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Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions x to the equation given elements g and h of a finite cyclic group G. The difficulty of this problem is the basis for the security of several cryptographic systems, including Diffie–Hellman key agreement, ElGamal encryption, the ElGamal signature scheme, the Digital Signature Algorithm, and the elliptic curve cryptography analogs of these. Common choices for G used in these algorithms include the multiplicative group of integers modulo p, the multiplicative group of a finite field, and the group of points on an elliptic curve over a finite field.

Attributes	Values
rdf:type	yago:WikicatAsymmetric-keyAlgorithms yago:WikicatComputationalHardnessAssumptions yago:WikicatLogarithms yago:WikicatWorldRecords yago:Abstraction100002137 yago:Accomplishment100035189 yago:Act100030358 yago:Action100037396 yago:Activity100407535 yago:Algorithm105847438 yago:Attainment100062806 yago:Communication100033020 yago:Event100029378 yago:Exponent106812417 yago:Logarithm106812631 yago:MathematicalNotation106808720 yago:Message106598915 yago:Notation106808493 yago:Postulate106753299 yago:Premise106753800 yago:Procedure101023820 yago:Proposition106750804 yago:PsychologicalFeature100023100 yago:Record100063014 yago:WorldRecord100063559 yago:Writing106359877 yago:WrittenCommunication106349220 yago:YagoPermanentlyLocatedEntity yago:Rule105846932 yago:Statement106722453
rdfs:label	Récords en logaritmos discretos (es) Discrete logarithm records (en)
rdfs:comment	Los récords en logaritmos discretos son los mejores resultados obtenidos hasta la fecha en la resolución del problema del logaritmo discreto, consistente en encontrar soluciones de x para la ecuación gx = h, dados dos elementos g y h pertenecientes a un grupo cíclico finito G. La dificultad de resolver el problema es la base de la seguridad de numerosos sistemas criptográficos, entre ellos el protocolo Diffie-Hellman, el cifrado ElGamal, el Algoritmo de Firma Digital (DSA), o la criptografía de curvas elípticas. La elección más habitual de G utilizada en esos algoritmos incluye el grupo multiplicativo de enteros módulo p, el grupo multiplicativo de un cuerpo finito, y el conjunto de puntos de una curva elíptica sobre un cuerpo finito. (es) Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions x to the equation given elements g and h of a finite cyclic group G. The difficulty of this problem is the basis for the security of several cryptographic systems, including Diffie–Hellman key agreement, ElGamal encryption, the ElGamal signature scheme, the Digital Signature Algorithm, and the elliptic curve cryptography analogs of these. Common choices for G used in these algorithms include the multiplicative group of integers modulo p, the multiplicative group of a finite field, and the group of points on an elliptic curve over a finite field. (en)
dcterms:subject	Asymmetric-key algorithms Computational hardness assumptions Modular arithmetic Logarithms World records
Wikipage page ID	30250507 (xsd:integer)
Wikipage revision ID	1117456192 (xsd:integer)
Link from a Wikipage to another Wikipage	Number field sieve Paul Zimmermann Peter Montgomery (mathematician) University of Waterloo Elliptic curve cryptography Cryptographic Safe prime Elliptic curve Graz University of Technology Nadia Heninger Asymmetric-key algorithms Antoine Joux Strong prime Computational hardness assumptions Function field sieve Pollard's kangaroo algorithm CINVESTAV Modular arithmetic Certicom Cyclic group Daniel J. Bernstein Logarithms Finite field World records Digital Signature Algorithm Discrete logarithm Pollard's rho algorithm for logarithms Finite fields Prime number ElGamal encryption ElGamal signature scheme dbr:Ralf_Zimmermann PlayStation 3 Field-programmable gate array Intel Xeon RSA-240 Virtex-6 Tanja Lange Arjen K. Lenstra AlphaServer GS1280 dbr:Peter_Schwabe Diffie–Hellman dbr:Christof_Paar dbr:Erich_Wenger dbr:Kintex-7 dbr:Koblitz_curve dbr:Paul_Wolfger dbr:Ruben_Niederhagen dbr:Susanne_Engels
Link from a Wikipage to an external page	https://dldb.loria.fr/ https://www.nvidia.com/en-us/data-center/v100/ https://github.com/JeanLucPons
sameAs	Discrete logarithm records Discrete logarithm records Discrete logarithm records Discrete logarithm records Discrete logarithm records
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