Functional encryption

Functional encryption is a type of public-key encryption in which possessing a secret key allows one to learn a function of what the ciphertext is encrypting.

More precisely, a functional encryption scheme for a given functionality $F$ consists of the following four algorithms:

• $(pk,msk)\leftarrow Setup(1^{\lambda })$: creates a public key $pk$ and a master secret key $msk$.
• $sk\leftarrow Keygen(msk,k)$: uses the master secret key to generate a new secret key $sk$ for value $k$.
• $c\leftarrow Enc(pk,x)$: uses the public key to encrypt a message $x$.
• $F(k,x)\leftarrow Dec(sk,c)$: uses secret key calculate a function of the value $c$ encrypts.

Functional encryption generalizes several existing primitives including Identity-based encryption (IBE) and Attribute-based encryption (ABE). In the IBE case, define $F(k,x)$ to be equal to $x$ when $k$ corresponds to an identity that is allowed to decrypt, and $\perp$ otherwise. Similarly, in the ABE case, define $F(k,x)=x$ when $k$ encodes attributes with permission to decrypt and $\perp$ otherwise.

Background

Functional encryption was proposed by Sahai and Waters in 2005 and formalized by Boneh, Sahai and Waters in 2010. Until recently, however, most instantiations of Functional Encryption supported only limited function classes such as boolean formulae. In 2012, several researchers developed Functional Encryption schemes that support arbitrary functions.