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Jean-Charles Faugère
Jean-Charles Faugère is the head of the POLSYS project-team (Solvers for Algebraic Systems and Applications) of the Laboratoire d'Informatique de Paris 6 (LIP6) and Paris–Rocquencourt center of INRIA, in Paris. The team was formerly known as SPIRAL and SALSA. Faugère obtained his Ph.D. in mathematics in 1994 at the University of Paris VI, with the dissertation ''"Résolution des systemes d’équations algébriques"'' (Solving systems of algebraic equations), under the supervision of Daniel Lazard. He works on Gröbner bases and their applications, in particular, in cryptology. With his collaborators, he has devised the FGLM algorithm for computing Gröbner bases; he has also introduced the F4 and F5 algorithms for calculating Gröbner bases. In particular, his F5 algorithm allowed him to solve various problems in cryptography such as HFE; he also introduced a new type of cryptanalysis Cryptanalysis (from the Greek ''kryptós'', "hidden", and ''analýein'', "to analyze" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laboratoire D'Informatique De Paris 6
The LIP6, the computer science laboratory of Sorbonne University's Faculty of Science and Engineering is a joint research laboratory of Sorbonne University and CNRS, the French national research organization. The current name comes from the acronym of its historical name, Laboratoire d'Informatique de P aris 6. It was founded in January, 1997, with the fusion of three smaller laboratories: LAFORIA, LITP, and MASI. Employing over 150 permanent professors and research scientists, LIP6 is one of the largest computer science laboratories in France. Research activities LIP6's research activities are organized around five general areas of research: *Embedded systems *Scientific computation * Networking and Distributed systems *Databases and Machine learning *Decision making and Optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Faugère's F4 And F5 Algorithms
In computer algebra, the Faugère F4 algorithm, by Jean-Charles Faugère, computes the Gröbner basis of an ideal of a multivariate polynomial ring. The algorithm uses the same mathematical principles as the Buchberger algorithm, but computes many normal forms in one go by forming a generally sparse matrix and using fast linear algebra to do the reductions in parallel. The Faugère F5 algorithm first calculates the Gröbner basis of a pair of generator polynomials of the ideal. Then it uses this basis to reduce the size of the initial matrices of generators for the next larger basis: If ''G''prev is an already computed Gröbner basis (''f''2, …, ''f''''m'') and we want to compute a Gröbner basis of (''f''1) + ''G''prev then we will construct matrices whose rows are ''m'' ''f''1 such that ''m'' is a monomial not divisible by the leading term of an element of ''G''prev. This strategy allows the algorithm to apply two new criteria based on what Faugère calls ''s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre And Marie Curie University Alumni
Pierre is a masculine given name. It is a French form of the name Peter. Pierre originally meant "rock" or "stone" in French (derived from the Greek word πέτρος (''petros'') meaning "stone, rock", via Latin "petra"). It is a translation of Aramaic כיפא (''Kefa),'' the nickname Jesus gave to apostle Simon Bar-Jona, referred in English as Saint Peter. Pierre is also found as a surname. People with the given name * Abbé Pierre, Henri Marie Joseph Grouès (1912–2007), French Catholic priest who founded the Emmaus Movement * Monsieur Pierre, Pierre Jean Philippe Zurcher-Margolle (c. 1890–1963), French ballroom dancer and dance teacher * Pierre (footballer), Lucas Pierre Santos Oliveira (born 1982), Brazilian footballer * Pierre, Baron of Beauvau (c. 1380–1453) * Pierre, Duke of Penthièvre (1845–1919) * Pierre, marquis de Fayet (died 1737), French naval commander and Governor General of Saint-Domingue * Prince Pierre, Duke of Valentinois (1895–1964), fathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptanalysis
Cryptanalysis (from the Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown. In addition to mathematical analysis of cryptographic algorithms, cryptanalysis includes the study of side-channel attacks that do not target weaknesses in the cryptographic algorithms themselves, but instead exploit weaknesses in their implementation. Even though the goal has been the same, the methods and techniques of cryptanalysis have changed drastically through the history of cryptography, adapting to increasing cryptographic complexity, ranging from the pen-and-paper methods of the past, through machines like the British Bombes and Colossus computers at Bletchley Park in World War II, to the mathematically advanced comput ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hidden Field Equations
Hidden Fields Equations (HFE), also known as HFE trapdoor function, is a public key cryptosystem which was introduced at Eurocrypt in 1996 and proposed by Jacques Patarin following the idea of the Matsumoto and Imai system. It is based on polynomials over finite fields \mathbb_q of different size to disguise the relationship between the private key and public key. HFE is in fact a family which consists of basic HFE and combinatorial versions of HFE. The HFE family of cryptosystems is based on the hardness of the problem of finding solutions to a system of multivariate quadratic equations (the so-called MQ problem) since it uses private affine transformations to hide the extension field and the private polynomials. Hidden Field Equations also have been used to construct digital signature schemes, e.g. Quartz and Sflash. Mathematical background One of the central notions to understand how Hidden Field Equations work is to see that for two extension fields \mathbb_ \mathbb_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security ( data confidentiality, data integrity, authentication, and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications. Cryptography prior to the modern age was effectively synonymo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Pure And Applied Algebra
The ''Journal of Pure and Applied Algebra'' is a monthly peer-reviewed scientific journal covering that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications. Its founding editors-in-chief were Peter J. Freyd (University of Pennsylvania) and Alex Heller (City University of New York). The current managing editors are Eric Friedlander (University of Southern California), Charles Weibel (Rutgers University), and Srikanth Iyengar (University of Utah). Abstracting and indexing The journal is abstracted and indexed in Current Contents/Physics, Chemical, & Earth Sciences, Mathematical Reviews, PASCAL, Science Citation Index, Zentralblatt MATH, and Scopus. According to the ''Journal Citation Reports'', the journal has a 2016 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Symbolic Computation
The ''Journal of Symbolic Computation'' is a peer-reviewed monthly scientific journal covering all aspects of symbolic computation published by Academic Press and then by Elsevier. It is targeted to both mathematicians and computer scientists. It was established in 1985 by Bruno Buchberger, who served as its editor until 1994. The journal covers a wide variety of topics, including: * Computer algebra, for which it is considered the top journal * Computational geometry * Automated theorem proving * Applications of symbolic computation in education, science, and industry According to the ''Journal Citation Reports'', its 2020 impact factor is 0.847. The journal is abstracted and indexed by Scopus and the Science Citation Index. See also * ''Higher-Order and Symbolic Computation'' * International Symposium on Symbolic and Algebraic Computation ISSAC, the International Symposium on Symbolic and Algebraic Computation, is an academic conference in the field of computer algebra. IS ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Institute For Research In Computer Science And Automation
The National Institute for Research in Digital Science and Technology (Inria) () is a French national research institution focusing on computer science and applied mathematics. It was created under the name ''Institut de recherche en informatique et en automatique'' (IRIA) in 1967 at Rocquencourt near Paris, part of Plan Calcul. Its first site was the historical premises of SHAPE (central command of NATO military forces), which is still used as Inria's main headquarters. In 1980, IRIA became INRIA. Since 2011, it has been styled ''Inria''. Inria is a Public Scientific and Technical Research Establishment (EPST) under the double supervision of the French Ministry of National Education, Advanced Instruction and Research and the Ministry of Economy, Finance and Industry. Administrative status Inria has 9 research centers distributed across France (in Bordeaux, Grenoble- Inovallée, Lille, Lyon, Nancy, Paris-Rocquencourt, Rennes, Saclay, and Sophia Antipolis) and one center abro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
