CCA2-Secure Threshold Broadcast Encryption with Shorter Ciphertexts

In a threshold broadcast encryption scheme, a sender chooses (ad-hoc) a set of n receivers and a threshold t, and then encrypts a message by using the public keys of all the receivers, in such a way that the original plaintext can be recovered only if at least t receivers cooperate. Previously proposed threshold broadcast encryption schemes have ciphertexts whose length is at least n + O(1). In this paper, we propose new schemes, for both PKI and identity-based scenarios, where the ciphertexts’ length is n − t + O(1). The constructions use secret sharing techniques and the Canetti-Halevi-Katz transformation to achieve chosen-ciphertext security. The security of our schemes is formally proved under the Decisional Bilinear Diffie-Hellman (DBDH) Assumption.