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In the paper about ABE (like this), the access structure is defined as follow:

Let ${P_1,P_2,...,P_n}$ be a set of parties. A collection $A⊆2^{\{P_1,P_2,...,P_n\}}$ is monotone if $∀B,C$: if $B∈A$ and $B⊆C$ then $C∈A$ ...

What is the meaning of this notation: $2^{\{P_1,P_2,...,P_n\}}$? Can you give some example while explaining?

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  • $\begingroup$ you can accept the answer if it satisfactorily answered your question $\endgroup$
    – kodlu
    Jul 31, 2022 at 14:41

1 Answer 1

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It is the powerset of all subsets of $\{P_1,\ldots,P_n\}$. Therefore

$$2^{\{P_1,P_2,P_3\}}=\{\{ \},\{P_1\},\{P_2\},\{P_3\},\{P_1,P_2\},\{P_1,P_3\}, \{P_2,P_3\},\{P_1,P_2,P_3\}\} $$ for example.

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    $\begingroup$ Thanks for the answer. I thought the number 2 indicates certain restrictions about the elements in the subset. But it turns out to be a symbol. $\endgroup$
    – Z. Chen
    Aug 2, 2022 at 7:45

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