# Authentication Based on Non-Interactive Zero-Knowledge Proofs for the Internet of Things
## 1 Introduction  
The Internet of Things (IoT) is a trending concept that arises from the need to monitor and interconnect billions of information devices, typically equipped with sensors, actuators, microprocessors, communication interfaces and/or power sources. New challenges related to wireless security appear in IoT because the most common medium used for communication among hyper-connected devices is wireless. Thus, since most IoT objects have limited processing power, finite memory and low battery life, new lightweight cryptographic algorithms, in terms of processing and memory requirements, are necessary to obtain the efficiency of end-to-end communication and applicability to low-resource devices [1].  
With the advent of increasingly powerful technology that is reduced in size and weight, the security level of the cryptographic schemes that are used in wireless communications has been increasing due to the rise of new algorithms based on harder mathematical problems, such as elliptic curves. In particular, the evolution of networks towards IoT has implied that this process is now accelerated.  
Due to the emergence of this new paradigm of interconnected objects, where the physical dimension mimics the logical dimension, it is necessary to encode more than 100,000 million objects [2], because each person is surrounded by approximately 3000 objects. As previously mentioned, a key aspect to consider is the way of communication between these objects. Thus, the mobile nature and small size of many of these devices that form the IoT usually imply that such a communication is wireless and that the resulting network is established as a mobile _ad hoc_ network (MANET), which is a network composed of mobile devices, wirelessly connected, and generally characterized by properties of auto-configuration.  
Each device that is a member of a MANET can move freely, which involves that the link conditions between different devices can be continuously changing and requires that any node can act as a router for the communications of other nodes. Another important aspect of these networks is that, in general, they can operate independently or be connected to the Internet. When a member of the network is connected to the Internet, usually the network enables Internet access to the other devices that do not have a direct Internet connection.  
Regarding security, in MANETs, many types of threats exist that can affect their use. Two of the most dangerous attacks are against the security of wireless communications through denial-of-service and man in the middle (MitM) attacks.  
The proposal described in this work aims to be applied mainly to IoT devices used in mobile environments, such as vehicles, for example. In particular, this work proposes the design and implementation of a new lightweight cryptographic scheme to enable secure wireless communications in a MANET. It describes the design and analysis of a new scheme based on a non-interactive zero-knowledge proof for the authenticated exchange of confidential information in IoT, which allows a receiver node to authenticate the sender and to compute a shared secret key from the received message.  
This paper is organized as follows. Section 2 introduces a few related works. Some necessary preliminaries are defined in Section 3. Then, a non-interactive zero-knowledge proof authentication scheme is proposed in Section 4. Several applications of the proposed scheme in sensors and IoT are briefly described in Section 5. Security aspects of the proposal are analyzed in Section 6. The performance evaluation is presented in Section 7, followed by a comparative analysis given in Section 8. Finally, Section 9 closes the paper with a few conclusions.