Publication: Métodos algebraicos en criptografía multivariable
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2019-05-10
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Universidad Complutense de Madrid
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Abstract
La criptografía de curva elíptica no es la solución a largo plazo que esperábamos que fuera. Por tanto, nos hemos visto obligados a replantear nuestra estrategia”. Con estas palabras alertaba en el 2015 la Agencia Nacional de Seguridad estadounidense (NSA) sobre la necesidad de encontrar nuevas herramientas criptográficas que permitan mantener la seguridad en Internet. En un comunicado de su web, la agencia ha mostrado su interés en “iniciar una transición a algoritmos potencialmente resistentes a ordenadores cuánticos en un futuro no muy lejano”.Consideran un objetivo principal disponer de herramientas de seguridad ante un posible ordenador cuántico.En las últimas décadas Internet ha adquirido un papel central en la sociedad. Uno de los pilares sobre los que se sostiene la red es la criptografía de clave pública, que permite las comunicaciones privadas, la identificación de los usuarios en un servidor y la firma de documentos. Entre los diferentes métodos que se utilizan para llevar acabo este tipo de algoritmos está el algoritmo RSA, que se basa en la factorización de números enteros muy grandes. Sin embargo, en el año 1994 Peter Shor presentó un algoritmo que permite factorizar números enteros grandes y podría echar abajo este sistema. La única razón por la que aún el algoritmo de Shor no ha puesto en peligro la seguridad de Internet es que para ello necesita un ordenador cuántico de miles de q-bits. Por el momento dicho ordenador no existe, pero los progresos actuales en computación cuántica permiten pensar que dentro de unas décadas se podrá construir un ordenador cuántico con esas características. Por tanto, es necesario enfrentar este nuevo escenario lo antes posible...
Elliptic Curve Cryptography is not the long term solution many once hoped it would be. Thus, we have been obligated to update our strategy’. With these words, the National Security Agency (NSA) of the United States of America alerted about the necessity of finding new cryptographic tools that would allow us to maintain security over the Internet. In a statement on their website, the agency has shown interest in ‘initiating a migration to potentially quantum-resistant cryptographic algorithms in the near future’. They consider essential the disposal of security tools against a possible quantum computer. One of the main corner stones on which the network is supported is public key cryptography (PKC), which allows private communications, authentication of users in a server and signature of data. Among the different PKC schemes, there is the RSA algorithm, whose securityis dependent on the difficulty of factorizing a big composite number. However, in1994 Peter Shor presented a polynomial-time factorization algorithm, which would make RSA insecure. The only reason why Shor’s algorithm has not endangered Internet’s security is that it was designed to be programmed in a quantum computerwith thousands of q-bits. Currently, such a computer does not exist, but the ongoing progress in quantum computation suggests that a quantum computer with the necessary characteristics will be plausible within some decades. Therefore, it is necessary to confront such a new scenario as soon as possible.
Elliptic Curve Cryptography is not the long term solution many once hoped it would be. Thus, we have been obligated to update our strategy’. With these words, the National Security Agency (NSA) of the United States of America alerted about the necessity of finding new cryptographic tools that would allow us to maintain security over the Internet. In a statement on their website, the agency has shown interest in ‘initiating a migration to potentially quantum-resistant cryptographic algorithms in the near future’. They consider essential the disposal of security tools against a possible quantum computer. One of the main corner stones on which the network is supported is public key cryptography (PKC), which allows private communications, authentication of users in a server and signature of data. Among the different PKC schemes, there is the RSA algorithm, whose securityis dependent on the difficulty of factorizing a big composite number. However, in1994 Peter Shor presented a polynomial-time factorization algorithm, which would make RSA insecure. The only reason why Shor’s algorithm has not endangered Internet’s security is that it was designed to be programmed in a quantum computerwith thousands of q-bits. Currently, such a computer does not exist, but the ongoing progress in quantum computation suggests that a quantum computer with the necessary characteristics will be plausible within some decades. Therefore, it is necessary to confront such a new scenario as soon as possible.
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Tesis de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 21-06-2018