Defesa de Tese de Doutorado: Homomorphic Cryptography Applied in SIR and SIRV Models

Orientadores:
Fábio Borges de Oliveira - Laboratório Nacional de Computação Científica - LNCC

Banca Examinadora:
Fábio Borges de Oliveira - Laboratório Nacional de Computação Científica - LNCC (presidente)
Renato Portugal - Laboratório Nacional de Computação Científica - LNCC
Raphael Carlos Santos Machado - Universidade Federal Fluminense - UFF
Franklin de Lima Marquezino - Universidade Federal do Rio de Janeiro - UFRJ/COPPE
Pedro Carlos da Silva Lara - Centro Federal de Educação Tecnológica Celso Suckow da Fonseca - CEFET/RJ

Suplentes:
Bruno Richard Schulze - Laboratório Nacional de Computação Científica - LNCC
Max Mühlhäuser - TU Darmstadt

Resumo:

In this work we deal with the theoretical calculat ion of the complexities of the Partial Homomorphic Encrypt (PHE) and Fully Homomorphic Encrypt (FHE) schemes. Based on this, we found a more secure encryption scheme to numerically solve systems related to the SIR (susceptible-infected-removed population) and SIRV (susceptible-infected-removedvaccinated population) models. For this, we use the Forward Euler Method and the Finite Difference Method. These methods allow us to implement them in Python to obtain the desired results based on the dynamics of the populations involved, and the comparison of results obtained with and without the use of encryption, that is, we apply homomorphic encryption to public health data. Finally, yet equally significant, we have a strong result in cryptography for security and privacy. Given the NTRU and LWE algorithms (considered of the best FHE algorithms), the χ distribution, and the error arising from LWE, we arrive at the equivalence of breaking the NTRU trapdoor attack if and only if we brea k the LWE trapdoor attack.