|
Discrete Logarithm Records
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 g^x=h 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. The current record for integers modulo prime numbers, set in December 2019, is a discrete logarithm computation modulo a prime with 240 digits. For characteristic 2, the current record for finite fields, set in July 2019, is a discrete logarithm over GF ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Logarithm
In mathematics, for given real numbers ''a'' and ''b'', the logarithm log''b'' ''a'' is a number ''x'' such that . Analogously, in any group ''G'', powers ''b''''k'' can be defined for all integers ''k'', and the discrete logarithm log''b'' ''a'' is an integer ''k'' such that . In number theory, the more commonly used term is index: we can write ''x'' = ind''r'' ''a'' (mod ''m'') (read "the index of ''a'' to the base ''r'' modulo ''m''") for ''r''''x'' ≡ ''a'' (mod ''m'') if ''r'' is a primitive root of ''m'' and gcd(''a'',''m'') = 1. Discrete logarithms are quickly computable in a few special cases. However, no efficient method is known for computing them in general. Several important algorithms in public-key cryptography, such as ElGamal base their security on the assumption that the discrete logarithm problem over carefully chosen groups has no efficient solution. Definition Let ''G'' be any group. Denote its group operation by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antoine Joux
Antoine Joux (born 1967) is a French cryptographer,"Antoine Joux, Prix Gödel 2013" Bulletin de la société informatique de France – numéro 1, septembre 2013 one of the three 2013 Gödel Prize laureates., specifically cited for his paper ''A one round protocol for tripartite Diffie-Hellman''. He was at the Université de Versailles Saint-Quentin-en-Yvelines and researcher in the CRYPT team of the laboratory of computer science PRISM of CNRS, currently he is Chair of Cryptology of the ''Fondation partenariale'' of Université Pierre et Marie Curie, UPMC, ''professeur associé'' at the Laboratoire d'informatique de Paris 6, and Senior Crypto-Security Expert at CryptoExperts. References {{DEFAULTSORT:Joux, Antoine 1967 births Living people French cryptographers P ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erich Wenger
The given name Eric, Erich, Erikk, Erik, Erick, or Eirik is derived from the Old Norse name ''Eiríkr'' (or ''Eríkr'' in Old East Norse due to monophthongization). The first element, ''ei-'' may be derived from the older Proto-Norse ''* aina(z)'', meaning "one, alone, unique", ''as in the form'' ''Æ∆inrikr'' explicitly, but it could also be from ''* aiwa(z)'' "everlasting, eternity", as in the Gothic form ''Euric''. The second element ''- ríkr'' stems either from Proto-Germanic ''* ríks'' "king, ruler" (cf. Gothic ''reiks'') or the therefrom derived ''* ríkijaz'' "kingly, powerful, rich, prince"; from the common Proto-Indo-European root * h₃rḗǵs. The name is thus usually taken to mean "sole ruler, autocrat" or "eternal ruler, ever powerful". ''Eric'' used in the sense of a proper noun meaning "one ruler" may be the origin of ''Eriksgata'', and if so it would have meant "one ruler's journey". The tour was the medieval Swedish king's journey, when newly elected, to s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PlayStation 3
The PlayStation 3 (PS3) is a home video game console developed by Sony Computer Entertainment. The successor to the PlayStation 2, it is part of the PlayStation brand of consoles. It was first released on November 11, 2006, in Japan, November 17, 2006, in North America, and March 23, 2007, in Europe and Australia. The PlayStation 3 competed primarily against Microsoft's Xbox 360 and Nintendo's Wii as part of the seventh generation of video game consoles. The console was first officially announced at E3 2005, and was released at the end of 2006. It was the first console to use Blu-ray Disk technology as its primary storage medium. The console was the first PlayStation to integrate social gaming services, including the PlayStation Network, as well as the first to be controllable from a handheld console, through its remote connectivity with PlayStation Portable and PlayStation Vita. In September 2009, the ''Slim'' model of the PlayStation 3 was released. It no longer provided the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Montgomery (mathematician)
Peter Lawrence Montgomery (September 25, 1947 – February 18, 2020) was an American mathematician who worked at the System Development Corporation and Microsoft Research. He is best known for his contributions to computational number theory and mathematical aspects of cryptography, including the Montgomery multiplication method for arithmetic in finite fields, the use of Montgomery curves in applications of elliptic curves to integer factorization and other problems, and the Montgomery ladder, which is used to protect against side-channel attacks in elliptic curve cryptography. Education and career Montgomery began his undergraduate career at the University of California, Riverside, in 1965 and transferred to Berkeley in 1967, earning a BA in mathematics in 1969 and an MA in mathematics in 1971, He joined the System Development Corporation (SDC) in 1972, where he worked for many years as a programmer implementing algorithms for the CDC 7600 and PDP series of computers, in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pollard's Rho Algorithm For Logarithms
Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm problem, analogous to Pollard's rho algorithm to solve the integer factorization problem. The goal is to compute \gamma such that \alpha ^ \gamma = \beta, where \beta belongs to a cyclic group G generated by \alpha. The algorithm computes integers a, b, A, and B such that \alpha^a \beta^b = \alpha^A \beta^B. If the underlying group is cyclic of order n, by substituting \beta as a^ and noting that two powers are equal if and only if the exponents are equivalent modulo the order of the base, in this case modulo n, we get that \gamma is one of the solutions of the equation (B-b) \gamma = (a-A) \pmod n. Solutions to this equation are easily obtained using the extended Euclidean algorithm. To find the needed a, b, A, and B the algorithm uses Floyd's cycle-finding algorithm to find a cycle in the sequence x_i = \alpha^ \beta^, where the function f: x_i \map ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Koblitz Curve
Neal I. Koblitz (born December 24, 1948) is a Professor of Mathematics at the University of Washington. He is also an adjunct professor with the Centre for Applied Cryptographic Research at the University of Waterloo. He is the creator of hyperelliptic curve cryptography and the independent co-creator of elliptic curve cryptography. Biography Koblitz received his undergraduate degree from Harvard University in 1969. While at Harvard, he was a Putnam Fellow in 1968. He received his Ph.D. from Princeton University in 1974 under the direction of Nick Katz. From 1975 to 1979 he was an instructor at Harvard University. In 1979 he began working at the University of Washington. Koblitz's 1981 article "Mathematics as Propaganda" criticized the misuse of mathematics in the social sciences and helped motivate Serge Lang's successful challenge to the nomination of political scientist Samuel P. Huntington to the National Academy of Sciences. In ''The Mathematical Intelligencer'', Kob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Certicom
BlackBerry Limited is a Canadian software company specializing in cybersecurity. Founded in 1984, it was originally known as Research In Motion (RIM). As RIM, it developed the BlackBerry brand of interactive pagers, smartphones, and tablets. It transitioned to a cybersecurity enterprise software and services company under Chief Executive Officer John S. Chen. Its products are used by various businesses, car manufacturers, and government agencies to prevent hacking and ransomware attacks. They include BlackBerry Cylance's artificial intelligence based cyber-security solutions, the BlackBerry AtHoc emergency communication system (ECS) platform; the QNX real-time operating system; and BlackBerry Enterprise Server (BlackBerry Unified Endpoint Manager), a Unified Endpoint Management (UEM) platform. BlackBerry was founded in 1984 as Research In Motion by Mike Lazaridis and Douglas Fregin. In 1992, Lazaridis hired Jim Balsillie, and Lazaridis and Balsillie served as co-CEOs unti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intel Xeon
Xeon ( ) is a brand of x86 microprocessors designed, manufactured, and marketed by Intel, targeted at the non-consumer workstation, server, and embedded system markets. It was introduced in June 1998. Xeon processors are based on the same architecture as regular desktop-grade CPUs, but have advanced features such as support for ECC memory, higher core counts, more PCI Express lanes, support for larger amounts of RAM, larger cache memory and extra provision for enterprise-grade reliability, availability and serviceability (RAS) features responsible for handling hardware exceptions through the Machine Check Architecture. They are often capable of safely continuing execution where a normal processor cannot due to these extra RAS features, depending on the type and severity of the machine-check exception (MCE). Some also support multi-socket systems with two, four, or eight sockets through use of the Ultra Path Interconnect (UPI) bus. Overview The ''Xeon'' brand has been mainta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Waterloo
The University of Waterloo (UWaterloo, UW, or Waterloo) is a public research university with a main campus in Waterloo, Ontario, Canada. The main campus is on of land adjacent to "Uptown" Waterloo and Waterloo Park. The university also operates three satellite campuses and four affiliated university colleges. The university offers academic programs administered by six faculties and thirteen faculty-based schools. Waterloo operates the largest post-secondary co-operative education program in the world, with over 20,000 undergraduate students enrolled in the university's co-op program. Waterloo is a member of the U15, a group of research-intensive universities in Canada. The institution originates from the Waterloo College Associate Faculties, established on 4 April 1956; a semi-autonomous entity of Waterloo College, which was an affiliate of the University of Western Ontario. This entity formally separated from Waterloo College and was incorporated as a university with the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CINVESTAV
The Center for Research and Advanced Studies of the National Polytechnic Institute (in Spanish: ''Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional'' or simply as ''CINVESTAV-IPN'') is a Mexican non-governmental scientific research institution affiliated with the National Polytechnic Institute and founded by president Adolfo López Mateos on 17 April 1961, initially planned as a postgraduate department of the National Polytechnic Institute; this was later modified by President José López Portillo, on 17 September 1982. The modification by President Portillo stipulates that it is a decentralized organ of public interest, with legal personality and own patrimony. Cinvestav receives an annual subsidy by the Federal Government to fund its operations. Organization Campuses The institute is divided into 10 research centers; 3 of these are in Mexico City, while the others are dispersed across the country. They are located as follows: * Mexic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Field Sieve
In mathematics the Function Field Sieve is one of the most efficient algorithms to solve the Discrete Logarithm Problem (DLP) in a finite field. It has heuristic subexponential complexity. Leonard Adleman developed it in 1994 and then elaborated it together with M. D. Huang in 1999.L. Adleman, M.D. Huang. "Function Field Sieve Method for Discrete Logarithms over Finite Fields". In: Inf. Comput. 151 (May 1999), pp. 5-16. DOI: 10.1006/inco.1998.2761. Previous work includes the work of D. Coppersmith about the DLP in fields of characteristic two. The discrete logarithm problem in a finite field consists of solving the equation a^x = b for a,b \in \mathbb_ , p a prime number and n an integer. The function f: \mathbb_ \to \mathbb_, x \mapsto a^x for a fixed a \in \mathbb_ is a one-way function used in cryptography. Several cryptographic methods are based on the DLP such as the Diffie-Hellman key exchange, the El Gamal cryptosystem and the Digital Signature Algorithm. Nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> PlayStation 3"){kind=logo}
