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Bruno Dias Final Instituto Politécnico de Beja Escola Superior de Tecnologia e Gestão Mestrado em Engenharia de Segurança Informática Implementação de Cifras Caóticas sobre Caos Modular Orientador: Professor Doutor Rui Miguel Silva Discente: Bruno Filipe Elias Dias, nº 14697 Beja, 24 de novembro de 2017 Implementação de Cifras Caóticas sobre Caos Modular Instituto Politécnico de Beja Escola Superior de Tecnologia e Gestão Mestrado em Engenharia de Segurança Informática Curso: Mestrado em Engenharia de Segurança Informática Título: Implementação de Cifras Caóticas sobre Caos Modular Dissertação de Mestrado apresentada na Escola Superior de Tecnologia e Gestão do Instituto Politécnico de Beja Orientador: Professor Doutor Rui Miguel Silva Discente: Bruno Filipe Elias Dias, nº 14697 Beja, 24 de novembro de 2017 III Mestrado em Engenharia de Segurança Informática Implementação de Cifras Caóticas sobre Caos Modular IV Mestrado em Engenharia de Segurança Informática Implementação de Cifras Caóticas sobre Caos Modular RESUMO Nesta dissertação, foi realizado um estudo aprofundado sobre Criptografia, Sistemas Caóticos, Cifras Caóticas, Caos Modular e um estudo final exaustivo do funcionamento da Cifra Caótica eLoBa. O objetivo desta dissertação foi implementar e melhorar a estrutura da Cifra Caótica eLoBa em outros sistemas caóticos além do Sistema Caótico de Lorenz, de modo a que, depois de implementados, foram recolhidas 1 milhão de chaves de cada Sistema Caótico para cada uma das duas sementes com apenas um caractere diferente. No final, são apresentados os resultados em tabelas e gráficos dos dados recolhidos da Bateria de Testes Estatísticos a Números Pseudo-aleatórios, NIST 800-22, com as amostras dos Sistemas Caóticos. De acordo com os dados recolhidos ficou confirmado que é possível a aplicação dos Sistemas Caóticos em Criptografia. Palavras-chave: Criptografia, Chaves, Cifras, Sistemas Caóticos, Nist 800-22 V Mestrado em Engenharia de Segurança Informática Implementação de Cifras Caóticas sobre Caos Modular VI Mestrado em Engenharia de Segurança Informática Implementação de Cifras Caóticas sobre Caos Modular ABSTRACT In this work an in - depth study was carried out on Cryptography, Chaotic Systems, Chaotic Figures, Modular Chaos and a final exhaustive study of the functioning of the Chaotic Cipher eLoba. The objective of this work was to implement and improve the structure of the Chaotic Cipher eLoBa in other chaotic systems besides the Chaotic System of Lorenz, so that once implemented, 1 million keys were collected from each Chaotic System for each of the two seeds with only a different character. At the end, the results were presented in tables and graphs of the information collected from the Battery of Statistical Tests to Pseudo-Random Numbers, NIST 800- 22, with the samples of the Chaotic systems. According to the data collected it was confirmed that it is possible to apply the Chaotic Systems in Cryptography. Keywords: Cryptography, Keys, Ciphers, Chaotic Systems, Nist800-22 VII Mestrado em Engenharia de Segurança Informática Implementação de Cifras Caóticas sobre Caos Modular VIII Mestrado em Engenharia de Segurança Informática Implementação de Cifras Caóticas sobre Caos Modular AGRADECIMENTOS Os meus agradecimentos a todos os que possibilitaram a realização desta dissertação nomeadamente: Ao meu orientador, Professor Doutor Rui Miguel Silva, por me auxiliar sempre que precisei; Aos meus pais, Ilda e Francisco, e irmã, Isa, que me apoiaram incondicionalmente; À minha namorada e melhor amiga, Savannah Salgueiro, por estar sempre ao meu lado e por todo o apoio e força de vontade que me tem emprestado para conseguir chegar até aqui, Aos meus amigos, Diogo Bentes, José Santos e Tobias Cintrão pela ajuda técnica que existiu da sua parte; Deixo os meus sinceros agradecimentos a todos os que não foram citados, mas que, de alguma forma, auxiliaram na realização deste trabalho. IX Mestrado em Engenharia de Segurança Informática Implementação de Cifras Caóticas sobre Caos Modular X Mestrado em Engenharia de Segurança Informática Implementação de Cifras Caóticas sobre Caos Modular ÍNDICE RESUMO ......................................................................................................................... V ABSTRACT ................................................................................................................ VII AGRADECIMENTOS ................................................................................................. IX ÍNDICE .......................................................................................................................... XI LISTA DE ABREVIATURAS .................................................................................. XIII ÍNDICE DE FIGURAS E GRÁFICOS ................................................................... XIV ÍNDICE DE TABELAS .............................................................................................. XV 1. INTRODUÇÃO .......................................................................................................... 1 1.1. CONTEXTUALIZAÇÃO ...................................................................................... 2 1.2. ESTRUTURA DA DISSERTAÇÃO ........................................................................ 2 2. CRIPTOGRAFIA E SISTEMAS CAÓTICOS ........................................................ 4 2.1. CRIPTOGRAFIA................................................................................................. 4 2.1.1. Algoritmo de Chave Simétrica ......................................................... 4 2.1.2. Algoritmo de Chave Assimétrica ...................................................... 5 2.2. SISTEMAS CAÓTICOS ....................................................................................... 6 2.2.1. Contínuos ............................................................................................ 7 2.2.2. Discretos.............................................................................................. 7 2.2.3. Contínuos Discreteados ..................................................................... 7 2.3. CIFRAS CAÓTICAS ........................................................................................... 8 2.3.1. Cifra Caótica eLoba – Enhanced Lorenz Based ............................. 8 3. CAOS MODULAR ..................................................................................................... 9 3.1. MÓDULOS DA ARQUITETURA .......................................................................... 9 3.2. ESTRUTURA DA ARQUITETURA ..................................................................... 10 3.3. FUNCIONAMENTO DA ARQUITETURA ............................................................ 10 3.3.1. Inicialização ...................................................................................... 10 3.3.2. Sub-Sistema Caótico ........................................................................ 13 3.3.3. Sub-Sistema de Perturbação Caótica ............................................ 13 3.3.4. Sub-Sistema de Mistura de Chaves ................................................ 14 4. IMPLEMENTAÇÃO DE CIFRAS CAÓTICAS ................................................... 15 4.1. CRITÉRIOS DE SELEÇÃO DE SISTEMAS CAÓTICOS ........................................ 15 4.2. SISTEMAS CAÓTICOS ESCOLHIDOS ............................................................... 15 XI Mestrado em Engenharia de Segurança Informática Implementação de Cifras Caóticas sobre Caos Modular 4.2.1. Não implementados ......................................................................... 15 4.2.2. Implementados, mas rejeitados ...................................................... 16 4.2.3. Implementados ................................................................................. 16 4.3. IMPLEMENTAÇÃO .......................................................................................... 18 4.4. RECOLHA DE RESULTADOS ........................................................................... 18 5. AVALIAÇÃO E COMPARAÇÃO DE RESULTADOS ...................................... 20 5.1. BATERIA DE TESTES ...................................................................................... 20 5.2. PROCEDIMENTOS PARA TESTE ...................................................................... 20 5.2.1. Teste Realizados e Rejeitados ......................................................... 21 5.2.2. Testes Realizados e Aprovados ....................................................... 21 5.3. RESULTADOS .................................................................................................. 22 5.3.1. Condições iniciais ............................................................................. 22 5.3.2. Balanço Binário ................................................................................ 26 5.3.3. Entropia Média ................................................................................ 27 5.3.4. Resultados da Bateria de Testes ..................................................... 29 6. INTERPRETAÇÃO DE RESULTADOS E CONCLUSÕES FINAIS ................ 31 6.1. TRABALHOS FUTUROS ................................................................................... 32 7. BIBLIOGRAFIA ...................................................................................................... 33 8. ANEXOS ................................................................................................................... 38 XII Mestrado em Engenharia de Segurança Informática Implementação
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