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Fast Syndrome Based Hash
In cryptography, the fast syndrome-based hash functions (FSB) are a family of cryptographic hash functions introduced in 2003 by Daniel Augot, Matthieu Finiasz, and Nicolas Sendrier. Unlike most other cryptographic hash functions in use today, FSB can to a certain extent be proven to be secure. More exactly, it can be proven that breaking FSB is at least as difficult as solving a certain NP-complete problem known as regular syndrome decoding so FSB is provably secure. Though it is not known whether NP-complete problems are solvable in polynomial time, it is often assumed that they are not. Several versions of FSB have been proposed, the latest of which was submitted to the SHA-3 cryptography competition but was rejected in the first round. Though all versions of FSB claim provable security, some preliminary versions were eventually broken. The design of the latest version of FSB has however taken this attack into account and remains secure to all currently known attacks. As usu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Daniel Augot
Daniel commonly refers to: * Daniel (given name), a masculine given name and a surname * List of people named Daniel * List of people with surname Daniel * Daniel (biblical figure) * Book of Daniel, a biblical apocalypse, "an account of the activities and visions of Daniel" Daniel may also refer to: Arts and entertainment Literature * ''Daniel'' (Old English poem), an adaptation of the Book of Daniel * ''Daniel'', a 2006 novel by Richard Adams * ''Daniel'' (Mankell novel), 2007 Music * "Daniel" (Bat for Lashes song) (2009) * "Daniel" (Elton John song) (1973) * "Daniel", a song from ''Beautiful Creature'' by Juliana Hatfield * ''Daniel'' (album), a 2024 album by Real Estate Other arts and entertainment * ''Daniel'' (1983 film), by Sidney Lumet * ''Daniel'' (2019 film), a Danish film * Daniel (comics), a character in the ''Endless'' series Businesses * Daniel (department store), in the United Kingdom * H & R Daniel, a producer of English porcelain between 1827 and 1846 * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Vector Space
In mathematics and physics, a vector space (also called a linear space) is a set (mathematics), set whose elements, often called vector (mathematics and physics), ''vectors'', can be added together and multiplied ("scaled") by numbers called scalar (mathematics), ''scalars''. The operations of vector addition and scalar multiplication must satisfy certain requirements, called ''vector axioms''. Real vector spaces and complex vector spaces are kinds of vector spaces based on different kinds of scalars: real numbers and complex numbers. Scalars can also be, more generally, elements of any field (mathematics), field. Vector spaces generalize Euclidean vectors, which allow modeling of Physical quantity, physical quantities (such as forces and velocity) that have not only a Magnitude (mathematics), magnitude, but also a Orientation (geometry), direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrix (mathematics), matrices, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Spartan 6
Xilinx, Inc. ( ) was an American technology and semiconductor company that primarily supplied programmable logic devices. The company is renowned for inventing the first commercially viable field-programmable gate array (FPGA). It also pioneered the first fabless manufacturing model.Jonathan Cassell, iSuppli.A Forgettable Year for Memory Chip Makers: iSuppli releases preliminary 2008 semiconductor rankings." December 1, 2008. Retrieved January 15, 2009.John Edwards, EDN." June 1, 2006. Retrieved January 15, 2009. Xilinx was co-founded by Ross Freeman, Bernard Vonderschmitt, and James V Barnett II in 1984. The company went public on the Nasdaq in 1990. In October 2020, AMD announced its acquisition of Xilinx, which was completed on February 14, 2022, through an all-stock transaction valued at approximately $60 billion. Xilinx remained a wholly owned subsidiary of AMD until the brand was phased out in June 2023, with Xilinx's product lines now branded under AMD. Company overview ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Tanja Lange
Tanja Lange is a German cryptographer and number theorist at the Eindhoven University of Technology. She is known for her research on post-quantum cryptography. Education and career Lange earned a diploma in mathematics in 1998 from the Technical University of Braunschweig. She completed her Ph.D. in 2001 at the Universität Duisburg-Essen. Her dissertation, jointly supervised by Gerhard Frey and YoungJu Choie, concerned ''Efficient Arithmetic on Hyperelliptic Curves''. After postdoctoral studies at Ruhr University Bochum, she became an associate professor at the Technical University of Denmark in 2005. She moved to the Eindhoven University of Technology as a full professor in 2007. At Eindhoven, she chairs the coding theory and cryptology group and is scientific director of the Eindhoven Institute for the Protection of Systems and Information. She is also the coordinator of PQCRYPTO, a European multi-university consortium to make electronic communications future-proof against ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Binary Goppa Code
In mathematics and computer science, the binary Goppa code is an error-correcting code that belongs to the class of general Goppa codes originally described by Valerii Denisovich Goppa, but the binary structure gives it several mathematical advantages over non-binary variants, also providing a better fit for common usage in computers and telecommunication. Binary Goppa codes have interesting properties suitable for cryptography in McEliece-like cryptosystems and similar setups. Construction and properties An irreducible binary Goppa code is defined by a polynomial g(x) of degree t over a finite field GF(2^m) with no repeated roots, and a sequence L_1, ..., L_n of n distinct elements from GF(2^m) that are not roots of g. Codewords belong to the kernel of the syndrome function, forming a subspace of \^n: : \Gamma(g,L)=\left\ The code defined by a tuple (g,L) has dimension at least n-mt and distance at least 2t+1, thus it can encode messages of length at least n-mt using codeword ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Linear Cryptanalysis
In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine Affine may describe any of various topics concerned with connections or affinities. It may refer to: * Affine, a Affinity_(law)#Terminology, relative by marriage in law and anthropology * Affine cipher, a special case of the more general substi ... approximations to the action of a cipher. Attacks have been developed for block ciphers and stream ciphers. Linear cryptanalysis is one of the two most widely used attacks on block ciphers; the other being differential cryptanalysis. The discovery is attributed to Mitsuru Matsui, who first applied the technique to the FEAL cipher (Matsui and Yamagishi, 1992). Subsequently, Matsui published an attack on the Data Encryption Standard (DES), eventually leading to the first experimental cryptanalysis of the cipher reported in the open community (Matsui, 1993; 1994). The attack on DES is not generally practical, requiring 247 known pla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Worst-case Complexity
In computer science (specifically computational complexity theory), the worst-case complexity measures the resources (e.g. running time, memory) that an algorithm requires given an input of arbitrary size (commonly denoted as in asymptotic notation). It gives an upper bound on the resources required by the algorithm. In the case of running time, the worst-case time complexity indicates the longest running time performed by an algorithm given ''any'' input of size , and thus guarantees that the algorithm will finish in the indicated period of time. The order of growth (e.g. linear, logarithmic) of the worst-case complexity is commonly used to compare the efficiency of two algorithms. The worst-case complexity of an algorithm should be contrasted with its average-case complexity, which is an average measure of the amount of resources the algorithm uses on a random input. Definition Given a model of computation and an algorithm \mathsf that halts on each input s, the mapping ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Provably Secure Cryptographic Hash Function
In cryptography, cryptographic hash functions can be divided into two main categories. In the first category are those functions whose designs are based on mathematical problems, and whose security thus follows from rigorous mathematical proofs, complexity theory and formal reduction. These functions are called ''provably secure cryptographic hash functions''. To construct these is very difficult, and few examples have been introduced. Their practical use is limited. In the second category are functions which are not based on mathematical problems, but on an ad-hoc constructions, in which the bits of the message are mixed to produce the hash. These are then believed to be hard to break, but no formal proof is given. Almost all hash functions in widespread use reside in this category. Some of these functions are already broken, and are no longer in use. ''See'' Hash function security summary. Types of security of hash functions Generally, the ''basic'' security of cryptographic ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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3-dimensional Matching
In the mathematical discipline of graph theory, a 3-dimensional matching is a generalization of bipartite matching (also known as 2-dimensional matching) to 3-partite hypergraphs, which consist of hyperedges each of which contains 3 vertices (instead of edges containing 2 vertices in a usual graph). 3-dimensional matching, often abbreviated as 3DM, is also the name of a well-known computational problem: finding a largest 3-dimensional matching in a given hypergraph. 3DM is one of the first problems that were proved to be NP-hard. Definition Let ''X'', ''Y'', and ''Z'' be finite sets, and let ''T'' be a subset of ''X'' × ''Y'' × ''Z''. That is, ''T'' consists of triples (''x'', ''y'', ''z'') such that ''x'' ∈ ''X'', ''y'' ∈ ''Y'', and ''z'' ∈ ''Z''. Now ''M'' ⊆ ''T'' is a 3-dimensional matching if the following holds: for any two distinct triples (''x''1, ''y''1, ''z''1) ∈ ''M'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Decoding Methods
In coding theory, decoding is the process of translating received messages into Code word (communication), codewords of a given code. There have been many common methods of mapping messages to codewords. These are often used to recover messages sent over a noisy channel, such as a binary symmetric channel. Notation C \subset \mathbb_2^n is considered a binary code with the length n; x,y shall be elements of \mathbb_2^n; and d(x,y) is the distance between those elements. Ideal observer decoding One may be given the message x \in \mathbb_2^n, then ideal observer decoding generates the codeword y \in C. The process results in this solution: :\mathbb(y \mbox \mid x \mbox) For example, a person can choose the codeword y that is most likely to be received as the message x after transmission. Decoding conventions Each codeword does not have an expected possibility: there may be more than one codeword with an equal likelihood of mutating into the received message. In such a case, the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Coding Theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and computer data storage, data storage. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data. There are four types of coding: # Data compression (or ''source coding'') # Error detection and correction, Error control (or ''channel coding'') # Cryptography, Cryptographic coding # Line code, Line coding Data compression attempts to remove unwanted redundancy from the data from a source in order to transmit it more efficiently. For example, DEFLATE data compression makes files small ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers. The set (mathematics), set of all integers is often denoted by the boldface or blackboard bold The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the set of natural numbers, the set of integers \mathbb is Countable set, countably infinite. An integer may be regarded as a real number that can be written without a fraction, fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , 5/4, and Square root of 2, are not. The integers form the smallest Group (mathematics), group and the smallest ring (mathematics), ring containing the natural numbers. In algebraic number theory, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |