Interaction between lattices and error-correcting codes in cryptography

Author(s)

Rosemberg André da Silva

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Computação
• Defense date: 2011-10-14

Examining board members

Ricardo Dahab; Anderson Clayton Alves Nascimento; Paulo Sergio Licciardi Messeder Barreto; Julio César López Hernández; Reginaldo Palazzo Júnior

• Advisor: Ricardo Dahab

Abstract

Recent results have pointed out the feasibility of reusing cryptographic schemes across the domains of Lattice and Codes, as seen in the work of Kawachi, Tanaka and Xagawa [57] and Cayrel, Lindner, Rueckert and Silva [21] and [22]. These authors have used the similarity between hard problems from each domain, replaced one by the other and applied particular lattice instances in order to obtain good performance. In the present dissertation, we expand the variety of schemes to which such approach is suitable, discussing issues related to performance and security of such adaptations. We also aim to establish worst-case hardness in our schemes, in resemblance to what Ajtai [5] obtained (AU)

• FAPESP's process: 08/07949-8 - Error-Correcting Codes and Lattice Applications to Public-Key Cryptography.
• Grantee: Rosemberg André da Silva
• Support Opportunities: Scholarships in Brazil - Doctorate