Submitted by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-11-04T10:36:45Z No. of bitstreams: 2 arquivototal.pdf: 4819014 bytes, checksum: b89987c92ac5294da134e67b82d09cd2 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-11-04T11:40:46Z (GMT) No. of bitstreams: 2 arquivototal.pdf: 4819014 bytes, checksum: b89987c92ac5294da134e67b82d09cd2 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-11-04T11:40:46Z (GMT). No. of bitstreams: 2 arquivototal.pdf: 4819014 bytes, checksum: b89987c92ac5294da134e67b82d09cd2 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-04-15 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this paper we are studying cryptography’s evolution throughout history; analyzing the difference between symmetric and asymmetric cryptographies; enunciating definitions and theorems about binary relations, group theories, primitive roots and discrete logarithms; understanding the procedure of Diffie-Hellman’s key change protocol. In the last part in this work, we are proposing three activities to be applied in classroom. / Neste trabalho, vamos estudar a evolução da criptografia ao longo da história; analisar a diferença entre as criptografias simétricas e assimétricas; enunciar definições e teoremas sobre relações binárias, teoria dos grupos, raízes primitivas e logaritmos discretos; entender o procedimento do protocolo da troca de chaves de Diffie-Hellman; e, na parte final deste trabalho, iremos propor três atividades para serem aplicadas em sala de aula.

This thesis focuses on the lower bounds for generic algorithms for discrete logarithms problem and Diffie-Hellman's problems. This thesis introduces two diffrent models of Black-Box for that purpose. On these models thesis approxi- mates and compares success probability of generic algorithms for given problems including Maurer's reduction. This reduction solves discrete logarithms problem using a appropriate elliptic curve and a Diffie-Hellman's oracle. This thesis also researches generic algorithm for identifiaction schemes, that are based on discrete logarithms problem. 1