Paper 2014/225

Adaptively Secure Functional Encryption for Finite Languages from DLIN Assumption

Tapas Pandit and Rana Barua

Abstract

In this paper, we present Functional Encryption (FE) schemes for finite languages from standard static assumption, viz., \textit{Decisional Linear} (DLIN) assumption. These finite languages are described by Deterministic Finite Automatas (DFAs). Our first scheme is ciphertext-policy functional encryption (CP-FE), where a key $\sk_w$ is labeled with a string $w$ over a fixed alphabet $\Sigma$ and a ciphertext $\cipher_\amn$ is associated with a DFA $\amn$ over the same alphabet $\Sigma$. The key $\sk_w$ can extract the message from the ciphertext $\cipher_\amn$ if the DFA $\amn$ accepts the string $w$. This CP-FE scheme is constructed based on attribute-based encryption (ABE) structure of Okamoto-Takashima in Asiacrypt, 2012. To achieve the adaptive security, we put bounds on number of occurrences of any symbol in a string and in the set of transition tuples of a DFA. Due to this restriction, the size of key space (where the keys are indexed with strings) is reduced to finite. Hence, the functional scope of any DFA in our system can capture only finite language. Similarly, we obtain our second adaptively secure FE scheme in key-policy flavor from DLIN assumption. Both the schemes are shown to be secure in the standard model.