Scalable Attribute-Based Encryption Under the Strictly Weaker Assumption Family

Attribute-Based Encryption (ABE) is a special type of public key encryption that allows users to share sensitive data efficiently through fine-grained access control. The security involved in existing ABE systems is currently insufficient. These systems are usually built on the Decisional Bilinear Diffie-Hellman (DBDH) assumption or the q-type DBDH assumption, which is stronger than the DBDH assumption. However, once the DBDH assumption is unsecure, all concerned ABEs become vulnerable to threats. To address this problem, the k-BDH assumption family proposed by Benson et al. is adopted. Any assumption in the k-BDH assumption family is associated with parameter k and becomes strictly weaker as k increased. We propose a framework to implement Ciphertext-Policy Attribute Based Encryption (CP-ABE) under the arbitrary assumption in the k-BDH assumption family. When the k′-BDH assumption in the k-BDH assumption family becomes unsecure, where k′-BDH is the assumption on which our ABE relies, the scheme can be shifted to rely on the l′-BDH assumption instead, where l′ > k′. This condition guarantees security as the underlying assumption of our scheme becomes weaker. In addition, we define the formal security model of our schemes and prove the security of CP-ABE in the selective attribute model.