On the theory, design and optimization of Classical and Quantum algorithms for Isogeny-based Cryptography
In this work, we present the theory behind Elliptic Curve Cryptography (ECC) and Isogeny-based cryptography. We start with a quick introduction to Complexity Theory and Cryptography. We give a detailed description of elliptic curves and discuss how they are used to create secure protocols. We presen...
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| 格式: | bachelorThesis |
| 语言: | eng |
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2021
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| 在线阅读: | http://repositorio.yachaytech.edu.ec/handle/123456789/304 |
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| author | Caamaño Mayorga, Renzo Sebastián |
| author_facet | Caamaño Mayorga, Renzo Sebastián |
| author_role | author |
| collection | Repositorio Universidad Yachay Tech |
| dc.contributor.none.fl_str_mv | Anton Castro, Francesc |
| dc.creator.none.fl_str_mv | Caamaño Mayorga, Renzo Sebastián |
| dc.date.none.fl_str_mv | 2021-05-18T22:15:41Z 2021-05-18T22:15:41Z 2021-04 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://repositorio.yachaytech.edu.ec/handle/123456789/304 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Universidad de Investigación de Tecnología Experimental Yachay |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:Repositorio Universidad Yachay Tech instname:Universidad Yachay Tech instacron:Yachay |
| dc.subject.none.fl_str_mv | Curvas elípticas Isogenias Criptosistemas de clave pública cuántico-resistentes Algoritmo de Shor Elliptic curves Isogenies Quantum-resistant public-key cryptosystems Shor's Algorithm |
| dc.title.none.fl_str_mv | On the theory, design and optimization of Classical and Quantum algorithms for Isogeny-based Cryptography |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/bachelorThesis |
| description | In this work, we present the theory behind Elliptic Curve Cryptography (ECC) and Isogeny-based cryptography. We start with a quick introduction to Complexity Theory and Cryptography. We give a detailed description of elliptic curves and discuss how they are used to create secure protocols. We present the strength of this scheme and also its weaknesses regarding quantum computation. To show the necessity for other protocols, we review some basic concepts of Quantum Computing and present how Shor's Quantum Algorithm breaks ECC. Then, we survey the rich theory of isogenies between ordinary and supersingular elliptic curves to end with cryptographic protocols, that use these isogenies to create post-quantum cryptographic systems. |
| eu_rights_str_mv | openAccess |
| format | bachelorThesis |
| id | Yachay_7bf9030d3e4fc60a3361a82e8e2b9d29 |
| instacron_str | Yachay |
| institution | Yachay |
| instname_str | Universidad Yachay Tech |
| language | eng |
| network_acronym_str | Yachay |
| network_name_str | Repositorio Universidad Yachay Tech |
| oai_identifier_str | oai:repositorio.yachaytech.edu.ec:123456789/304 |
| publishDate | 2021 |
| publisher.none.fl_str_mv | Universidad de Investigación de Tecnología Experimental Yachay |
| reponame_str | Repositorio Universidad Yachay Tech |
| repository.mail.fl_str_mv | . |
| repository.name.fl_str_mv | Repositorio Universidad Yachay Tech - Universidad Yachay Tech |
| repository_id_str | 10284 |
| spelling | On the theory, design and optimization of Classical and Quantum algorithms for Isogeny-based CryptographyCaamaño Mayorga, Renzo SebastiánCurvas elípticasIsogeniasCriptosistemas de clave pública cuántico-resistentesAlgoritmo de ShorElliptic curvesIsogeniesQuantum-resistant public-key cryptosystemsShor's AlgorithmIn this work, we present the theory behind Elliptic Curve Cryptography (ECC) and Isogeny-based cryptography. We start with a quick introduction to Complexity Theory and Cryptography. We give a detailed description of elliptic curves and discuss how they are used to create secure protocols. We present the strength of this scheme and also its weaknesses regarding quantum computation. To show the necessity for other protocols, we review some basic concepts of Quantum Computing and present how Shor's Quantum Algorithm breaks ECC. Then, we survey the rich theory of isogenies between ordinary and supersingular elliptic curves to end with cryptographic protocols, that use these isogenies to create post-quantum cryptographic systems.En este trabajo, presentamos la teoría detrás de la criptografía de curva elíptica (ECC) y la criptografía basada en isogenia. Comenzamos con una rápida introducción a la teoría de la complejidad y la criptografía. Damos una descripción detallada de las curvas elípticas y discutimos como se utilizan para crear protocolos seguros. Presentamos la fortaleza de este esquema y también sus debilidades con respecto a la computación cuántica. Para mostrar la necesidad de otros protocolos, revisamos algunos conceptos básicos de Computación Cuántica y presentamos como el algoritmo cuántico de Shor rompe ECC. A partir de entonces, examinamos la rica teoría de las isogenias entre las curvas elípticas ordinarias y supersingulares para terminar con protocolos criptográficos que utilizan estas isogenias para crear sistemas criptográficos post-cuánticos.Matemático/aUniversidad de Investigación de Tecnología Experimental YachayAnton Castro, Francesc2021-05-18T22:15:41Z2021-05-18T22:15:41Z2021-04info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bachelorThesisapplication/pdfhttp://repositorio.yachaytech.edu.ec/handle/123456789/304enginfo:eu-repo/semantics/openAccessreponame:Repositorio Universidad Yachay Techinstname:Universidad Yachay Techinstacron:Yachay2025-07-08T17:51:49Zoai:repositorio.yachaytech.edu.ec:123456789/304Institucionalhttps://repositorio.yachaytech.edu.ec/Universidad públicahttps://www.yachaytech.edu.ec/https://repositorio.yachaytech.edu.ec/oaiEcuador...opendoar:102842025-07-08T17:51:49falseInstitucionalhttps://repositorio.yachaytech.edu.ec/Universidad públicahttps://www.yachaytech.edu.ec/https://repositorio.yachaytech.edu.ec/oai.Ecuador...opendoar:102842025-07-08T17:51:49Repositorio Universidad Yachay Tech - Universidad Yachay Techfalse |
| spellingShingle | On the theory, design and optimization of Classical and Quantum algorithms for Isogeny-based Cryptography Caamaño Mayorga, Renzo Sebastián Curvas elípticas Isogenias Criptosistemas de clave pública cuántico-resistentes Algoritmo de Shor Elliptic curves Isogenies Quantum-resistant public-key cryptosystems Shor's Algorithm |
| status_str | publishedVersion |
| title | On the theory, design and optimization of Classical and Quantum algorithms for Isogeny-based Cryptography |
| title_full | On the theory, design and optimization of Classical and Quantum algorithms for Isogeny-based Cryptography |
| title_fullStr | On the theory, design and optimization of Classical and Quantum algorithms for Isogeny-based Cryptography |
| title_full_unstemmed | On the theory, design and optimization of Classical and Quantum algorithms for Isogeny-based Cryptography |
| title_short | On the theory, design and optimization of Classical and Quantum algorithms for Isogeny-based Cryptography |
| title_sort | On the theory, design and optimization of Classical and Quantum algorithms for Isogeny-based Cryptography |
| topic | Curvas elípticas Isogenias Criptosistemas de clave pública cuántico-resistentes Algoritmo de Shor Elliptic curves Isogenies Quantum-resistant public-key cryptosystems Shor's Algorithm |
| url | http://repositorio.yachaytech.edu.ec/handle/123456789/304 |