Mutations in Brauer Configuration Algebras and Some of Its Cryptographic Applications
gráficas, tablas
- Autores:
-
Camacho Vega, Juan David
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/82265
- Palabra clave:
- Criptografía
Símbolos
Signs and symbols
Advanced Encryption Standard (AES)
Automata
Brauer configuration algebra
cryptography
diophantine equations
Chicken McNugget Problem (CMP)
polytope
- Rights
- openAccess
- License
- Atribución-CompartirIgual 4.0 Internacional
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Mutations in Brauer Configuration Algebras and Some of Its Cryptographic Applications |
| dc.title.translated.spa.fl_str_mv |
Mutaciones en algebras de configuración de Brauer y algunas aplicaciones a la criptografía |
| title |
Mutations in Brauer Configuration Algebras and Some of Its Cryptographic Applications |
| spellingShingle |
Mutations in Brauer Configuration Algebras and Some of Its Cryptographic Applications Criptografía Símbolos Signs and symbols Advanced Encryption Standard (AES) Automata Brauer configuration algebra cryptography diophantine equations Chicken McNugget Problem (CMP) polytope |
| title_short |
Mutations in Brauer Configuration Algebras and Some of Its Cryptographic Applications |
| title_full |
Mutations in Brauer Configuration Algebras and Some of Its Cryptographic Applications |
| title_fullStr |
Mutations in Brauer Configuration Algebras and Some of Its Cryptographic Applications |
| title_full_unstemmed |
Mutations in Brauer Configuration Algebras and Some of Its Cryptographic Applications |
| title_sort |
Mutations in Brauer Configuration Algebras and Some of Its Cryptographic Applications |
| dc.creator.fl_str_mv |
Camacho Vega, Juan David |
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Agustín, Moreno Cañadas |
| dc.contributor.author.none.fl_str_mv |
Camacho Vega, Juan David |
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Terenufia-Unal |
| dc.subject.lemb.spa.fl_str_mv |
Criptografía Símbolos |
| topic |
Criptografía Símbolos Signs and symbols Advanced Encryption Standard (AES) Automata Brauer configuration algebra cryptography diophantine equations Chicken McNugget Problem (CMP) polytope |
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Signs and symbols |
| dc.subject.proposal.eng.fl_str_mv |
Advanced Encryption Standard (AES) Automata Brauer configuration algebra cryptography diophantine equations Chicken McNugget Problem (CMP) polytope |
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gráficas, tablas |
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2021 |
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2021 |
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2022-09-07T12:56:23Z |
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Trabajo de grado - Maestría |
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Universidad Nacional de Colombia |
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Repositorio Institucional Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/ |
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Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
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eng |
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eng |
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Human Interaction Proofs Based on Emerging Images; A Practical Application of the Theory of Representation of Algebras, M.A.O. Angarita, 2019 Elements of the Representation Theory of Associative Algebras, I. Assem et all 2006 Canakci and R. Schiffler, Snake graph calculus and cluster algebras from surfaces, J. Algebra 382 (2013), 240-281. Cluster algebras and continued fractions, Compositio Mathematica 154 (2018),no. 3, 565-593. A.M. Cañadas, J.D. Camacho, and I. D. Marin, Relationships between the Chicken McNugget Problem, Mutations of Brauer Configuration Algebras and the Advanced Encryption Standard, Mathematics 9 (2021), no. 16. A.M. Cañadas and M.A.O. Angarita, Brauer configuration algebras for multimedia based encryption and applications, Multimed Tools Appl 80 (2021), 23485-23510. S.T. Chapman and C. O’Neill, Factoring in the Chicken McNugget monoid, Mathematics Magazine 91 (2015), no. 5, 323-336. F. Curtis, On formulas for the Frobenius number of a numerical semigroup., Mathematica Scandinavica 67 (1990), 190. J.A. De Loera, The many aspects of counting lattice points in polytopes, Mathematische Semesterberichte (2005), 175-195. S. Eilenberg, Automata, Languages, and Machines, Vol. B, Academic Press, 111 Fifth Avenue, New York, New York 10003, 1974. P.F.F. Espinosa, Categorification of Integer Sequences and Its Applications, National University of Colombia, 2020. PhD Dissertation. S. Fomin, M. Shapiro, and D. Thurston, Cluster algebras and triangulated surfaces.Part I: Cluster complexes., Acta Math. 201 (2008), 83-146. S. Fomin and A. Zelevinsky, Cluster algebras. I: Foundations., J. Amer. Math. Soc. 15 (2002), 497-529. Cluster algebras. II: Finite type classification., Invent. Math. 154 (2003), no. 1, 63-121. Cluster algebras. IV: Coefficients., Compositio Mathematica 143 (2007), 112- 164. P. Gabriel and A.V. Roiter, Representations of Finite Dimensional Algebras, Algebra VIII, Encyclopedia of Math. Sc., vol. 73, Springer-Verlag, 1992. 177p. E.L. Green and S. Schroll, Brauer configuration algebras: A generalization of Brauer graph algebras, Bull. Sci. Math. 141 (2017), 539–572. G. H. Hardy, E. M. Wright, D. R. Heath-Brown, and J. H. Silverman, An Introduction to the Theory of Numbers, Oxford University Press, 2008. E. C. i Ll´opez, Some Contributions to the Algebraic Theory of Automata, Facultat de Ci´encies Matem´atiques Universitat de Val´encia, 2015. B. Keller, Cluster algebras, quiver representations and triangulated categories, Cambridge University Press, 2010. In T. Holm, Jørgensen and R. Rouquier (Eds.), Triangulated Categories (London Mathematical Society Lecture Note Series, 76-160). G. Musiker, R. Schiffler, and L. Williams, Positivity for cluster algebras from surfaces, Adv. Math. 227 (2011), 2241-2308. S.Y. Oudot, Persistence Theory: From Quiver Representations to Data Analysis, American Mathematical Society, 2015. 55 J.E. Pin and X. Soler-Escriv`a, Languages and formations generated by D4 and Q8, Theoretical Computer Science 800 (2019), 155-172. J.L. Ram´ırez-Alfons´ın, Complexity of the Frobenius problem, Combinatorica 16 (1996), 143–147. The Diophantine Frobenius Problem, Vol. 16, Oxford University Press, 1996. 1–457. S. Rees, The Automata that define Representations of monomial algebras, Algebr Represent Theor 11 (2008), 207-214. J. Rutten, A. Ballester-Bolinches, and E.C. i Ll´opez, Varieties and covarieties of languages, ENTCS 298 (2013), 7-28. I. K. Rystsov, Affine Automata and Classical Fractals, Cybernetics and Systems Analysis 54 (2018), 11-20. J. Sakarovitch, Elements of Automata Theory, Cambridge University Press, 2013. R. Shiffler, Quiver Representations, Springer, 2010. S. Schroll, Brauer Graph Algebras, Springer, Cham, 2018. In: Assem I., Trepode S. (eds), Homological Methods, Representation Theory, and Cluster Algebras, CRM Short Courses, 177-223. A. Sierra, The dimension of the center of a Brauer configuration algebra, J. Algebra 510 (2018), 289-318. D.R. Stinson and M.B. Paterson, Cryptography; Theory and Practice, Chapman and Hall/CRC, 2018. G. M. Ziegler, Lectures on Polytopes, Springer, 1998. AES, Vol. https://searchsecurity.techtarget.com/definition/Advanced-EncryptionStandard, TechTarget. |
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58 páginas |
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application/pdf |
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Universidad nacional de Colombia |
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Bogotá - Ciencias - Maestría en Ciencias - Matemáticas |
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Departamento de Matemáticas |
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Facultad de Ciencias |
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Bogotá, Colombia |
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Universidad Nacional de Colombia - Sede Bogotá |
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Atribución-CompartirIgual 4.0 Internacionalhttp://creativecommons.org/licenses/by-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Agustín, Moreno Cañadas061517362f5adfa88904f7da7646d32cCamacho Vega, Juan Davidd0825a37accd1aec73feca36dce8100aTerenufia-Unal2022-09-07T12:56:23Z2022-09-07T12:56:23Z2021https://repositorio.unal.edu.co/handle/unal/82265Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/gráficas, tablasLas mutaciones de las algebras de configuración de Brauer son exploradas y estudiadas como herramientas para obtener soluciones para algunas generalizaciones del problema de los McNuggets de pollo junto con una exposici´on de unos autómatas asociados a los conglomerados de configuración. Este acercamiento permite construir una descripción algebraica del itinerario de las claves AES por medio de un autómata no determinista adecuado. (Texto tomado de la fuente)Mutations on Brauer configurations are explored as tools to obtain a solution for some generalizations of the chicken McNugget problem, along with some associated automata to the configuration clusters. This approach allows us to give an algebraic description of the schedule of an AES key via some suitable non-deterministic automata (NFA)MaestríaMagíster en Ciencias - MatemáticasTeoría de representación de algebras58 páginasapplication/pdfengUniversidad nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasDepartamento de MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede BogotáMutations in Brauer Configuration Algebras and Some of Its Cryptographic ApplicationsMutaciones en algebras de configuración de Brauer y algunas aplicaciones a la criptografíaTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMHuman Interaction Proofs Based on Emerging Images; A Practical Application of the Theory of Representation of Algebras, M.A.O. Angarita, 2019Elements of the Representation Theory of Associative Algebras, I. Assem et all 2006Canakci and R. Schiffler, Snake graph calculus and cluster algebras from surfaces, J. Algebra 382 (2013), 240-281.Cluster algebras and continued fractions, Compositio Mathematica 154 (2018),no. 3, 565-593.A.M. Cañadas, J.D. Camacho, and I. D. Marin, Relationships between the Chicken McNugget Problem, Mutations of Brauer Configuration Algebras and the Advanced Encryption Standard, Mathematics 9 (2021), no. 16.A.M. Cañadas and M.A.O. Angarita, Brauer configuration algebras for multimedia based encryption and applications, Multimed Tools Appl 80 (2021), 23485-23510.S.T. Chapman and C. O’Neill, Factoring in the Chicken McNugget monoid, Mathematics Magazine 91 (2015), no. 5, 323-336.F. Curtis, On formulas for the Frobenius number of a numerical semigroup., Mathematica Scandinavica 67 (1990), 190.J.A. De Loera, The many aspects of counting lattice points in polytopes, Mathematische Semesterberichte (2005), 175-195.S. Eilenberg, Automata, Languages, and Machines, Vol. B, Academic Press, 111 Fifth Avenue, New York, New York 10003, 1974.P.F.F. Espinosa, Categorification of Integer Sequences and Its Applications, National University of Colombia, 2020. PhD Dissertation.S. Fomin, M. Shapiro, and D. Thurston, Cluster algebras and triangulated surfaces.Part I: Cluster complexes., Acta Math. 201 (2008), 83-146.S. Fomin and A. Zelevinsky, Cluster algebras. I: Foundations., J. Amer. Math. Soc. 15 (2002), 497-529.Cluster algebras. II: Finite type classification., Invent. Math. 154 (2003), no. 1, 63-121.Cluster algebras. IV: Coefficients., Compositio Mathematica 143 (2007), 112- 164.P. Gabriel and A.V. Roiter, Representations of Finite Dimensional Algebras, Algebra VIII, Encyclopedia of Math. Sc., vol. 73, Springer-Verlag, 1992. 177p.E.L. Green and S. Schroll, Brauer configuration algebras: A generalization of Brauer graph algebras, Bull. Sci. Math. 141 (2017), 539–572.G. H. Hardy, E. M. Wright, D. R. Heath-Brown, and J. H. Silverman, An Introduction to the Theory of Numbers, Oxford University Press, 2008.E. C. i Ll´opez, Some Contributions to the Algebraic Theory of Automata, Facultat de Ci´encies Matem´atiques Universitat de Val´encia, 2015.B. Keller, Cluster algebras, quiver representations and triangulated categories, Cambridge University Press, 2010. In T. Holm, Jørgensen and R. Rouquier (Eds.), Triangulated Categories (London Mathematical Society Lecture Note Series, 76-160).G. Musiker, R. Schiffler, and L. Williams, Positivity for cluster algebras from surfaces, Adv. Math. 227 (2011), 2241-2308.S.Y. Oudot, Persistence Theory: From Quiver Representations to Data Analysis, American Mathematical Society, 2015. 55J.E. Pin and X. Soler-Escriv`a, Languages and formations generated by D4 and Q8, Theoretical Computer Science 800 (2019), 155-172.J.L. Ram´ırez-Alfons´ın, Complexity of the Frobenius problem, Combinatorica 16 (1996), 143–147.The Diophantine Frobenius Problem, Vol. 16, Oxford University Press, 1996. 1–457.S. Rees, The Automata that define Representations of monomial algebras, Algebr Represent Theor 11 (2008), 207-214.J. Rutten, A. Ballester-Bolinches, and E.C. i Ll´opez, Varieties and covarieties of languages, ENTCS 298 (2013), 7-28.I. K. Rystsov, Affine Automata and Classical Fractals, Cybernetics and Systems Analysis 54 (2018), 11-20.J. Sakarovitch, Elements of Automata Theory, Cambridge University Press, 2013.R. Shiffler, Quiver Representations, Springer, 2010.S. Schroll, Brauer Graph Algebras, Springer, Cham, 2018. In: Assem I., Trepode S. (eds), Homological Methods, Representation Theory, and Cluster Algebras, CRM Short Courses, 177-223.A. Sierra, The dimension of the center of a Brauer configuration algebra, J. Algebra 510 (2018), 289-318.D.R. Stinson and M.B. Paterson, Cryptography; Theory and Practice, Chapman and Hall/CRC, 2018.G. M. Ziegler, Lectures on Polytopes, Springer, 1998.AES, Vol. https://searchsecurity.techtarget.com/definition/Advanced-EncryptionStandard, TechTarget.CriptografíaSímbolosSigns and symbolsAdvanced Encryption Standard (AES)AutomataBrauer configuration algebracryptographydiophantine equationsChicken McNugget Problem (CMP)polytopeEstudiantesInvestigadoresMaestrosPúblico generalLICENSElicense.txtlicense.txttext/plain; charset=utf-84675https://repositorio.unal.edu.co/bitstream/unal/82265/1/license.txtb577153cc0e11f0aeb5fc5005dc82d8aMD51ORIGINAL1020828115_2021.pdf1020828115_2021.pdfTesis de Maestría en Matemáticasapplication/pdf597126https://repositorio.unal.edu.co/bitstream/unal/82265/2/1020828115_2021.pdf572b905ad5eb6248ae99459a2251b495MD52THUMBNAIL1020828115_2021.pdf.jpg1020828115_2021.pdf.jpgGenerated 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