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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/220231
Criptografia postquàntica LWE
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L’objectiu d’aquest treball és establir un marc teòric per als criptosistemes basats en reticles, especialment aquells basats en el problema Learning With Errors (LWE). Aquests criptosistemes postquàntics ofereixen una alternativa prometedora a aquells que depenen del problema de factorització d’enters o el problema del logaritme discret, ja que es consideren segurs contra atacs tant clàssics com quàntics. El treball explora algorismes clau com el Lenstra–Lenstra–Lovász (LLL), que comprometen la seguretat dels criptosistemes basats en reticles. També presenta un enfocament pràctic per atacar el LWE a través de la tècnica d’embediment de Kannan i l’LLL.
The aim of this study is to establish a theoretical framework for lattice-based cryptosystems, especially those based on the Learning With Errors (LWE) problem. These postquantum cryptosystems offer a promising alternative to those reliant on the integer factorization problem or the discrete logarithm problem, as they are thought to be secure against both classical and quantum attacks. This project explores key algorithms such as the Lenstra–Lenstra–Lovász (LLL), which compromise the security of lattice-based cryptosystems. It also presents a practical approach to attack LWE through Kannan’s embedding technique and LLL.
The aim of this study is to establish a theoretical framework for lattice-based cryptosystems, especially those based on the Learning With Errors (LWE) problem. These postquantum cryptosystems offer a promising alternative to those reliant on the integer factorization problem or the discrete logarithm problem, as they are thought to be secure against both classical and quantum attacks. This project explores key algorithms such as the Lenstra–Lenstra–Lovász (LLL), which compromise the security of lattice-based cryptosystems. It also presents a practical approach to attack LWE through Kannan’s embedding technique and LLL.
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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2024, Director: Xavier Guitart Morales
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MARTÍN COLLADO, Belén. Criptografia postquàntica LWE. [consulted: 13 of October of 2026]. Available at: https://hdl.handle.net/2445/220231