Combinatorial Subset Difference Public Key Broadcast Encryption Scheme for Secure Multicast

Public key broadcast encryption is a cryptographic method to securely transmit a message from anyone to a group of receivers such that only privileged users can decrypt it. A secure multicast system allows a user to send a message to a dynamically changing group of users. The secure multicast can be realized by the broadcast encryption. In this paper, we propose a novel combinatorial subset difference (CSD) public key broadcast encryption algorithm which allows a generalized subset different representation in which wildcards can be placed at any position. The proposed CSD is applicable to a secure multicast as well as minimizes the header size compared with existing public key broadcast encryption schemes without sacrificing key storage and encryption/decryption performance. Experimental results show that the proposed CSD scheme not only reduces the ciphertext header size by 17% and 31% but also improves encryption performance (per subset) by 6 and 1.3 times, and decryption performance by 10 and 19 times compared with existing efficient subset difference (SD) and interval schemes, respectively. Furthermore, especially for subsets represented in a non-hierarchical manner, the proposed CSD reduces the number of subsets by a factor of 1000 times compared with SD and interval approaches. We prove semantic security of our proposed CSD scheme under l-BDHE assumption without the random oracle model.