Efficient ZHFE Key Generation
In this paper we present a new algorithm to construct the keys of the multivariate public key encryption scheme ZHFE. Constructing ZHFE’s trapdoor involves finding a low degree polynomial of q-Hamming-weight-three, as an aid to invert a pair of q-Hamming-weight-two polynomials of high degree and hig...
- Autores:
-
Baena Giraldo, John Bayron
Cabarcas Jaramillo, Daniel
Porras Barrera, Jaiberth
Verbel Herrera, Javier Alfonso
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2016
- Institución:
- Tecnológico de Antioquia
- Repositorio:
- Repositorio Tdea
- Idioma:
- eng
- OAI Identifier:
- oai:dspace.tdea.edu.co:tdea/4202
- Acceso en línea:
- https://dspace.tdea.edu.co/handle/tdea/4202
- Palabra clave:
- Multivariate public key cryptography
Criptografía de clave pública multivariante
Encryption schemes
Esquemas de cifrado
ZHFE
Block diagonal matrix
Matriz diagonal de bloques
Algoritmo
Algorithm
Algorithme
- Rights
- closedAccess
- License
- http://purl.org/coar/access_right/c_14cb
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Efficient ZHFE Key Generation |
| title |
Efficient ZHFE Key Generation |
| spellingShingle |
Efficient ZHFE Key Generation Multivariate public key cryptography Criptografía de clave pública multivariante Encryption schemes Esquemas de cifrado ZHFE Block diagonal matrix Matriz diagonal de bloques Algoritmo Algorithm Algorithme |
| title_short |
Efficient ZHFE Key Generation |
| title_full |
Efficient ZHFE Key Generation |
| title_fullStr |
Efficient ZHFE Key Generation |
| title_full_unstemmed |
Efficient ZHFE Key Generation |
| title_sort |
Efficient ZHFE Key Generation |
| dc.creator.fl_str_mv |
Baena Giraldo, John Bayron Cabarcas Jaramillo, Daniel Porras Barrera, Jaiberth Verbel Herrera, Javier Alfonso |
| dc.contributor.author.none.fl_str_mv |
Baena Giraldo, John Bayron Cabarcas Jaramillo, Daniel Porras Barrera, Jaiberth Verbel Herrera, Javier Alfonso |
| dc.subject.proposal.none.fl_str_mv |
Multivariate public key cryptography Criptografía de clave pública multivariante Encryption schemes Esquemas de cifrado ZHFE Block diagonal matrix Matriz diagonal de bloques |
| topic |
Multivariate public key cryptography Criptografía de clave pública multivariante Encryption schemes Esquemas de cifrado ZHFE Block diagonal matrix Matriz diagonal de bloques Algoritmo Algorithm Algorithme |
| dc.subject.tee.none.fl_str_mv |
Algoritmo Algorithm Algorithme |
| description |
In this paper we present a new algorithm to construct the keys of the multivariate public key encryption scheme ZHFE. Constructing ZHFE’s trapdoor involves finding a low degree polynomial of q-Hamming-weight-three, as an aid to invert a pair of q-Hamming-weight-two polynomials of high degree and high rank. This is done by solving a large sparse linear system of equations. We unveil the combinatorial structure of the system in order to reveal the hidden structure of the matrix associated with it. When the system’s variables and equations are organized accordingly, an almost block diagonal shape emerges. We then exploit this shape to solve the system much faster than when ZHFE was first proposed. The paper presents the theoretical details explaining the structure of the matrix. We also present experimental data that confirms the notable improvement of the key generation complexity, which makes ZHFE more suitable for practical implementations. Keywords Multivariate public key cryptography Encryption schemes ZHFE Block diagonal matrix |
| publishDate |
2016 |
| dc.date.issued.none.fl_str_mv |
2016 |
| dc.date.accessioned.none.fl_str_mv |
2023-11-17T19:39:05Z |
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2023-11-17T19:39:05Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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Text |
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info:eu-repo/semantics/article |
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http://purl.org/redcol/resource_type/ART |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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0302-9743 |
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https://dspace.tdea.edu.co/handle/tdea/4202 |
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1611-3349 |
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0302-9743 1611-3349 |
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eng |
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eng |
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232 |
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213 |
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9606 |
| dc.relation.ispartofjournal.spa.fl_str_mv |
Lecture Notes in Computer Science |
| dc.relation.references.spa.fl_str_mv |
Bernstein, D.J., Buchmann, J., Dahmen, E.: Post-quantum Cryptography, 1st edn. Springer, Heidelberg (2009) Bettale, L., Faugère, J.C., Perret, L.: Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic. Des. Codes Crypt. 69(1), 1–52 (2013) Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symbolic Comput. 24(3–4), 235–265 (1997). http://dx.doi.org/10.1006/jsco.1996.0125, computational algebra and number theory (London, 1993) Ding, J., Gower, J.E., Schmidt, D.S.: Multivariate Public Key Cryptosystems. AISC, vol. 25. Springer, New York (2006) Ding, J., Schmidt, D.: Rainbow, a new multivariable polynomial signature scheme. In: Ioannidis, J., Keromytis, A.D., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 164–175. Springer, Heidelberg (2005) Faugère, J.C.: A new efficient algorithm for computing Gröbner bases \((F_4)\). J. Pure Appl. Algebra 139(1–3), 61–88 (1999). Effective methods in algebraic geometry (Saint-Malo, 1998) Faugère, J.-C., Joux, A.: Algebraic cryptanalysis of hidden field equation (HFE) cryptosystems using Gröbner bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 44–60. Springer, Heidelberg (2003) Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1990) Kipnis, A., Shamir, A.: Cryptanalysis of the HFE public key cryptosystem by relinearization. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 19–30. Springer, Heidelberg (1999) Patarin, J.: Hidden fields equations (HFE) and isomorphisms of polynomials (IP): two new families of asymmetric algorithms. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 33–48. Springer, Heidelberg (1996) Perlner, R.A., Smith-Tone, D.: Security analysis and key modification for ZHFE. In: Proceedings of the 7th International Conference Post-Quantum Cryptography, PQCrypto 2016, 24–26 February 2016, Fukuoka, Japan (2016, to appear) Porras, J., Baena, J., Ding, J.: ZHFE, a new multivariate public key encryption scheme. In: Mosca, M. (ed.) PQCrypto 2014. LNCS, vol. 8772, pp. 229–245. Springer, Heidelberg (2014) Porras, J., Baena, J., Ding, J.: New candidates for multivariate trapdoor functions. Rev. Colomb. Matemáticas 49, 57–76 (2015) Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999). (Electronic) Zhang, W., Tan, C.H.: Personal communication (2015) |
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closedAccess |
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Baena Giraldo, John Bayronaba9dd71-b0fa-4f08-90cc-9bd6834af1a4Cabarcas Jaramillo, Daniel83a112f9-58f2-4b22-a683-b3715bdc8161Porras Barrera, Jaiberth36cff746-f2bc-40f6-a968-a13c8638f61cVerbel Herrera, Javier Alfonsof4b0de66-db97-4497-b0d8-73e8290ab4822023-11-17T19:39:05Z2023-11-17T19:39:05Z20160302-9743https://dspace.tdea.edu.co/handle/tdea/42021611-3349In this paper we present a new algorithm to construct the keys of the multivariate public key encryption scheme ZHFE. Constructing ZHFE’s trapdoor involves finding a low degree polynomial of q-Hamming-weight-three, as an aid to invert a pair of q-Hamming-weight-two polynomials of high degree and high rank. This is done by solving a large sparse linear system of equations. We unveil the combinatorial structure of the system in order to reveal the hidden structure of the matrix associated with it. When the system’s variables and equations are organized accordingly, an almost block diagonal shape emerges. We then exploit this shape to solve the system much faster than when ZHFE was first proposed. The paper presents the theoretical details explaining the structure of the matrix. We also present experimental data that confirms the notable improvement of the key generation complexity, which makes ZHFE more suitable for practical implementations. Keywords Multivariate public key cryptography Encryption schemes ZHFE Block diagonal matrix20 páginasimage/jpegengSpringerSuizahttps://link.springer.com/chapter/10.1007/978-3-319-29360-8_14#citeasEfficient ZHFE Key GenerationArtículo de revistahttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a852322139606Lecture Notes in Computer ScienceBernstein, D.J., Buchmann, J., Dahmen, E.: Post-quantum Cryptography, 1st edn. Springer, Heidelberg (2009)Bettale, L., Faugère, J.C., Perret, L.: Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic. Des. Codes Crypt. 69(1), 1–52 (2013)Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symbolic Comput. 24(3–4), 235–265 (1997). http://dx.doi.org/10.1006/jsco.1996.0125, computational algebra and number theory (London, 1993)Ding, J., Gower, J.E., Schmidt, D.S.: Multivariate Public Key Cryptosystems. AISC, vol. 25. Springer, New York (2006)Ding, J., Schmidt, D.: Rainbow, a new multivariable polynomial signature scheme. In: Ioannidis, J., Keromytis, A.D., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 164–175. Springer, Heidelberg (2005)Faugère, J.C.: A new efficient algorithm for computing Gröbner bases \((F_4)\). J. Pure Appl. Algebra 139(1–3), 61–88 (1999). Effective methods in algebraic geometry (Saint-Malo, 1998)Faugère, J.-C., Joux, A.: Algebraic cryptanalysis of hidden field equation (HFE) cryptosystems using Gröbner bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 44–60. Springer, Heidelberg (2003)Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1990)Kipnis, A., Shamir, A.: Cryptanalysis of the HFE public key cryptosystem by relinearization. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 19–30. Springer, Heidelberg (1999)Patarin, J.: Hidden fields equations (HFE) and isomorphisms of polynomials (IP): two new families of asymmetric algorithms. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 33–48. Springer, Heidelberg (1996)Perlner, R.A., Smith-Tone, D.: Security analysis and key modification for ZHFE. In: Proceedings of the 7th International Conference Post-Quantum Cryptography, PQCrypto 2016, 24–26 February 2016, Fukuoka, Japan (2016, to appear)Porras, J., Baena, J., Ding, J.: ZHFE, a new multivariate public key encryption scheme. In: Mosca, M. (ed.) PQCrypto 2014. LNCS, vol. 8772, pp. 229–245. Springer, Heidelberg (2014)Porras, J., Baena, J., Ding, J.: New candidates for multivariate trapdoor functions. Rev. Colomb. Matemáticas 49, 57–76 (2015)Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999). (Electronic)Zhang, W., Tan, C.H.: Personal communication (2015)info:eu-repo/semantics/closedAccesshttp://purl.org/coar/access_right/c_14cbMultivariate public key cryptographyCriptografía de clave pública multivarianteEncryption schemesEsquemas de cifradoZHFEBlock diagonal matrixMatriz diagonal de bloquesAlgoritmoAlgorithmAlgorithmeTHUMBNAILEfficient ZHFE Key Generation.jpg.jpgEfficient ZHFE Key Generation.jpg.jpgGenerated Thumbnailimage/jpeg12029https://dspace.tdea.edu.co/bitstream/tdea/4202/3/Efficient%20ZHFE%20Key%20Generation.jpg.jpg57d0ebbe624559cb8daa5e65c47d6dacMD53open accessLICENSElicense.txtlicense.txttext/plain; charset=utf-814828https://dspace.tdea.edu.co/bitstream/tdea/4202/2/license.txt2f9959eaf5b71fae44bbf9ec84150c7aMD52open accessORIGINALEfficient ZHFE Key Generation.jpgEfficient ZHFE Key Generation.jpgDatos del documentoimage/jpeg162679https://dspace.tdea.edu.co/bitstream/tdea/4202/1/Efficient%20ZHFE%20Key%20Generation.jpgcae90a40660f423da2283a22bb515ffcMD51open accesstdea/4202oai:dspace.tdea.edu.co:tdea/42022023-11-18 03:03:02.263open accessRepositorio Institucional Tecnologico de 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 incorporada en las Obras Colectivas.

b.	Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.

c.	Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.
Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).

4. Restricciones.
La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:

a.	Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).

b.	Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.

c.	Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.

d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:

i.	Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.

ii.	Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.

e.	Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.

5. Representaciones, Garantías y Limitaciones de Responsabilidad.
A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

6. Limitación de responsabilidad.
A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

7. Término.

a.	Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.

b.	Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.

8. Varios.

a.	Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.

b.	Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.

c.	Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.

d.	Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.
 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