2012 | OriginalPaper | Buchkapitel
Functional Encryption for Regular Languages
verfasst von : Brent Waters
Erschienen in: Advances in Cryptology – CRYPTO 2012
Verlag: Springer Berlin Heidelberg
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We provide a functional encryption system that supports functionality for regular languages. In our system a secret key is associated with a Deterministic Finite Automata (DFA)
M
. A ciphertext CT encrypts a message
m
and is associated with an
arbitrary length
string
w
. A user is able to decrypt the ciphertext CT if and only if the DFA
M
associated with his private key accepts the string
w
.
Compared with other known functional encryption systems, this is the first system where the functionality is capable of recognizing an unbounded language. For example, in (Key-Policy) Attribute-Based Encryption (ABE) a private key SK is associated with a single boolean formula
φ
which operates over a
fixed
number of boolean variables from the ciphertext. In contrast, in our system a DFA
M
will meaningfully operate over an arbitrary length input
w
.
We propose a system that utilizes bilinear groups. Our solution is a “public index” system, where the message
m
is hidden, but the string
w
is not. We prove security in the selective model under a variant of the decision ℓ-Bilinear Diffie-Hellman Exponent (BDHE) assumption that we call the decision ℓ-Expanded BDHE problem.