Functional encryption explained

Functional encryption
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:( pk , msk ) \leftarrow sf{Setup}(1 ^{λ)}

creates a public key

pk and a master secret key msk .sk \leftarrow sf{Keygen}( msk , f)

uses the master secret key to generate a new secret key

sk for the function f .c \leftarrow sf{Enc}( pk , x)

uses the public key to encrypt a message

x .y \leftarrow sf{Dec}( 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.^[1]

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^[2] and formalized by Dan Boneh, Amit Sahai and Brent Waters in 2010.^[3] 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.^{[4] [5] [6]}

Notes and References

1. Book: Reusable garbled circuits and succinct functional encryption - Stoc 13 Proceedings of the 2013 ACM Symposium on Theory of Computing. Goldwasser. Shafi. Kalai. Yael. Ada Popa. Raluca. Vaikuntanathan. Vinod. Zeldovich. Nickolai. ACM. 2013. 978-1-4503-2029-0. New York, NY, USA. 555–564. en.
2. Advances in Cryptology . 457–473 . Amit Sahai . Brent Waters . Fuzzy Identity-Based Encryption . EUROCRYPT 2005: 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. 2005 . Ronald Cramer . Springer . 978-3-540-25910-7. en. 2005926095 .
3. Boneh. Dan . Amit Sahai . Brent Waters. Functional Encryption: Definitions and Challenges. Proceedings of Theory of Cryptography Conference (TCC) 2011. 2011.
4. Gorbunov. Sergey . Hoeteck Wee . Vinod Vaikuntanathan. Attribute-Based Encryption for Circuits. 2013. Proceedings of STOC.
5. Web site: Sahai. Amit. Brent Waters. Attribute-Based Encryption for Circuits from Multilinear Maps. 2012 . 1210.5287 .
6. Goldwasser. Shafi . Yael Kalai . Raluca Ada Popa . Vinod Vaikuntanathan . Nickolai Zeldovich. Advances in Cryptology – CRYPTO 2013 . How to Run Turing Machines on Encrypted Data . Crypto 2013. Lecture Notes in Computer Science . 2013. 8043 . 536–553 . 10.1007/978-3-642-40084-1_30 . 978-3-642-40083-4 . http://eprint.iacr.org/2013/229.pdf. free . 1721.1/91472 . free .