The Internet of Things (IoT) vision is a groundbreaking networking evolution that connects all things that were not meant to be connected to the Internet. Thus, identification technologies and Internet-enabled wireless sensor nodes will be incorporated in homes, cities, vehicles, watches, etc. making them uniquely identified and able to process and communicate information via Internet. Hence, the emergence of the Internet of Things paradigm will bring a lot of smartness to our daily life and will improve the way people monitor their goods, expenses, environment and health status. The smart connected things in the IoT interact with each other and/or with the regular Internet hosts according to two communications styles: Thing-to-Thing(s) (T2T) and Human-to-Thing (H2T). Enabling security for such communications is a real issue especially in H2T interactions. This is mainly due to scarce resources of the connected objects and the asymmetric nature of the communications between those smart things and the ordinary Internet hosts. In this paper we address this problematic and we propose an asymmetric security model that mitigates H2T communication heterogeneities and provides reasonable security costs.

The Internet of Things (IoT) vision is a groundbreaking networking evolution that connects all things that were not meant to be connected to the Internet. Thus, identification technologies and Internet-enabled wireless sensor nodes will be incorporated in homes, cities, vehicles, watches, etc. making them uniquely identified and able to process and communicate information via Internet. Hence, the emergence of the Internet of Things paradigm will bring a lot of smartness to our daily life and will improve the way people monitor their goods, expenses, environment and health status. The smart connected things in the IoT interact with each other and/or with the regular Internet hosts according to two communications styles: Thing-to-Thing(s) (T2T) and Human-to-Thing (H2T). Enabling security for such communications is a real issue especially in H2T interactions. This is mainly due to scarce resources of the connected objects and the asymmetric nature of the communications between those smart things and the ordinary Internet hosts. In this paper we address this problematic and we propose an asymmetric security model that mitigates H2T communication heterogeneities and provides reasonable security costs.

In this paper, we show that the asymptotic expansion of a double Laplace-type integral with a non-stationary minimum point, located on the boundary of the domain of integration, is governed by the order of contact between the boundary curve and the level curve of the phase through the minimum point. This achievement will enable us to construct complete asymptotic expansions in more general settings. Especially, the problem will be completely solved if the phase and the boundary curve of the domain of integration are analytic near the minimum point.

In this paper, we show that the asymptotic expansion of a double Laplace-type integral with a non-stationary minimum point, located on the boundary of the domain of integration, is governed by the order of contact between the boundary curve and the level curve of the phase through the minimum point. This achievement will enable us to construct complete asymptotic expansions in more general settings. Especially, the problem will be completely solved if the phase and the boundary curve of the domain of integration are analytic near the minimum point.