Secure communication
Encryption is a method in which data is rendered hard to read by an unauthorized party. Since encryption methods are created to extremely hard to break, many communication methods either use deliberately weaker encryption than possible, or have backdoors inserted to permit rapid decryption. In some cases government authorities have required backdoors be installed in secret. Many methods of encryption are also subject to "man in the middle" attack whereby a third party who can 'see' the establishment of the secure communication is made privy to the encryption method, this would apply for example to interception of computer use at an ISP. Provided it is correctly programmed, sufficiently powerful, and the keys not intercepted, encryption would usually be considered secure. The article on key size examines the key requirements for certain degrees of encryption security.
Functional encryption
More precisely, a functional encryption scheme for a given functionality formula_1 consists of the following four algorithms:Functional encryption generalizes several existing primitives including Identity-based encryption (IBE) and Attribute-based encryption (ABE).
In the IBE case, define formula_12 to be equal to formula_9 when formula_7 corresponds to an identity that is allowed to decrypt, and formula_15 otherwise.
Similarly, in the ABE case, define formula_16 when formula_7 encodes attributes with permission to decrypt and formula_15 otherwise.