Eciency and security of ZHFE

In this thesis we describe the hidden structure in the key generation process for the multivariate public key cryptosystem ZHFE. Based on such structure, we propose a new method for the mentioned process. We compare the time and memory required between our new method and the original key generation...

Full description

Autores:
Verbel Herrera, Javier Alfonso
Tipo de recurso:
Fecha de publicación:
2015
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/55749
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/55749
http://bdigital.unal.edu.co/51211/
Palabra clave:
51 Matemáticas / Mathematics
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_e79d79495c604716286a5ff9c30b0b8e
oai_identifier_str oai:repositorio.unal.edu.co:unal/55749
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Cabarcas Jaramillo, DanielVerbel Herrera, Javier Alfonsof77bf09c-4425-4e7e-91ea-e96810abd4a63002019-07-02T11:27:28Z2019-07-02T11:27:28Z2015https://repositorio.unal.edu.co/handle/unal/55749http://bdigital.unal.edu.co/51211/In this thesis we describe the hidden structure in the key generation process for the multivariate public key cryptosystem ZHFE. Based on such structure, we propose a new method for the mentioned process. We compare the time and memory required between our new method and the original key generation process. We also analyze the security of ZHFE with respect to the MinRank Attack. We show that with high probability there exist a linear combination of Frobenious power of the core polynomials F and ~ F of low rank. Furthermore, we show that such linear combination can be extracted from the public key.Resumen: En esta tesis describimos la estructura oculta en el proceso de generación de llave para el criptosistema de llave pública multivariada ZHFE. Basados en tal estructura, proponemos un nuevo método para tal proceso. Comparamos los tiempos y memoria requerida entre nuestro nuevo método y el método original de generación. También analizamos la seguridad de ZHFE respecto al Ataque del MinRank. Demostramos que con alta probabilidad existe de una combinanción lineal de las potencias de Frobenious de los polinomios centrales F y ~ F de rango pequeño. Más aún, demostramos que tal combinación puede ser extraída de la llave pública.Maestríaapplication/pdfspaUniversidad Nacional de Colombia Sede Medellín Facultad de Ciencias Escuela de MatemáticasEscuela de MatemáticasVerbel Herrera, Javier Alfonso (2015) Eciency and security of ZHFE. Maestría thesis, Universidad Nacional de Colombia - Sede Medellín.51 Matemáticas / MathematicsEciency and security of ZHFETrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMORIGINAL1143358050.2015.pdfTesis de Maestría en Ciencias - Matemáticasapplication/pdf723676https://repositorio.unal.edu.co/bitstream/unal/55749/1/1143358050.2015.pdf3d44e6468fbf2fa2eafeb9e6422a4880MD51THUMBNAIL1143358050.2015.pdf.jpg1143358050.2015.pdf.jpgGenerated Thumbnailimage/jpeg3623https://repositorio.unal.edu.co/bitstream/unal/55749/2/1143358050.2015.pdf.jpg38fa5c879a42733a98a12efcd22055a7MD52unal/55749oai:repositorio.unal.edu.co:unal/557492023-04-18 11:18:35.434Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Eciency and security of ZHFE
title Eciency and security of ZHFE
spellingShingle Eciency and security of ZHFE
51 Matemáticas / Mathematics
title_short Eciency and security of ZHFE
title_full Eciency and security of ZHFE
title_fullStr Eciency and security of ZHFE
title_full_unstemmed Eciency and security of ZHFE
title_sort Eciency and security of ZHFE
dc.creator.fl_str_mv Verbel Herrera, Javier Alfonso
dc.contributor.author.spa.fl_str_mv Verbel Herrera, Javier Alfonso
dc.contributor.spa.fl_str_mv Cabarcas Jaramillo, Daniel
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
topic 51 Matemáticas / Mathematics
description In this thesis we describe the hidden structure in the key generation process for the multivariate public key cryptosystem ZHFE. Based on such structure, we propose a new method for the mentioned process. We compare the time and memory required between our new method and the original key generation process. We also analyze the security of ZHFE with respect to the MinRank Attack. We show that with high probability there exist a linear combination of Frobenious power of the core polynomials F and ~ F of low rank. Furthermore, we show that such linear combination can be extracted from the public key.
publishDate 2015
dc.date.issued.spa.fl_str_mv 2015
dc.date.accessioned.spa.fl_str_mv 2019-07-02T11:27:28Z
dc.date.available.spa.fl_str_mv 2019-07-02T11:27:28Z
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TM
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/55749
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/51211/
url https://repositorio.unal.edu.co/handle/unal/55749
http://bdigital.unal.edu.co/51211/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Medellín Facultad de Ciencias Escuela de Matemáticas
Escuela de Matemáticas
dc.relation.references.spa.fl_str_mv Verbel Herrera, Javier Alfonso (2015) Eciency and security of ZHFE. Maestría thesis, Universidad Nacional de Colombia - Sede Medellín.
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/55749/1/1143358050.2015.pdf
https://repositorio.unal.edu.co/bitstream/unal/55749/2/1143358050.2015.pdf.jpg
bitstream.checksum.fl_str_mv 3d44e6468fbf2fa2eafeb9e6422a4880
38fa5c879a42733a98a12efcd22055a7
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
repository.mail.fl_str_mv repositorio_nal@unal.edu.co
_version_ 1814089514113564672

Publicaciones similares