This paper describes the design and analysis of a new scheme for the authenticated exchange of confidential information in insecure environments within the Internet of Things, which allows a receiver of a message to authenticate the sender and compute a secret key shared with it. The proposal is based on the concept of a non-interactive zero-knowledge proof, so that in a single communication, relevant data may be inferred to verify the legitimacy of the sender. Besides, the new scheme uses the idea under the Diffie–Hellman protocol for the establishment of a shared secret key. The proposal has been fully developed for platforms built on the Android Open Source Project, so it can be used in any device or sensor with this operating system. This work provides a performance study of the implementation and a comparison between its promising results and others obtained with similar schemes.