About: Diffie–Hellman problem

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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.

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rdfs:label	Diffie-Hellman-Problem (de) Diffie–Hellman problem (en) Problème de Diffie-Hellman (fr) Problema Diffie–Hellman (pt)
rdfs:comment	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. (en) 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. (fr) 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. (pt)
dct:subject	Computational hardness assumptions Finite fields
Wikipage page ID	3237741 (xsd:integer)
Wikipage revision ID	1101881731 (xsd:integer)
Link from a Wikipage to another Wikipage	Multiplicative group Ueli Maurer (cryptographer) Decisional Diffie–Hellman assumption Cryptography One-way functions Elliptic curve Generating set of a group Computational hardness assumptions Computational Diffie–Hellman assumption Pairing Whitfield Diffie Lecture Notes in Computer Science Dan Boneh Finite field Diffie–Hellman key exchange Group (mathematics) EUROCRYPT Finite fields ElGamal encryption Martin Hellman Richard Lipton Discrete logarithm problem CRYPTO
Link from a Wikipage to an external page	http://eprint.iacr.org/2004/306 https://archive.org/details/3rdacmconference00asso https://archive.org/details/3rdacmconference00asso/page/31 https://www.di.ens.fr/~bresson/papers/BreChePoi02b.pdf
sameAs	Diffie–Hellman problem Diffie–Hellman problem Diffie–Hellman problem Diffie–Hellman problem Diffie–Hellman problem Diffie–Hellman problem Diffie–Hellman problem Diffie–Hellman problem
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has abstract	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. (en) 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. (fr) 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. (pt)
gold:hypernym	Problem
prov:wasDerivedFrom	wikipedia-en:Diffie–Hellman_problem?oldid=1101881731&ns=0
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is Link from a Wikipage to another Wikipage of	XTR Algebraic Eraser Decisional Diffie–Hellman assumption Index of cryptography articles Proth prime Elliptic-curve Diffie–Hellman Computational Diffie–Hellman assumption DHP Lattice-based cryptography Evi Nemeth Diffie–Hellman key exchange Cheon, Jung Hee Integrated Encryption Scheme Diffie-Hellman problem Naor–Reingold pseudorandom function Secure channel Pairing-based cryptography Decision Diffie–Hellman problem Computational Diffie-Hellman problem Computational Diffie–Hellman problem Diffie-Hellman assumption

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