Functional encryption (FE) is a generalization of

public-key encryption Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic alg ...

in which possessing a secret key allows one to learn a function of what the

ciphertext In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext ...

is encrypting.

Formal definition

More precisely, a functional encryption scheme for a given functionality

f

consists of the following four algorithms: *

(\text, \text) \leftarrow \textsf(1^\lambda)

: creates a public key

\text

and a master secret key

\text

. *

\text \leftarrow \textsf(\text, f)

: uses the master secret key to generate a new secret key

\text

for the function

f

. *

c \leftarrow \textsf(\text, x)

: uses the public key to encrypt a message

x

. *

y \leftarrow \textsf(\text, c)

: uses secret key to calculate

y = f(x)

where

x

is the value that

c

encrypts. The

security" \n\n\nsecurity.txt is a proposed standard for websites' security information that is meant to allow security researchers to easily report security vulnerabilities. The standard prescribes a text file called \"security.txt\" in the well known locat ...

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 ID-based encryption, or identity-based encryption (IBE), is an important primitive of ID-based cryptography. As such it is a type of public-key encryption in which the public key of a user is some unique information about the identity of the use ...

(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 Amit Sahai (born 1974) is an American computer scientist. He is a professor of computer science at UCLA and the director of the Center for Encrypted Functionalities. Biography Amit Sahai was born in 1974 in Thousand Oaks, California, to parents ...

and Brent Waters in 2005 and formalized by Dan Boneh,

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.

References

{{reflist Cryptographic_primitives