Threshold Ciphertext Policy Attribute-Based Encryption with Constant Size Ciphertexts

In PKC 2010, Herranz

et al

. proposed the first ciphertext policy attribute-based encryption (CP-ABE) scheme with constant size ciphertexts for threshold predicates. However, their scheme was only secure against chosen plaintext attacks (CPA), which was impossible to obtain security against chosen ciphertext attacks (CCA) in the standard model, and they left open the following three problems for CP-ABE schemes with constant size ciphertexts, i.e., how to achieve full security (i.e., not only the selective security), CCA security in the standard model, and security reduction to a more standard mathematical problem. In this paper, we answer the last two of these three problems affirmatively. Towards our goal, we first design a CPA secure threshold CP-ABE scheme, which can be further upgraded to the CCA security. The security of our schemes can be proved under the decisional

q

-Bilinear Diffie-Hellman Exponent (

q

-BDHE) assumption in the selective model. To the best of our knowledge, this is the first construction of CCA secure CP-ABE scheme with constant size ciphertexts that can support flexible threshold access structure in the standard model.