Assuring information authenticity is an important issue in the field of information security. A new broadcast authentication protocol is proposed. The protocol is based on time synchronization and uses chains constructed with the squaring function. The proposed solution is efficient for transmissions over long periods of time since the chains have an unbounded length. The protocol assures information authenticity at the reduced cost of almost one modular multiplication for each broadcasted packet. Time synchronization issues are discussed and the security of the protocol is equivalent to factoring since the squaring function is used. A failure mode analysis of the protocol is done; this is also an aspect of novelty and applies to other protocols based on time synchronization as well.