The convexity in triangular norm (for short, ⊗−convexity) is a generalization of Zadeh’s quasiconvexity. The aggregation of two ⊗−convex sets is under the aggregation operator ⊗ is also ⊗−convex, but the aggregation operator ⊗ is not unique. To solve it in complexity, in the present paper, we give some sufficient conditions for aggregation operators preserve ⊗−convexity. In particular, when aggregation operators are triangular norms, we have that several results such as arbitrary triangular norm preserve ⊗ D − convexity and ⊗ a − convexity on bounded lattices, ⊗ M preserves ⊗ H − convexity in the real unite interval [ 0 , 1 ] .

In recent years, cloud storage has become an attractive solution due to its elasticity, availability and scalability. However, the security issue has started to prevent public clouds becoming more popular. Traditional encryption algorithms (both symmetric and asymmetric ones) fail to support achieving effective secure cloud storage due to severe issues such as complex key management and heavy redundancy. Ciphertext-policy attribute-based encryption (CP-ABE) scheme overcomes the aforementioned issues and provides fine-grained access control as well as deduplication features. CP-ABE has become a possible solution to cloud storage. However, its high complexity has prevented it from being widely adopted. This paper parallelises CP-ABE where issues to ensure secured cloud storage are considered and deployed in cloud storage environments. Major performance bottlenecks such as key management and encryption/decryption process are identified and accelerated, and a new AES encryption operation mode is adopted for further performance gains. Experimental results have demonstrated its effectiveness and such design is promising.

Recently, cloud storage has become quite attractive due to its elasticity, availability and scalability. However, the security issue has started to prevent public clouds from getting even more popular. Traditional encryption algorithms (both symmetric and asymmetric ones) fail to help achieve effective secure cloud storage due to their severe issues such as complex key management and heavy redundancy. Ciphertext-Policy Attribute Based Encryption (CP-ABE) scheme overcomes the aforementioned issues and provides fine-grained access control as well as deduplication features. CP-ABE has becomes a possible solution to cloud storage. However, its high complexity has prevented it from being widely adopted. This paper proposes a P-CP-ABE scheme to parallelize CP-ABE and port it to multi-core architecture machines. Major performance bottlenecks such as key management and encryption/decryption process are identified and accelerated. New AES encryption operation mode is adopted for further performance gains. Experimental results have demonstrated its effectiveness.