Attribute-based encryption (ABE) is crucial for ciphertext access control in cloud settings. In this paper, we evaluate the resilience of classical ABE schemes to specific attacks, ensuring only robust schemes are employed and informing the design of secure ABE schemes. We demonstrate an attribute-key attack on two ciphertext-policy ABE (CP-ABE) schemes using illegitimate private keys. To quantify the security of private keys against collusion, we propose a novel attribute-key security model. At last, we present a hidden-policy CP-ABE (HP-CP-ABE) scheme, proving its selective security and resistance to collusion attacks.

Attribute-based encryption achieves fine-grained access control, especially in a cloud computing environment. In a ciphertext-policy attribute-based encryption (CP-ABE) scheme, the ciphertexts are associated with the access policies, while the secret keys are determined by the attributes. In recent years, people have tried to find more effective access structures to improve the efficiency of encryption systems. This paper presents a ciphertext-policy attribute-based encryption scheme that supports arithmetic span programs. On the composite-order bilinear group, the security of the scheme is proven by experimental sequence based on the combination of composite-order bilinear entropy expansion lemma and subgroup decision (SD) assumption. And, it is an adaptively secure scheme with constant-size public parameters.