Secure aggregation enables federated learning (FL) to perform collaborative training of clients from local gradient updates without exposing raw data. However, existing secure aggregation schemes inevitably perform an expensive fresh setup per round because each client needs to establish fresh input-independent secrets over different rounds. The latest research, Flamingo (S&P 2023), designed a share-transfer-based reusable secret key to support the server continuously performing multiple rounds of aggregation. Nevertheless, the share transfer mechanism it proposed can only be achieved with P probability, which has limited reliability. To tackle the aforementioned problems, we propose a more reliable and anonymously authenticated scheme called Chu-ko-nu for multi-round secure aggregation. Specifically, in terms of share transfer, Chu-ko-nu breaks the probability P barrier by supplementing a redistribution process of secret key components (the sum of all components is the secret key), thus ensuring the reusability of the secret key. Based on this reusable secret key, Chu-ko-nu can efficiently perform consecutive aggregation in the following rounds. Furthermore, considering the client identity authentication and privacy protection issue most approaches ignore, Chu-ko-nu introduces a zero-knowledge proof-based authentication mechanism. It can support clients anonymously participating in FL training and enables the server to authenticate clients effectively in the presence of various attacks. Rigorous security proofs and extensive experiments demonstrated that Chu-ko-nu can provide reliable and anonymously authenticated aggregation for FL with low aggregation costs, at least a 21.02% reduction compared to the state-of-the-art schemes.