Abstract:

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.

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