Criptografia e a Matemática

Bibliographic Details
Main Author: Oliveira, Vinícius Matos de
Publication Date: 2021
Format: Master thesis
Language: por
Source: Repositório Institucional da UFS
Download full: http://ri.ufs.br/jspui/handle/riufs/15776
Summary: The present dissertation aims to align the mathematical knowledge to the RSA encryption system theme. Initially, a historical line is made on the evolution of cryptography, showing the need for rulers, kings, commanders to pass confidential information throughout history. Next, the essential mathematical knowledge is studied to understand the most used cryptographic system today: the RSA system. Among this mathematical knowledge, prime numbers stand out in basic arithmetic, and the congruence system in the modular arithmetic. Soon after, it is demonstrated how works the system Encryption RSA, as well as is guaranteed enormous difficulty in breaking the message encrypted from the prime numbers chosen for its composition.
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spelling Oliveira, Vinícius Matos deSantos, Naldisson dos2022-05-25T21:07:08Z2022-05-25T21:07:08Z2021-02-22OLIVEIRA, Vinícius Matos de. Criptografia e a Matemática. 2021. 54 f. Dissertação (Mestrado Profissional em Matemática) - Universidade Federal de Sergipe, São Cristóvão, 2021.http://ri.ufs.br/jspui/handle/riufs/15776The present dissertation aims to align the mathematical knowledge to the RSA encryption system theme. Initially, a historical line is made on the evolution of cryptography, showing the need for rulers, kings, commanders to pass confidential information throughout history. Next, the essential mathematical knowledge is studied to understand the most used cryptographic system today: the RSA system. Among this mathematical knowledge, prime numbers stand out in basic arithmetic, and the congruence system in the modular arithmetic. Soon after, it is demonstrated how works the system Encryption RSA, as well as is guaranteed enormous difficulty in breaking the message encrypted from the prime numbers chosen for its composition.A presente dissertação visa alinhar o conhecimento matemático ao sistema de criptografia RSA. Inicialmente, é feita uma linha histórica sobre a evolução da criptografia, mostrando a necessidade de governantes, reis, comandantes passarem informações confidenciais ao longo da história. A seguir, é estudado o conhecimento matemático essencial para entender o sistema criptográfico mais utilizado atualmente: o sistema RSA. Entre este conhecimento matemático, os números primos se destacam na aritmética básica, e o sistema de congruência na aritmética modular. Em seguida, é demonstrado como funciona o sistema RSA de criptografia, assim como é garantida enorme dificuldade em quebrar a mensagem criptografada a partir dos números primos escolhidos para sua composição.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESSão CristóvãoporMatemáticaNúmeros primosCongruências e restosCriptografiaCongruênciasSistema RSAPrime numbersCongruencesCryptographyRSA systemCIENCIAS EXATAS E DA TERRA::MATEMATICACriptografia e a Matemáticainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisMestrado Profissional em MatemáticaUniversidade Federal de Sergipereponame:Repositório Institucional da UFSinstname:Universidade Federal de Sergipe (UFS)instacron:UFSinfo:eu-repo/semantics/openAccessLICENSElicense.txtlicense.txttext/plain; charset=utf-81475https://ri.ufs.br/jspui/bitstream/riufs/15776/1/license.txt098cbbf65c2c15e1fb2e49c5d306a44cMD51ORIGINALVINICIUS_MATOS_OLIVEIRA.pdfVINICIUS_MATOS_OLIVEIRA.pdfapplication/pdf1143402https://ri.ufs.br/jspui/bitstream/riufs/15776/2/VINICIUS_MATOS_OLIVEIRA.pdfbcad5969efa2d19ca04d86f9794ada59MD52TEXTVINICIUS_MATOS_OLIVEIRA.pdf.txtVINICIUS_MATOS_OLIVEIRA.pdf.txtExtracted texttext/plain103818https://ri.ufs.br/jspui/bitstream/riufs/15776/3/VINICIUS_MATOS_OLIVEIRA.pdf.txtd31b05935a9da0dfeba1e894be030a7cMD53THUMBNAILVINICIUS_MATOS_OLIVEIRA.pdf.jpgVINICIUS_MATOS_OLIVEIRA.pdf.jpgGenerated Thumbnailimage/jpeg1222https://ri.ufs.br/jspui/bitstream/riufs/15776/4/VINICIUS_MATOS_OLIVEIRA.pdf.jpg81995fc22c763cf588dd214d66e73939MD54riufs/157762022-11-17 21:01:56.945oai:oai:ri.ufs.br:repo_01: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Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2022-11-18T00:01:56Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false
dc.title.pt_BR.fl_str_mv Criptografia e a Matemática
title Criptografia e a Matemática
spellingShingle Criptografia e a Matemática
Oliveira, Vinícius Matos de
Matemática
Números primos
Congruências e restos
Criptografia
Congruências
Sistema RSA
Prime numbers
Congruences
Cryptography
RSA system
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Criptografia e a Matemática
title_full Criptografia e a Matemática
title_fullStr Criptografia e a Matemática
title_full_unstemmed Criptografia e a Matemática
title_sort Criptografia e a Matemática
author Oliveira, Vinícius Matos de
author_facet Oliveira, Vinícius Matos de
author_role author
dc.contributor.author.fl_str_mv Oliveira, Vinícius Matos de
dc.contributor.advisor1.fl_str_mv Santos, Naldisson dos
contributor_str_mv Santos, Naldisson dos
dc.subject.por.fl_str_mv Matemática
Números primos
Congruências e restos
Criptografia
Congruências
Sistema RSA
topic Matemática
Números primos
Congruências e restos
Criptografia
Congruências
Sistema RSA
Prime numbers
Congruences
Cryptography
RSA system
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Prime numbers
Congruences
Cryptography
RSA system
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description The present dissertation aims to align the mathematical knowledge to the RSA encryption system theme. Initially, a historical line is made on the evolution of cryptography, showing the need for rulers, kings, commanders to pass confidential information throughout history. Next, the essential mathematical knowledge is studied to understand the most used cryptographic system today: the RSA system. Among this mathematical knowledge, prime numbers stand out in basic arithmetic, and the congruence system in the modular arithmetic. Soon after, it is demonstrated how works the system Encryption RSA, as well as is guaranteed enormous difficulty in breaking the message encrypted from the prime numbers chosen for its composition.
publishDate 2021
dc.date.issued.fl_str_mv 2021-02-22
dc.date.accessioned.fl_str_mv 2022-05-25T21:07:08Z
dc.date.available.fl_str_mv 2022-05-25T21:07:08Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv OLIVEIRA, Vinícius Matos de. Criptografia e a Matemática. 2021. 54 f. Dissertação (Mestrado Profissional em Matemática) - Universidade Federal de Sergipe, São Cristóvão, 2021.
dc.identifier.uri.fl_str_mv http://ri.ufs.br/jspui/handle/riufs/15776
identifier_str_mv OLIVEIRA, Vinícius Matos de. Criptografia e a Matemática. 2021. 54 f. Dissertação (Mestrado Profissional em Matemática) - Universidade Federal de Sergipe, São Cristóvão, 2021.
url http://ri.ufs.br/jspui/handle/riufs/15776
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.program.fl_str_mv Mestrado Profissional em Matemática
dc.publisher.initials.fl_str_mv Universidade Federal de Sergipe
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFS
instname:Universidade Federal de Sergipe (UFS)
instacron:UFS
instname_str Universidade Federal de Sergipe (UFS)
instacron_str UFS
institution UFS
reponame_str Repositório Institucional da UFS
collection Repositório Institucional da UFS
bitstream.url.fl_str_mv https://ri.ufs.br/jspui/bitstream/riufs/15776/1/license.txt
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https://ri.ufs.br/jspui/bitstream/riufs/15776/3/VINICIUS_MATOS_OLIVEIRA.pdf.txt
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