This paper addresses the challenge of best arm identification in stochastic multi-armed bandit (MAB) models under privacy-preserving constraints, such as in dynamic spectrum access networks where secondary users must privately detect underutilized channels. While previous network security research has explored securing MAB algorithms through techniques such as homomorphic encryption or differential privacy, these methods often suffer from high computational overhead or introduce noise that strictly decreases accuracy. In contrast, this work focuses on lightweight solutions that ensure data confidentiality without compromising the accuracy of best arm identification. We introduce two secure protocols that leverage additive secret sharing and threshold secret sharing. The proposed model, employing aggregation nodes and a comparator node, securely distributes computations to prevent any entity from accessing complete reward or ranking data. Furthermore, the protocol ensures resistance to collusion and fault tolerance, while maintaining computational efficiency. These contributions establish a scalable and robust framework for privacy-preserving best arm identification, offering practical and secure solutions that use MAB methods for network security.