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# Functional Encryption for Regular Languages

• Brent Waters
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7417)

## Abstract

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 $$\text {CT}$$ encrypts a message m and is associated with an arbitrary length string w. A user is able to decrypt the ciphertext $$\text {CT}$$ 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 $$\text {SK}$$ is associated with a single boolean formula $$\phi$$ 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 $$\ell$$-Bilinear Diffie-Hellman Exponent (BDHE) assumption that we call the decision $$\ell$$-Expanded BDHE problem.

## Keywords

Random Oracle Regular Language Public Parameter Deterministic Finite Automaton Challenge Ciphertext
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© International Association for Cryptologic Research 2012 2012

## Authors and Affiliations

1. 1.The University of Texas at AustinAustinUSA
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