Functional encryption

Functional encryption

General
Designers	Amit Sahai, Brent Waters, Dan Boneh, Shafi Goldwasser, Yael Kalai
Derived from	Public-key encryption
Related to	Homomorphic encryption

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

Formal definition

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

• $(\text{pk},\text{msk})\leftarrow \mathsf{\text{𝖲𝖾𝗍𝗎𝗉}}(1^{\lambda })$: creates a public key $\text{pk}$ and a master secret key $\text{msk}$.
• $\text{sk}\leftarrow \mathsf{\text{𝖪𝖾𝗒𝗀𝖾𝗇}}(\text{msk},f)$: uses the master secret key to generate a new secret key $\text{sk}$ for the function $f$.
• $c\leftarrow \mathsf{\text{𝖤𝗇𝖼}}(\text{pk},x)$: uses the public key to encrypt a message $x$.
• $y\leftarrow \mathsf{\text{𝖣𝖾𝖼}}(\text{sk},c)$: uses secret key to calculate $y=f(x)$ where $x$ is the value that $c$ encrypts.

The security of FE requires that any information an adversary learns from an encryption of $x$ is revealed by $f(x)$. Formally, this is defined by simulation.

Applications

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.

History

Functional encryption was proposed by Amit Sahai and Brent Waters in 2005 and formalized by Dan Boneh, Amit Sahai and Brent 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.