Introdução à criptografia usando aritmética modular
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Data
2017-09-01
Autores
Lopes, Marco Antônio [UNESP]
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Universidade Estadual Paulista (Unesp)
Resumo
A troca de informações confidenciais sempre foi um problema que nos desafiou. O conhecimento de técnicas que visam ocultar uma mensagem data de alguns séculos a.C., tais como, a esteganografia e a criptografia. A esteganografia consiste na técnica de ocultar a mensagem que será enviada sem, no entanto, esconder seu significado. Já a criptografia consiste na técnica de ocultar o significado da mensagem através de sua codificação, que pode ser feita de várias maneiras, e cujo conteúdo só pode ser decodificado pelo destinatário, que tem a chave de decodificação. Essas técnicas evoluíram com o tempo, principalmente a criptografia, por ter uma natureza mais complexa na decodificação e que, por isso mesmo, torna-se mais adequada atualmente. Isso porque, com o desenvolvimento de novas tecnologias de comunicação, garantir a segurança das informações tornou-se uma preocupação maior do que já era. Nesse sentido, destacamos a internet, que, além de exigir segurança, é compartilhada pela grande maioria de nossos alunos. Como a segurança da internet faz uso da criptografia, e como esta está associada a modelos matemáticos, podemos então explorar o uso desta, em sala de aula, a fim de despertar no aluno, além de sua curiosidade, seu interesse por temas, muitas vezes de difícil compreensão, dada a maturidade dos mesmos para enfrentá-los. Teorias como funções e suas funções inversas, aritmética das classes residuais, etc., podem ser trabalhados em sala de aula usando o Código de Caesar e permite ao professor lidar de forma mais didática as diferenças existentes em sala de aula.
The exchange of confidential information has always been a problem that challenged us. The techniques knowledge that aimed to concealing a message dates back to some centuries BC, such as steganography and cryptography Steganography consists on the technique of hiding the message that will be sent however, without, hide its meaning. However, encryption is the technique of hide the meaning of the message through its coding, which can be done in several ways, whose content can only be decoded by the recipient, who has the decryption key. These techniques have evolved over time, especially cryptography, because it has a more complex decoding nature and, therefore, it is more suitable today. That's because, with the development of new communication technologies, guarantee information security has become a greater concern than it used to be. On this side, we highlight the internet, which, in addition to requiring security, it’s shared by the vast majority of our students. As Internet security uses the encryption, and it’s associated with mathematical models, we can explore the use of encryption in classroom in order to arouse the student’s curiosity, his interest in subjects, often difficult to understand, given their maturity to face them. Theories as functions and their inverse functions, arithmetic of the residual classes, etc., can be worked in classroom using the Caesar Code, and it allows the teacher to deal in a didactic way with the differences existing in the classroom.
The exchange of confidential information has always been a problem that challenged us. The techniques knowledge that aimed to concealing a message dates back to some centuries BC, such as steganography and cryptography Steganography consists on the technique of hiding the message that will be sent however, without, hide its meaning. However, encryption is the technique of hide the meaning of the message through its coding, which can be done in several ways, whose content can only be decoded by the recipient, who has the decryption key. These techniques have evolved over time, especially cryptography, because it has a more complex decoding nature and, therefore, it is more suitable today. That's because, with the development of new communication technologies, guarantee information security has become a greater concern than it used to be. On this side, we highlight the internet, which, in addition to requiring security, it’s shared by the vast majority of our students. As Internet security uses the encryption, and it’s associated with mathematical models, we can explore the use of encryption in classroom in order to arouse the student’s curiosity, his interest in subjects, often difficult to understand, given their maturity to face them. Theories as functions and their inverse functions, arithmetic of the residual classes, etc., can be worked in classroom using the Caesar Code, and it allows the teacher to deal in a didactic way with the differences existing in the classroom.
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Palavras-chave
Criptografia, Função, Função inversa, Classes residuais, Cryptography, Function, Reverse function, Residual classes