Functional encryption

Functional encryption 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.

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

• ${\displaystyle (pk,msk)\leftarrow Setup(1^{\lambda })}$: creates a public key $pk$ and a master secret key ${\displaystyle msk}$.
• ${\displaystyle sk\leftarrow Keygen(msk,k)}$: uses the master secret key to generate a new secret key ${\displaystyle sk}$ for value $k$.
• ${\displaystyle c\leftarrow Enc(pk,x)}$: uses the public key to encrypt a message $x$.
• ${\displaystyle F(k,x)\leftarrow Dec(sk,c)}$: uses secret key to 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 ${\displaystyle F(k,x)}$ 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 ${\displaystyle F(k,x)=x}$ when $k$ encodes attributes with permission to decrypt and $\perp$ otherwise.

Background

Functional encryption was proposed by Amit Sahai and Brent Waters in 2005^[1] and formalized by Dan Boneh, Amit Sahai and Brent Waters in 2010.^[2] 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.^{[3][4][5] [6]}

References

1. Sahai, Amit; Brent Waters (2005). "Fuzzy Identity-Based Encryption" (PDF). Proceedings of Eurocrypt 2005.
2. Boneh, Dan; Amit Sahai; Brent Waters (2011). "Functional Encryption: Definitions and Challenges" (PDF). Proceedings of Theory of Cryptography Conference (TCC) 2011.
3. Goldwasser, Shafi; Yael Kalai; Raluca Ada Popa; Vinod Vaikuntanathan; Nickolai Zeldovich (2013). "Reusable Garbled Circuits and Succinct Functional Encryption" (PDF). Proceedings of STOC 2013.
4. Gorbunov, Serge; Hoeteck Wee; Vinod Vaikuntanathan (2013). "Attribute-Based Encryption for Circuits". Proceedings of STOC.
5. Sahai, Amit; Brent Waters. "Attribute-Based Encryption for Circuits from Multilinear Maps" (PDF).
6. Goldwasser, Shafi; Yael Kalai; Raluca Ada Popa; Vinod Vaikuntanathan; Nickolai Zeldovich (2013). "How to Run Turing Machines on Encrypted Data" (PDF). CRYPTO 2013.