Modelo matemático de transmissão da COVID-19 cifrado com Fully Homomorphic Encryption

• Autor(a) principal: Bernine, Elaine
• Data de Publicação: 2021
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/334
• topic: Covid-19; Processamento seguro; Criptografia homomórfica; Privacidade; CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO

The study, development, and application of Fully Homomorphic Encryption (FHE) schemes have been of great importance for the digital age we live in, because through them it is possible to have safe data storage and processing. This work presents a study of FHE schemes with a real implementation to deal with a privacy problem, a priori, to process the results of exams, with security and privacy, by using encryption. In this case study we consider the features present in the application Coronavirus SUS and its use by a large part of the Brazilian population. The application works by having users provide information regarding whether or not they are infected by the disease, if one user meets an infected user, the application issues an alert to the user susceptible to the disease. Thus, the data is passed on to the Ministry of Health of Brazil and accounted for. Through this encrypted data, we can generate forecasts of the next days of the pandemic, such forecasts include estimates for peak weeks of the disease. While writing this dissertation, we discussed the fundamental mathematical concepts for understanding Lattice, as well as three cryptosystems generated by Learning with Errors (LWE) and Ring Learning with Errors (RLWE) (schemes belonging to the Lattice family). Subsequently, we made the construction of a mathematical model for the COVID-19 transmission process, being represented by a Ordinary Differential Equations (ODE) system. Moreover, we developed a program capable of carrying out the operations present in the ODE system in a homomorphic way, with the help of the SEAL library, and verified its effectiveness. We emphasize that, in order to use the Brakerski, Fan e Vercauteren (BFV) scheme, implemented in the SEAL library, we deal with some limitations imposed by this scheme, since this scheme will only accept whole values as input, and the maximum value of the ciphertext and of course be 260.