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* '''Extract''': This algorithm is run by the PKG when a user requests his private key. Note that the verification of the [[Authentication|authenticity]] of the requestor and the secure transport of <math>\textstyle d</math> are problems with which IBE protocols do not try to deal. It takes as input <math>\textstyle \mathcal{P}</math>, <math>\textstyle K_m</math> and an identifier <math>\textstyle ID \in \left\{0,1\right\}^*</math> and returns the private key <math>\textstyle d</math> for user <math>\textstyle ID</math>.
* '''Encrypt''': Takes <math>\textstyle \mathcal{P}</math>, a message <math>\textstyle m \in \mathcal{M}</math> and <math>\textstyle ID \in \left\{0,1\right\}^*</math> and outputs the encryption <math>\textstyle c \in \mathcal{C}</math>.
* '''Decrypt''': Accepts <math>\textstyle d</math>, <math>\textstyle \mathcal{P}</math> and <math>\textstyle c \in \mathcal{C}</math> and returns <math>\textstyle m \in \mathcal{M}</math>.
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