Oblivious Transfer with Access Control : Realizing Disjunction without Duplication

Abstract

Oblivious Transfer with Access Control (AC-OT) is a protocol which allows a user to obtain a database record with a credential satisfying the access policy of the record while the database server learns nothing about the record or the credential. The only AC-OT construction that supports policy in disjunctive form requires duplication of records in the database, each with a different conjunction of attributes (representing one possible criterion for accessing the record). In this paper, we propose a new AC-OT construction secure in the standard model. It supports policy in disjunctive form directly, without the above duplication issue. Due to the duplication issue in the previous construction, the size of an encrypted record is in $O(\prod_{i=1}^{t}{n_i})$ for a CNF policy $(A_{1,1} \vee \ldots \vee A_{1,n_1}) \wedge \ldots \wedge (A_{t,1} \vee \ldots \vee A_{t,n_t})$ and in $O(\binom{n}{k})$ for a k-of-n threshold gate. In our construction, the encrypted record size can be reduced to $O(\sum_{i=1}^{t}{n_i})$ for CNF form and O(n) for threshold case.