Topology discovery is one of the most critical tasks of Software-Defined Network (SDN) controllers. Current SDN controllers use the OpenFlow Discovery Protocol (OFDP) as the de-facto protocol for discovering the underlying network topology. In a previous work, we have shown the functional, performance and security limitations of OFDP. In this paper, we introduce and detail a novel protocol called secure and efficient OpenFlow Discovery Protocol sOTDP. sOFTDP requires minimal changes to OpenFlow switch design, eliminates major vulnerabilities in the topology discovery process and improves its performance. We have implemented sOFTDP as a topology discovery module in Floodlight for evaluation. The results show that our implementation is more secure than OFDP and previous security workarounds. Also, sOFTDP reduces the topology discovery time several orders of magnitude compared to the original OFDP and existing OFDP improvements.