## On the Generalizations of Identity-Based Encryption

##### Abstract

Today public-key cryptographic is widely deployed and successfully used but still a major drawback
exists. In fact, from encrypted data a party can either decrypt or cannot learn anything at all about the
message other than intentionally leaked information such as its length. In the recent years, the cloud
computing paradigm has emerged as the new standard to use computing resources, such as storage
devices, that are delivered as a service over a network. In such a scenario, the notion of public key
cryptography is not enough. It would be desirable to specify a decryption policy in the encrypted data
in such a way that only the parties who satisfy the policy can decrypt. In a more general form, we may
want to only give access to a function of the message, depending on the decryptor’s authorization.
Thus, in the last decade researchers have started looking at a more sophisticated type of encryption
called functional encryption. A functionality F is a function F : K × M ! where K is the key
space and M is the message space. In the public-key setting, a functional encryption scheme for F
is a special encryption scheme in which, for every key k 2 K, the owner of the master secret key
msk associated with the master public key mpk can generate a special secret-key skk that allows the
computation of F(k,m) from a ciphertext of m 2 M computed under public key mpk . In other words,
whereas in traditional encryption schemes decryption is an all-or-nothing affair, in functional encryption
it is possible to finely control the amount of information that is revealed by a ciphertext. One of the most
notable example of functional encryption is identity-based encryption first introduced by Shamir as an
alternative to the standard notion of public-key encryption.
In this thesis, we discuss several instantiations of function encryption that can all be seen as generalisations
of identity-based encryption. We improve on previous constructions in terms of performance
and security guarantees. [edited by author]