Many applications widely use broadcast communications (BC) due to their efficiency in simultaneously distributing data to many receivers. More specifically, BC is essential in resource-constrained devices (RCDs) for conserving energy and bandwidth, which are vital for increasing the longevity and performance of RCDs. The three major challenges in BC are source authentication, data integrity and continuous authentication (CA). The first two challenges are effectively addressed in TESLA and its variants. However, achieving CA without incurring overheads on the sender and receiver sides remains an unresolved challenge. In this paper, we propose Infinite (Inf) TESLA++, assisted by Blockchain and smart contracts, to address the CA challenge with minimal overhead at sender and receiver. Our theoretical and simulation analysis demonstrates that Inf-TESLA++ incurs minimal overhead compared to existing protocols while eliminating the need for direct communication between the sender and receiver for synchronization.