Educational technologies refer to the set of digital tools, resources, applications, and methodologies used to facilitate the teaching–learning process. These technologies include software, online platforms, hardware devices (such as tablets, computers, and interactive whiteboards), and, if one wants to give special relevance, as it should be these days, to the issue of inclusion in education, assistive technologies, all aimed at improving access to education, personalizing learning paths, and fostering a more dynamic interaction between students and teachers. This entry explores the integration of educational technologies, highlighting their role in enhancing the teaching–learning process, promoting inclusive and personalized education. It analyses the pedagogical implications of the use of digital technologies, including assistive technologies (which foster learning in a Universal Design for Learning perspective), and the need to train competent teachers to adopt innovative teaching practices. This entry concludes by emphasizing the importance of a shared commitment to prepare future generations for a technologically changing world by creating more dynamic and accessible learning environments, including through virtual reality, augmented reality, and artificial intelligence.

This review explores the current state of public key cryptography based on idempotent semirings, with an emphasis on tropical semirings. It examines key hard problems, such as the tropical discrete logarithm problem, semidirect tropical product problem, the factorization of tropical polynomials, and the matrix power function, that underpin the security of these protocols. Given the significant number of compromised protocols based on tropical semirings, most of which are variations of the Stickel protocol, we present three algorithms and classify schemes of this type. The analysis is further illustrated with a figure that maps the relationships between tropical Stickel’s-like protocols and the attacks targeting them. Additionally, the review provides an in-depth exploration of the vulnerabilities that have led to many tropical semiring-based cryptosystems being compromised. To address these challenges, the review highlights promising alternative approaches, including non-tropical idempotent platforms and non-idempotent options, such as supertropical semirings, which offer potential solutions to overcome known limitations. Furthermore, a discussion on the interplay between tropical cryptography and post-quantum cryptography is presented, raising the following question: what is the future of tropical cryptography?

This review paper examines how Generative AI (GAI) and Large Language Models (LLMs) can transform smart cities in the Industry 5.0 era. Through selected case studies and portions of the literature, we analyze these technologies’ impact on industrial processes and urban management. The paper targets GAI as an enabler for industrial optimization and predictive maintenance, underlining how domain experts can work with LLMs to improve municipal services and citizen communication, while addressing the practical and ethical challenges in deploying these technologies. We also highlight promising trends, as reflected in real-world case studies ranging from factories to city-wide test-beds and identify pitfalls to avoid. Widespread adoption of GAI still faces challenges that include infrastructure and lack of specialized knowledge as a limitation of proper implementation. While LLMs enable new services for citizens in smart cities, they also expose certain privacy issues, which we aim to investigate in this study. Finally, as a way forward, the paper suggests future research directions covering new ethical AI frameworks and long-term studies on societal impacts. Our paper is a starting point for industrial pioneers and urban developers to navigate the complexity of GAI and LLM integration, balancing the demands of technological innovation on one hand and ethical responsibility on the other.

Educational technologies refer to the set of digital tools, resources, applications, and methodologies used to facilitate the teaching–learning process. These technologies include software, online platforms, hardware devices (such as tablets, computers, and interactive whiteboards), and, if one wants to give special relevance, as it should be these days, to the issue of inclusion in education, assistive technologies, all aimed at improving access to education, personalizing learning paths, and fostering a more dynamic interaction between students and teachers. This entry explores the integration of educational technologies, highlighting their role in enhancing the teaching–learning process, promoting inclusive and personalized education. It analyses the pedagogical implications of the use of digital technologies, including assistive technologies (which foster learning in a Universal Design for Learning perspective), and the need to train competent teachers to adopt innovative teaching practices. This entry concludes by emphasizing the importance of a shared commitment to prepare future generations for a technologically changing world by creating more dynamic and accessible learning environments, including through virtual reality, augmented reality, and artificial intelligence.

This review explores the current state of public key cryptography based on idempotent semirings, with an emphasis on tropical semirings. It examines key hard problems, such as the tropical discrete logarithm problem, semidirect tropical product problem, the factorization of tropical polynomials, and the matrix power function, that underpin the security of these protocols. Given the significant number of compromised protocols based on tropical semirings, most of which are variations of the Stickel protocol, we present three algorithms and classify schemes of this type. The analysis is further illustrated with a figure that maps the relationships between tropical Stickel’s-like protocols and the attacks targeting them. Additionally, the review provides an in-depth exploration of the vulnerabilities that have led to many tropical semiring-based cryptosystems being compromised. To address these challenges, the review highlights promising alternative approaches, including non-tropical idempotent platforms and non-idempotent options, such as supertropical semirings, which offer potential solutions to overcome known limitations. Furthermore, a discussion on the interplay between tropical cryptography and post-quantum cryptography is presented, raising the following question: what is the future of tropical cryptography?