Threshold public key encryption scheme resilient against continual leakage without random oracles

Threshold public key encryption allows a set of servers to decrypt a ciphertext if a given threshold of authorized servers cooperate. In the setting of threshold public key encryption, we consider the question of how to correctly decrypt a ciphertext where all servers continually leak information about their secret keys to an external attacker. Dodis et al. and Akavia et al. show two concrete schemes on how to store secrets on continually leaky servers. However, their constructions are only interactive between two servers. To achieve continual leakage security among more than two servers, we give the first threshold public key encryption scheme against adaptively chosen ciphertext attack in the continual leakage model under three static assumptions. In our model, the servers update their keys individually and asynchronously, without any communication between two servers. Moreover, the update procedure is re-randomized and the randomness can leak as well.