Functional Encryption (FE) is a generalization of public-key encryption in which a decryption key allows a user to learn a function of the encrypted data. Briefly, in functional encryption system for a functionality F(.,.) an authority holding a master-secret key can generate a secret-key that has the right to compute the function F(.,.) on encrypted data. More precisely, using the secret-key the decryptor can compute F(.,.) from encryption of x. In contrast, an adversary gathers only negligible information about x which guarantees the security of the system. It is the generalization of several existing cryptographic primitives including Identity-Based Encryption (IBE) and Attribute-Based Encryption (ABE). For IBE, define F(k, x) to be equal to x when k corresponds to an identity that is allowed to decrypt, and ⟂otherwise. Similarly, for ABE, define F(k,x)=x when k encodes attributes with permission to decrypt and ⟂ otherwise.