Reparable Threshold Paillier Encryption Scheme for Federated Learning

Abstract Threshold Paillier encryption scheme finds extensive application in the context of federated learning. However, the issue of client dropout frequently arises within the context of federated learning, rendering the conventional threshold Paillier encryption scheme ineffective for data decryption. To address this issue, this paper introduces a (n,k,d) repairable threshold Paillier encryption scheme by combining the repairable Shamir secret-sharing scheme with the Paillier encryption scheme. The proposed scheme has demonstrated several valuable capabilities. Specifically, we initially establish the security of the secret-sharing property of this scheme, namely, any group of k participants can collaboratively recover the private key, while k-1 or fewer participants cannot recover the private key. Moreover, we demonstrate the scheme's ability to handle the client dropout problem, namely, any group of d normal participants can collectively repair the private key segments of dropout clients. Ultimately, we substantiate that the (n,k,d) recoverable threshold Paillier encryption scheme consistently upholds the precision of decryption processes.