H2CT: Asynchronous Distributed Key Generation With High Computational Efficiency and Threshold Security in Blockchain Network

Asynchronous distributed key generation (ADKG) is a strong-robustness key management technology to bootstrap threshold cryptosystems without a global clock, which can enable decentralized security management for threshold digital wallets in blockchain network. However, the high computational cost of existing ADKG protocols makes it difficult to remove the “slow” connotation from the word “asynchronous” in a high-threshold security context. In this paper, we propose a simpler “two-high” ADKG protocol (H2CT) for blockchain to improve the computational efficiency of asynchronous communications while balancing it with threshold security. Concretely, we first construct a computationally efficient asynchronous complete secret sharing (ACSS) scheme using number theory transformation, reducing the computational complexity of share evaluation from O(n2) to O(nlogn) in the dealing phase. To eliminate the negative impact of up to t biased secrets brought by the implicate messages in the agreement phase, we extend the verifiable ACSS scheme to a publicly verifiable ACSS scheme (pvACSS) using Feldman polynomial commitment. Leveraging this enhanced randomness, the matrix computation cost and message size in the remaining phases are reduced to about half that of the existing works, i.e., O(2n2). Finally, considering the high scalability requirements, the network size n is increased to up to 1024 nodes and the results show that our pvACSS and the derived H2CT reduce the runtime by approximately 33.96 seconds and 824.46 seconds respectively over the state-of-the-art. Moreover, we perform simulations on an open-source blockchain testbed, fully demonstrating the efficiency advantages of our H2CT protocol.