In this article we extend the results about Gorenstein modules and Foxby duality to a non-commutative setting. This is done in §3 of the paper, where we characterize the Auslander and Bass classes which arise whenever we have a dualizing module associated with a pair of rings. In this situation it is known that flat modules have finite projective dimension. Since this property of a ring is of interest in its own right, we devote §2 of the paper to a consideration of such rings. Finally, in the paper’s final section, we consider a natural generalization of the notions of Gorenstein modules which arises when we are in the situation of §3, i.e. when we have a dualizing module.AMS 2000 Mathematics subject classification: Primary 16D20

The rapid growth of technology has resulted in the deployment of a large number of interconnected devices, resulting in a wide range of new societal services. Wireless sensor networks (WSNs) are a promising technology which is faced with the challenges of operating a large number of sensor nodes, information gathering, data transmission, and providing a means to act in different scenarios such as monitoring, surveillance, forest fire detection, and many others from the civil to military spectrum. The deployment scenario, the nature of the sensor-equipped nodes, and their communication methods make this architecture extremely vulnerable to attacks, tampering, and manipulation than conventional networks. Therefore, an optimal solution to ensure security in such networks which captures the major constraints of the network in terms of energy utilization, secured data transmission, bandwidth, and memory fingerprint to process data is required. This work proposes a fast, reliable, and secure method of key distribution and management that can be used to ensure the integrity of wireless sensor networks’ communications. Moreover, with regards to efficient energy utilization, an improvement of the Low Energy Adaptive Clustering Hierarchy (LEACH) algorithm (a cluster routing protocol that is mainly used in WSN) has been proposed to enhance the networks’ energy efficiency, simplicity, and load-balancing features. Therefore, in this paper, we propose a combination of a distributed key exchange and management methods based on elliptic curve cryptography to ensure security of node communication and an improved routing protocol based on the LEACH protocol to demonstrate better performance in parameters such as network lifespan, dead nodes, and energy consumption.

The influence of Artificial Intelligence in our society is becoming important due to the possibility of carrying out analysis of the large amount of data that the increasing number of interconnected devices capture and send as well as making autonomous and instant decisions from the information that machines are now able to extract, saving time and efforts in some determined tasks, specially in the cyberspace. One of the key issues concerns security of this cyberspace that is controlled by machines, so the system can run properly. A particular situation, given the heterogeneous and special nature of the environment, is the case of IoT. The limited resources of some components in such a network and the distributed nature of the topology make these types of environments vulnerable to many different attacks and information leakages. The capability of Generative Artificial Intelligence to generate contents and to autonomously learn and predict situations can be very useful for making decisions automatically and instantly, significantly enhancing the security of IoT systems. Our aim in this work is to provide an overview of Generative Artificial Intelligence-based existing solutions for the very diverse set of security issues in IoT environments and to try to anticipate future research lines in the field to delve deeper.

Security is a critical challenge for the effective expansion of all new emerging applications in the Internet of Things paradigm. Therefore, it is necessary to define and implement different mechanisms for guaranteeing security and privacy of data interchanged within the multiple wireless sensor networks being part of the Internet of Things. However, in this context, low power and low area are required, limiting the resources available for security and thus hindering the implementation of adequate security protocols. Group keys can save resources and communications bandwidth, but should be combined with public key cryptography to be really secure. In this paper, a compact and unified co-processor for enabling Elliptic Curve Cryptography along to Advanced Encryption Standard with low area requirements and Group-Key support is presented. The designed co-processor allows securing wireless sensor networks with independence of the communications protocols used. With an area occupancy of only 2101 LUTs over Spartan 6 devices from Xilinx, it requires 15% less area while achieving near 490% better performance when compared to cryptoprocessors with similar features in the literature.

As they emerge from the pandemic, universities worldwide are evaluating the adaptations in the education sector during the pandemic and determining their course of action for the future. In this work, drawing on the lessons from four courses across two different universities, a survey of over 300 students, and the literature, we present strategies for successfully implementing a flexible blended education format. The survey revealed that the performance of the cohort taking the course during the pandemic performed nearly the same as the cohorts that took the courses before the pandemic. However, the students did not prefer an entirely virtual format, felt that their social wellbeing was impacted, and preferred a hybrid education model with a lot of supplementary learning material. As a key contribution of this work, we have identified and elaborate on four key pillars for a flexible blended education format, namely, course design, pedagogical strategies incorporating active learning and providing a sense of online community, infrastructure for delivery and training, and incorporating activities that support student wellbeing.