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When designing pseudorandom generators what should one consider? Here is an example pseudorandom generator $F^t : \{0,1\}^n \rightarrow \{0,1\}^{4n}$. I have no idea what it means, so what does it kindly mean? It is one proposal written in a book for the truly random compression function $t : \{0,1\}^{2n} \rightarrow \{0,1\}^n$
Like how would I design one for truly random compression function such as $t : \{0,1\}^{2n} \rightarrow \{0,1\}^n$?
It just defines a function that expands the input size with the output size four times, where the output depends on configuration value $t$ as well. The hash function compresses the input to an output that is half the size (which is not common, usually a hash function outputs a constant size hash).
Here ^ is not a power function. It simply shows how many elements there are sequentially taken from the input set $\{0, 1\}$ - properly formatted it reads $\{0, 1\}^{4 \cdot n}$. So the $x$ in $\{0, 1\}^x$ simply defines an input or output consisting of $x$ bits - with value $0$ or $1$ of course.
n and then outputs 4 times n? Also, how would I design a PRG for the random compression function listed in my question?
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Dec 3 '18 at 0:28
t : {0,1}^2n -> {0,1}^n. The thing is, I didn't know anything about PRGs but just to get things started a PRG always start like F^t : {0,1}^n? The last bit -> {0,1}^xn where x is a number is how it ends right? I just wanna design a PRG for the random compression function. Just out of interest, why is the mentioned random compression function not a block cipher either?
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Dec 3 '18 at 0:37