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Aritmética modular, códigos elementares e criptografiaBarreto, Regene Chaves Pimentel Pereira 29 August 2014 (has links)
The main objective of this work is to treat the modular arithmetic of whole
numbers, and show evidence of some types of elementary code such as Cesar's, A m,
of Vigenere's, Hill's, RSA, Rabin's, MH and ElGamal, those found in cryptography,
highlighting the mathematics which exists behind the function of each of them. We
have studied the concepts of modular arithmetic and applied them to the study of
matrices and determinants that are necessary for the function of these codes and for
the evolution of cryptography. We also present some codes found in our day-to-day
life, aiming to stimulate the curiosity of the reader into discovering these codes.
Finally, for complementary information purposes, we reveal a brief collected history
of cryptography. / O presente trabalho tem como principal objetivo tratar de aritmética modular
dos inteiros e evidenciar alguns tipos de códigos elementares, a exemplo dos Códigos
de César, Afim, de Vigenère, de Hill, RSA, de Rabin, MH e ElGamal, existentes
na criptografia, ressaltando a matemática que existe por trás do funcionamento
de cada um deles. Estudamos conceitos de aritmética modular e os aplicamos ao
estudo de matrizes e determinantes que se fazem necessários para o funcionamento
desses códigos e para a evolução da criptografia. Apresentamos ainda alguns códigos
encontrados no nosso dia a dia, buscando estimular a curiosidade do leitor pelo
conhecimento dos códigos. Por fim, a título de informação complementar, expomos
um breve apanhado histórico da criptografia.
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