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Statements

Subject Item
dbr:Diffie–Hellman_problem
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Diffie–Hellman problem Diffie-Hellman-Problem Problème de Diffie-Hellman Problema Diffie–Hellman
rdfs:comment
Le problème de Diffie-Hellman (abrégé DHP de l'anglais Diffie-Hellman problem) est un problème mathématique évoqué en premier par Whitfield Diffie et Martin Hellman en cryptologie. Le leitmotiv de ce problème est le fait que beaucoup de systèmes de sécurité utilisent des opérations mathématiques rapides à calculer, mais très difficiles, voire impossibles à l'échelle humaine, à inverser. Par exemple il est facile de calculer le hash d'un message avec les fonctions mathématiques de hachage, mais très difficile de revenir au message originel. Si la résolution du problème de Diffie-Hellman était facile, ces systèmes seraient faciles à corrompre. The Diffie–Hellman problem (DHP) is a mathematical problem first proposed by Whitfield Diffie and Martin Hellman in the context of cryptography. The motivation for this problem is that many security systems use one-way functions: mathematical operations that are fast to compute, but hard to reverse. For example, they enable encrypting a message, but reversing the encryption is difficult. If solving the DHP were easy, these systems would be easily broken. Na criptografia, para certos grupos, presume-se que o DHP é difícil, e isso é frequentemente chamado de suposição de Diffie-Hellman. O problema sobreviveu ao escrutínio por algumas décadas e nenhuma solução "fácil" foi divulgada ainda.
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dbc:Computational_hardness_assumptions dbc:Finite_fields
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3237741
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1101881731
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dbr:Generating_set_of_a_group dbr:Cryptography dbr:Pairing dbr:Group_(mathematics) dbr:Computational_Diffie–Hellman_assumption dbr:Ueli_Maurer_(cryptographer) dbr:Martin_Hellman dbr:CRYPTO dbc:Computational_hardness_assumptions dbr:Richard_J._Lipton dbr:One-way_functions dbr:Diffie–Hellman_key_exchange dbr:Lecture_Notes_in_Computer_Science dbr:Dan_Boneh dbr:Elliptic_curve dbr:Finite_field dbr:EUROCRYPT dbr:Discrete_logarithm_problem dbr:Multiplicative_group dbr:Decisional_Diffie–Hellman_assumption dbr:Whitfield_Diffie dbr:ElGamal_encryption dbc:Finite_fields
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dbo:abstract
Na criptografia, para certos grupos, presume-se que o DHP é difícil, e isso é frequentemente chamado de suposição de Diffie-Hellman. O problema sobreviveu ao escrutínio por algumas décadas e nenhuma solução "fácil" foi divulgada ainda. A partir de 2006, o meio mais eficiente conhecido para resolver o DHP é resolver o problema do logaritmo discreto (DLP), que é encontrar x dados ge gx. Na verdade, um progresso significativo (por den Boer, Maurer, Wolf, Boneh e Lipton) foi feito no sentido de mostrar que em muitos grupos o DHP é quase tão difícil quanto o DLP. Não há prova até o momento de que o DHP ou o DLP sejam um problema difícil, exceto em grupos genéricos (por Nechaev e Shoup). Uma prova de que qualquer um dos problemas é difícil implica que P ≠ NP. The Diffie–Hellman problem (DHP) is a mathematical problem first proposed by Whitfield Diffie and Martin Hellman in the context of cryptography. The motivation for this problem is that many security systems use one-way functions: mathematical operations that are fast to compute, but hard to reverse. For example, they enable encrypting a message, but reversing the encryption is difficult. If solving the DHP were easy, these systems would be easily broken. Le problème de Diffie-Hellman (abrégé DHP de l'anglais Diffie-Hellman problem) est un problème mathématique évoqué en premier par Whitfield Diffie et Martin Hellman en cryptologie. Le leitmotiv de ce problème est le fait que beaucoup de systèmes de sécurité utilisent des opérations mathématiques rapides à calculer, mais très difficiles, voire impossibles à l'échelle humaine, à inverser. Par exemple il est facile de calculer le hash d'un message avec les fonctions mathématiques de hachage, mais très difficile de revenir au message originel. Si la résolution du problème de Diffie-Hellman était facile, ces systèmes seraient faciles à corrompre.
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