Efficient fully secure attribute-based encryption schemes for general access structures

Abstract

In this paper, we present an efficient ciphertext-policy attribute based encryption (CP-ABE) scheme with "short" ciphertext and a key-policy attribute based encryption (KP-ABE) scheme with "short" key for monotone access structures (MAS) which are fully secure in the standard model over composite order bilinear groups. We obtain our schemes by using a simple "encoding technique", representing the monotone access structure by their minimal sets only, thereby obtaining schemes whose ciphertext size or key size depends on number of minimal sets. Most of the recent CP-ABE/KP-ABE schemes have ciphertext size or key size roughly of the order of the size of the monotone span program (MSP) or the number of attributes. Consequently, our schemes will, in general, have shorter ciphertext or shorter key. To illustrate, we give examples of MAS where the number of minimal sets is constant whereas the size of the corresponding MSP is linear in the number of attributes. Using similar ideas, we show how to obtain a CP-ABE scheme with constant size key and a Hierarchical (H) KP-ABE scheme with constant size ciphertext for arbitrary access structures (not necessarily monotone) which are also fully secure in the standard model under three static assumptions over composite order bilinear groups. To date, for all general policies, the decryption cost is polynomial in the number of qualified rows in the span programs. But in all of our proposed schemes, the decryption cost is contant for general access structures. © 2012 Springer-Verlag.