Paper 2021/003

Ciphertext Policy Attribute Based Encryption for Arithmetic circuits

Mahdi Mahdavi Oliaee and Zahra Ahmadian

Abstract

Applying access structure to encrypted sensitive data is one of the challenges in communication networks and cloud computing. Various methods have been proposed to achieve this goal, one of the most interesting of which is Attribute-Based Encryption (ABE). In ABE schemes, the access structure, which is defined as a policy, can be applied to the key or ciphertext. Thus, if the policy is applied to the key, it is called the Key Policy Attribute-Based Encryption (KP-ABE), and on the other hand, if it is applied to the ciphertext, it is called the Ciphertext Policy Attribute-Based Encryption (CP-ABE). Since in the KP-ABE, the policy is selected once by a trusted entity and is fixed then, they are not suitable for applications where the policy needs to change repeatedly. This problem is solved in CP-ABE, where the policy is selected by the sender and changed for each message. Furthermore, the access structure should present a strong fine-grained access control. The arithmetic access structure can supply fine-grained access structures stronger than Boolean access structures. We present the first CP-ABE scheme with an arithmetic circuit access policy based on the multilinear maps. First, we outline a basic design and then two improved versions of this scheme, with or without the property of hidden attributes, are introduced. We also define the concept of Hidden Result Attribute Based Encryption (HR-ABE) which means that the result of the arithmetic function will not be revealed to the users. We define a new hardness assumption, called the (k-1)-Distance Decisional Diffie-Hellman assumption, which is at least as hard as the k-multilinear decisional Diffie-Hellman assumption. Under this assumption, we prove the adaptive security of the proposed scheme.