Homomorphic Message Authentication Code (HMAC) protects communications networks from pollution attacks by verifying every message. However, complex verification processes hinder current schemes from adoption, especially for large-scale systems. We introduce Low-Complexity Homomorphic Message Authentication Code, reducing verification complexity and significantly accelerating the process by employing advanced verification methods across multiple nodes. LC-HMAC leverages batch verifications and incorporates previous verification results, resulting in a more efficient verification. Simulations demonstrate that the best LC-HMAC variation, Adversary Rate-based Verification (ARV), reduces the added latency by up to 32.47% and 40%, respectively, compared to its counterpart Batch Verification (BV) and the state-of-the-art Single Packet Verification (SPV).