## Cryptology ePrint Archive: Report 2016/1029

Scalable Attribute-Based Encryption Under the Strictly Weaker Assumption Family

Yuqiao Deng, Ge Song

Abstract: 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.

Category / Keywords: public-key cryptography / KP-ABE; CP-ABE; $k$-BDH assumption family; selective security model; strictly weaker