PROJECT 1. Linkable anonymous credentials: how to apply self-managed identity to electronic voting with Blockchain and Smart Contracts.

Anonymous attribute-based credentials (ABC) provide the means for the implementation of self-managed identities (SSI) that transfer responsibility for the custody of personal data to the user, and allow them to have control over who, where and when they want to share such data.

Electronic voting systems suffer from a lack of transparency and the need for anonymity. Transparency is achieved with the use of Blockchain and Smart Contracts, but anonymity becomes a matter of trust. Self-managed identities guarantee this need for anonymity, but to a superlative degree, since it is not possible to link different presentations of the same attribute, and therefore does not apply to electronic voting.

Objective:

This project seeks to be able to give an individual the right to do something, preserving their privacy and once this right has been given, eliminate the need for trusted third parties, although ensuring that they can only exercise this right only once.

Thus, the concept of anonymous attributes linkable within the ABC is defined, which guarantee the anonymity and ownership of being unique within a given scope, making these attributes linkable and can be used in electronic voting, preserving anonymity and the property of being unique, even before a malicious user or a collusion between different actors.

As a result of this research, we want to achieve a protocol that ensures anonymity, that is, it is not possible to know who is behind given credentials, but that at the same time these credentials are unique within a given field to be able to detect the repeated use of these credentials. At the same time it is desired to be able to control the number of times that this repeated use can be carried out.

This protocol aims to demonstrate that it is possible to apply it to remote electronic voting based on Blockchain and Smart Contracts.

Actions already carried out:

• Study and design of the theoretical framework
• The first article on Anonymous Non-Reusable Credentials has been published in the indexed journal MDPI Mathematics: Attribute Based Pseudonyms: Anonymous and Linkable Scoped Credentials.
• A second article on Non-Reusable Anonymous Credentials and their real-world application is in the works.

PROJECT 2. Application of Serious Games in education at the UdA.

Objectives:

• Identify and study the use of technology associated with energy saving as a sustainability objective, with the aim of a proposal for the implementation of a serious game.
• Design a serious game and evaluate its feasibility in bringing it into the classrooms at the UdA.
• Carry out a pre and post data collection in the classrooms where it has been implemented.
• Compare the qualitative data obtained, in order to confirm or deny the hypothesis that Serious Games improve the teaching of sustainability objectives, especially those related to energy saving.

Actions already carried out:

• Study and design of the theoretical framework
• Development of the serious Game to be evaluated in the classrooms.

PROJECT 3. Influence of Large Language Models on Critical thinking of university students.

In recent years, large language models (LLM) based on artificial inteligence have experienced significant advances, and their potential to improve learning, teaching and communication in the academic environment has been acknowledged. Critical thinking in the academic field is a relevant topic, especially in the digital age in which we live. It is for this reason that it is considered important to analyze the contribution of language models in students’ critical thinking.

Objectives:

• Design instruments for the analysis of the use of large language models.
• Assess whether these tools encourage students’ critical thinking.
• Design strategies and tools to improve educational content while adapting to these new tools.

Actions developed:

• Design of a validated instrument for the evaluation of the current use of large language models at the University of Andorra.

PROJECT 4: Singularity Theory, Privacy, and Topological Data Analysis

Algebraic Geometry is one of the most active disciplines in Mathematics. Its roots can be found in the works of Hellenistic Greeks (5th century BC) and mathematicians such as René Descartes. The main idea of Algebraic Geometry is to understand geometric figures through algebraic tools: for example, a plane curve is the set of zeros of a polynomial in two variables. Often, these figures have singular points or points where the figure is not smooth, such as a curve with a sharp point or a fold that can be identified visually or simply through their corresponding equations and partial derivatives. Singularity Theory is a subfield of Algebraic Geometry dedicated to the study of these singular points and the information they encode. Topology emerged from Geometry, studying the properties of geometrical figures that are not altered when they are continuously deformed.

Singularity Theory is related to fields such as computer vision and cryptography. Topology is used in Topological Data Analysis. This project aims to study Singularity Theory and its applications, as well as Topological Data Analysis.

Objectives:

• To deepen the study of the relationship between the geometry and topology of plane curves.
• To develop algorithms for Singularity Theory.
• To deepen the study of Topological Data Analysis.
• To develop Cryptographic tools with the help of Algebraic Geometry.