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Integer Factorization Records
Integer factorization is the process of determining which prime numbers divide a given positive integer. Doing this quickly has applications in cryptography. The difficulty depends on both the size and form of the number and its prime factors; it is currently very difficult to factorize large semiprimes (and, indeed, most numbers which have no small factors). Numbers of a general form The first enormous distributed factorisation was RSA-129, a 129-digit challenge number described in the Scientific American article of 1977 which first popularised the RSA cryptosystem. It was factorised between September 1993 and April 1994, using MPQS, with relations contributed by about 600 people through the internet, and the final stages of the calculation performed on a MasPar supercomputer at Bell Labs. Between January and August 1999, RSA-155, a 155-digit challenge number prepared by the RSA company, was factorised using GNFS with relations again contributed by a large group, and the final ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Factorization
In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization. When the numbers are sufficiently large, no efficient non-quantum integer factorization algorithm is known. However, it has not been proven that such an algorithm does not exist. The presumed difficulty of this problem is important for the algorithms used in cryptography such as RSA public-key encryption and the RSA digital signature. Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing. In 2019, Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic, Nadia Heninger, Emmanuel Thomé and Paul Zimmermann factored a 240-digit (795-bit) number (RSA-240) utilizing approximately 900 core-years of computing power. The researchers estimated that a 1024-bit RSA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SGI Origin 200
The SGI Origin 200, code named ''Speedo'', was an entry-level server computer developed and manufactured by SGI, introduced in October 1996 to accompany their mid-range and high-end Origin 2000. It is based on the same architecture as the Origin 2000 but has an unrelated hardware implementation. At the time of introduction, these systems ran the IRIX 6.4, and later, the IRIX 6.5 operating systems. The Origin 200 was discontinued on 30 June 2002. Hardware The Origin 200 consists of one or two modules. In configurations with two modules, the NUMAlink 2 (originally CrayLink) interconnection fabric is used to connect the two modules together. Using two modules, the Origin 200's capabilities (the number of processors, the amount of memory, etc.) is doubled. The Origin 200 and the Origin 200 GIGAchannel enclosures can be configured as a tower with "skins" that covered the bare metal for cosmetic purposes, or as a rackmountable enclosure compatible with 19- or 21-inch racks. Modu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RSA-240
In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that were part of the RSA Factoring Challenge. The challenge was to find the prime factors of each number. It was created by RSA Laboratories in March 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers. The challenge was ended in 2007. RSA Laboratories (which is an acronym of the creators of the technique; Rivest, Shamir and Adleman) published a number of semiprimes with 100 to 617 decimal digits. Cash prizes of varying size, up to US$200,000 (and prizes up to $20,000 awarded), were offered for factorization of some of them. The smallest RSA number was factored in a few days. Most of the numbers have still not been factored and many of them are expected to remain unfactored for many years to come. , the smallest 23 of the 54 listed numbers have been factored. While the RSA challenge officially ended in 2007, people ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Opteron
Opteron is AMD's x86 former server and workstation processor line, and was the first processor which supported the AMD64 instruction set architecture (known generically as x86-64 or AMD64). It was released on April 22, 2003, with the ''SledgeHammer'' core (K8) and was intended to compete in the server and workstation markets, particularly in the same segment as the Intel Xeon processor. Processors based on the AMD K10 microarchitecture (codenamed ''Barcelona'') were announced on September 10, 2007, featuring a new quad-core configuration. The most-recently released Opteron CPUs are the Piledriver-based Opteron 4300 and 6300 series processors, codenamed "Seoul" and "Abu Dhabi" respectively. In January 2016, the first ARMv8-A based Opteron-branded SoC was released, though it is unclear what, if any, heritage this Opteron-branded product line shares with the original Opteron technology other than intended use in the server space. Technical description Two key capabilities Opt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Advanced Micro Devices
Advanced Micro Devices, Inc. (AMD) is an American multinational semiconductor company based in Santa Clara, California, that develops computer processors and related technologies for business and consumer markets. While it initially manufactured its own processors, the company later outsourced its manufacturing, a practice known as going fabless, after GlobalFoundries was spun off in 2009. AMD's main products include microprocessors, motherboard chipsets, embedded processors, graphics processors, and FPGAs for servers, workstations, personal computers, and embedded system applications. History First twelve years Advanced Micro Devices was formally incorporated by Jerry Sanders, along with seven of his colleagues from Fairchild Semiconductor, on May 1, 1969. Sanders, an electrical engineer who was the director of marketing at Fairchild, had, like many Fairchild executives, grown frustrated with the increasing lack of support, opportunity, and flexibility within th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RSA-768
In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that were part of the RSA Factoring Challenge. The challenge was to find the prime factors of each number. It was created by RSA Laboratories in March 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers. The challenge was ended in 2007. RSA Laboratories (which is an acronym of the creators of the technique; Rivest, Shamir and Adleman) published a number of semiprimes with 100 to 617 decimal digits. Cash prizes of varying size, up to US$200,000 (and prizes up to $20,000 awarded), were offered for factorization of some of them. The smallest RSA number was factored in a few days. Most of the numbers have still not been factored and many of them are expected to remain unfactored for many years to come. , the smallest 23 of the 54 listed numbers have been factored. While the RSA challenge officially ended in 2007, people ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
INRIA
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 ab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centrum Wiskunde & Informatica
The (abbr. CWI; English: "National Research Institute for Mathematics and Computer Science") is a research centre in the field of mathematics and theoretical computer science. It is part of the institutes organization of the Dutch Research Council (NWO) and is located at the Amsterdam Science Park. This institute is famous as the creation site of the programming language Python. It was a founding member of the European Research Consortium for Informatics and Mathematics (ERCIM). Early history The institute was founded in 1946 by Johannes van der Corput, David van Dantzig, Jurjen Koksma, Hendrik Anthony Kramers, Marcel Minnaert and Jan Arnoldus Schouten. It was originally called ''Mathematical Centre'' (in Dutch: ''Mathematisch Centrum''). One early mission was to develop mathematical prediction models to assist large Dutch engineering projects, such as the Delta Works. During this early period, the Mathematics Institute also helped with designing the wings of the Fokker F27 F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RSA-640
In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that were part of the RSA Factoring Challenge. The challenge was to find the prime factors of each number. It was created by RSA Security, RSA Laboratories in March 1991 to encourage research into computational number theory and the practical difficulty of Integer factorization, factoring large integers. The challenge was ended in 2007. RSA Laboratories (which is an acronym of the creators of the technique; Rivest, Shamir and Adleman) published a number of semiprimes with 100 to 617 decimal digits. Cash prizes of varying size, up to United States dollar, US$200,000 (and prizes up to $20,000 awarded), were offered for factorization of some of them. The smallest RSA number was factored in a few days. Most of the numbers have still not been factored and many of them are expected to remain unfactored for many years to come. , the smallest 23 of the 54 listed numbers have been factored. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RSA-200
In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that were part of the RSA Factoring Challenge. The challenge was to find the prime factors of each number. It was created by RSA Laboratories in March 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers. The challenge was ended in 2007. RSA Laboratories (which is an acronym of the creators of the technique; Rivest, Shamir and Adleman) published a number of semiprimes with 100 to 617 decimal digits. Cash prizes of varying size, up to US$200,000 (and prizes up to $20,000 awarded), were offered for factorization of some of them. The smallest RSA number was factored in a few days. Most of the numbers have still not been factored and many of them are expected to remain unfactored for many years to come. , the smallest 23 of the 54 listed numbers have been factored. While the RSA challenge officially ended in 2007, people ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rikkyo University
, also known as Saint Paul's University, is a private university, in Ikebukuro, Tokyo, Japan. Rikkyo is known as one of the six leading universities in the field of sports in Tokyo (東京六大学 "Big Six" — Rikkyo University, University of Tokyo, Keio University, Waseda University, Meiji University, and Hosei University). A leading liberal arts teaching and research institution, the university is the largest Anglican Christian affiliated university in Japan. The university is internationally oriented and involved in numerous international programmes and projects. Rikkyo maintains contact with more than 140 educational institutions abroad for the purpose of exchanging lecturers, students and projects. With more than 700 students from outside Japan, the institution has 20,000 students, and 2,700 teachers and staff members. Rikkyo University's deviation value is in the top 10 in the ranking of private universities in Japan. Rikkyo Gakuin Rikkyo Primary School, Rikkyo Ikebuk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
