Homomorphic cryptography applied in SIR and SIRV models

• Autor(a) principal: Lunkes, Aline de Lurdes Zuliani
• Data de Publicação: 2023
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/386
• topic: Criptografia; Criptografia homomórfica; PHE (Criptografia parcialmente homomórfica); FHE (Criptografia totalmente homomórfica); CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO::ANALISE DE ALGORITMOS E COMPLEXIDADE DE COMPUTACAO

In this work, we deal with the theoretical calculation of the complexities of the Partial Homomorphic Encrypt (PHE) and Fully Homomorphic Encrypt (FHE) schemes. Based on this, we have a strong result in cryptography for security and privacy. Given the Nth degree truncated polynomial ring (NTRU) and Learning with Errors (LWE) algorithms (considered of the best FHE algorithms), the χ distribution, and the error arising from LWE algorithm, we establish the equivalence between NTRU and LWE. In other words, one can break the NTRU if and only if one can break the LWE and vice versa. Finally, yet significant, we present a case study utilizing FHE to numerically solve systems related to the SIR (susceptible-infected-removed population) and SIRV (susceptible-infected-removed- vaccinated population) population models. For this, we use the Forward Euler Method and the Finite Difference Method. These methods were implemented in Python to obtain the desired results based on the dynamics of the populations involved, and by comparing the results obtained with and without the use of encryption, we applied homomorphic encryption to public health data