block sized block cipher in counter mode and filter out elements that are out of range.


0

For the definition of pseudorandomness, the family $F$ of functions can be any set of functions at all. But typically we take it to be a set where each function can be described by a rather short key/seed, and where one can efficiently compute the function output given the input (and the key). This is because we want the family $F$ to represent functions ...


2

IKEv2 uses the term PRF to refer to a negotiated keyed random-looking function (for example, possibly HMAC-SHA256). IKEv2 uses the term PRF+ to refer to a specific construction based on that underlying negotiated function, as defined in section 2.13: prf+ is defined as: prf+ (K,S) = T1 | T2 | T3 | T4 | ... where: T1 = prf (K, S | 0x01) T2 = prf (K, T1 | ...



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