Functional encryption

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Functional encryption
General
DesignersAmit Sahai, Brent Waters, Dan Boneh, Shafi Goldwasser, Yael Kalai
Derived fromPublic-key encryption
Related toHomomorphic 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)←Setup(1λ): creates a public key pk and a master secret key msk.
  • sk←Keygen(msk,f): uses the master secret key to generate a new secret key sk for the function f.
  • c←Enc(pk,x): uses the public key to encrypt a message x.
  • y←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 ⊥ otherwise. Similarly, in the ABE case, define F(k,x)=x when k encodes attributes with permission to decrypt and ⊥ 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.[1][4][5][6]

References

  1. ↑ 1.0 1.1 Goldwasser, Shafi; Kalai, Yael; Ada Popa, Raluca; Vaikuntanathan, Vinod; Zeldovich, Nickolai (2013) (in en). Reusable garbled circuits and succinct functional encryption - Stoc 13 Proceedings of the 2013 ACM Symposium on Theory of Computing. New York, NY, USA: ACM. pp. 555–564. ISBN 978-1-4503-2029-0. https://books.google.com/books?id=w-39uAEACAAJ&pg=PA555. 
  2. ↑ Amit Sahai; Brent Waters (2005). "Advances in Cryptology". in Ronald Cramer (in en). EUROCRYPT 2005: 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. Springer. pp. 457–473. ISBN 978-3-540-25910-7. https://books.google.com/books?id=HrCI4ZyuZL0C. 
  3. ↑ Boneh, Dan; Amit Sahai; Brent Waters (2011). "Functional Encryption: Definitions and Challenges". Proceedings of Theory of Cryptography Conference (TCC) 2011. http://eprint.iacr.org/2010/543.pdf. 
  4. ↑ Gorbunov, Sergey; Hoeteck Wee; Vinod Vaikuntanathan (2013). "Attribute-Based Encryption for Circuits". Proceedings of STOC. 
  5. ↑ Sahai, Amit; Brent Waters (2012). "Attribute-Based Encryption for Circuits from Multilinear Maps". http://eprint.iacr.org/2012/592.pdf. 
  6. ↑ Goldwasser, Shafi; Yael Kalai; Raluca Ada Popa; Vinod Vaikuntanathan; Nickolai Zeldovich (2013). "Advances in Cryptology – CRYPTO 2013". 8043. 536–553. doi:10.1007/978-3-642-40084-1_30. ISBN 978-3-642-40083-4. 



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