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In order for the whole system to work, one has to postulate that:
:<math> \forall m \in \mathcal{M}, ID \in \left\{0,1\right\}^*: \mathrm{Decrypt}\left(\mathrm{Extract}\left(\mathcal{P}, K_m, ID\right), \mathcal{P}, \mathrm{Encrypt}\left(\mathcal{P}, m, ID \right) \right) = m </math>
==Encryption schemes==
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