Consensus is fundamental for distributed systems since it underpins key functionalities of such systems ranging from distributed information fusion, decision-making, to decentralized control. In order to reach an agreement, existing consensus algorithms require each agent to exchange explicit state information with its neighbors. This leads to the disclosure of private state information, which is undesirable in cases where privacy is of concern. In this paper, we propose a novel approach that enables secure and privacy-preserving average consensus in a decentralized architecture in the absence of an aggregator or third-party. By leveraging partial homomorphic cryptography to embed secrecy in pairwise interaction dynamics, our approach can guarantee consensus to the exact value in a deterministic manner without disclosing a node's state to its neighbors. In addition to enabling resilience to passive attackers aiming to steal state information, the approach also allows easy incorporation of defending mechanisms against active attackers which try to alter the content of exchanged messages. Furthermore, in contrast to existing noise-injection based privacy-preserving mechanisms which have to reconfigure the entire network when the topology or number of nodes varies, our approach is applicable to dynamic environments with time-varying coupling topologies. This secure and privacy-preservation approach is also applicable to weighted average consensus as well as maximum/minimum consensus under a new update rule. The approach is light-weight in computation and communication. Implementation details and numerical examples are provided to demonstrate the capability of our approach.