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That definition is a standard definition which defines encryption as a function $E$. That function takes two inputs, a $\kappa$ bit key and a $n$ bit message. Hence it is defined over the cartesian product - denoted as $\times$ - over these two sets, i.e. all bitstring of length $\kappa$ and $n$ respectively. It maps - denoted as $\rightarrow$ - to an $n$ ...


3

As one of the authors of the paper, let me give you an answer. The operation $F$ is indeed applied to both $x$ and $x'$. By stating that $\oplus$ is invariant under rotation, we mean that if you first rotate $x$ and $x'$ and take the difference with $\oplus$, you get the same result as if you first take the difference with $\oplus$ and then rotate the ...


1

It contains the equivalence classes represented by $\{1,\ldots,6\}$. To elaborate on Nova's comment below, $\mathbb{Z}_p$ is the collection of congruence classes when you divide by $p$. When $p=7$, two integers represent the same congruence class when they have the same remainder when divided by $7$. As you probably know, the only possible remainders are ...


1

It means $Q$ divides $P-1$. In other words, $P-1$ is a multiple of $Q$.



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