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?

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

1 Answer 1


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.

  • 1
    $\begingroup$ 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
    Commented Aug 2, 2022 at 7:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.