Asynchronous Complete Secret Sharing (ACSS) is a foundational module for asynchronous networks, playing a critical role in cryptography. It is essential for Asynchronous Secure Multi-Party Computation (AMPC) and, with termination, is widely applied in Validated Asynchronous Byzantine Agreement (VABA) and Asynchronous Distributed Key Generation (ADKG) to support secure distributed systems. Currently, there are relatively few statistical secure ACSS protocols that can guarantee termination, and their communication complexity is relatively high. To reduce communication complexity, we propose a new multi-receiver signature scheme, ARICP, which supports linear operations on signatures. Leveraging the ARICP scheme and the properties of symmetric polynomials, we propose an ACSS protocol that ensures termination and optimal resilience ( \(t < n / 3\) ) with \(\mathcal {O}(n^{2}\kappa )\) bits per sharing. Compared with the best-known result of ACSS protocols that guarantee termination [CP23], the amortized communication complexity of our protocol is reduced by a factor of \(\mathcal {O}(n)\) .