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Inprobability theoryandstatistics, acopulais a multivariatecumulative distribution functionfor which themarginal probabilitydistribution of each variable isuniformon the interval [0, 1]. Copulas are used to describe/model thedependence(inter-correlation) betweenrandom variables.[1]Their name, introduced by applied math... | https://en.wikipedia.org/wiki/Copula_(probability_theory) |
Inmathematics, thedisintegration theoremis a result inmeasure theoryandprobability theory. It rigorously defines the idea of a non-trivial "restriction" of ameasureto ameasure zerosubset of themeasure spacein question. It is related to the existence ofconditional probability measures. In a sense, "disintegration" is th... | https://en.wikipedia.org/wiki/Disintegration_theorem |
Multivariate statisticsis a subdivision ofstatisticsencompassing the simultaneous observation and analysis of more than oneoutcome variable, i.e.,multivariate random variables.
Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and ... | https://en.wikipedia.org/wiki/Multivariate_statistics |
When twoprobability distributionsoverlap,statistical interferenceexists. Knowledge of the distributions can be used to determine the likelihood that one parameter exceeds another, and by how much.
This technique can be used forgeometric dimensioningof mechanical parts, determining when an applied load exceeds the str... | https://en.wikipedia.org/wiki/Statistical_interference |
Inprobability theory, apairwise independentcollection ofrandom variablesis a set of random variables any two of which areindependent.[1]Any collection ofmutually independentrandom variables is pairwise independent, but some pairwise independent collections are not mutually independent. Pairwise independent random vari... | https://en.wikipedia.org/wiki/Pairwise_independence |
In themathematicalfield ofgraph theory, agraph homomorphismis a mapping between twographsthat respects their structure. More concretely, it is a function between the vertex sets of two graphs that maps adjacentverticesto adjacent vertices.
Homomorphisms generalize various notions ofgraph coloringsand allow the express... | https://en.wikipedia.org/wiki/Graph_homomorphism |
In the mathematical field ofgraph theory, anautomorphismof agraphis a form ofsymmetryin which the graph ismappedonto itself while preserving the edge–vertexconnectivity.
Formally, an automorphism of a graphG= (V,E)is apermutationσof the vertex setV, such that the pair of vertices(u,v)form an edgeif and only ifthe pair... | https://en.wikipedia.org/wiki/Graph_automorphism_problem |
Thegraph isomorphism problemis thecomputational problemof determining whether two finitegraphsareisomorphic.[1]
The problem is not known to be solvable inpolynomial timenor to beNP-complete, and therefore may be in the computationalcomplexity classNP-intermediate. It is known that the graph isomorphism problem is in ... | https://en.wikipedia.org/wiki/Graph_isomorphism_problem |
Ingraph theory, a branch of mathematics,graph canonizationis the problem of finding acanonical formof a given graphG. A canonical form is alabeled graphCanon(G) that isisomorphictoG, such that every graph that is isomorphic toGhas the same canonical form asG. Thus, from a solution to the graph canonization problem, one... | https://en.wikipedia.org/wiki/Graph_canonization |
Ingraph theory, afractional isomorphism ofgraphswhoseadjacency matricesare denotedAandBis adoubly stochastic matrixDsuch thatDA=BD. If the doubly stochastic matrix is apermutation matrix, then it constitutes agraph isomorphism.[1][2]Fractional isomorphism is the coarsest of several differentrelaxationsofgraph isomorphi... | https://en.wikipedia.org/wiki/Fractional_graph_isomorphism |
Ingraph theory, acritical graphis anundirected graphall of whose proper subgraphs have smallerchromatic number. In such a graph, every vertex or edge is acritical element, in the sense that its deletion would decrease the number of colors needed in agraph coloringof the given graph. Each time a single edge or vertex (a... | https://en.wikipedia.org/wiki/Critical_graph |
Thegraph coloring gameis a mathematical game related tograph theory.Coloring game problemsarose as game-theoretic versions of well-knowngraph coloringproblems. In a coloring game, two players use a given set of colors to construct a coloring of agraph, following specific rules depending on the game we consider. One pla... | https://en.wikipedia.org/wiki/Graph_coloring_game |
Ingraph theory, a branch of mathematics, theHajós constructionis anoperation on graphsnamed afterGyörgy Hajós(1961) that may be used to construct anycritical graphor any graph whosechromatic numberis at least some given threshold.
LetGandHbe twoundirected graphs,vwbe an edge ofG, andxybe an edge ofH. Then the Hajós co... | https://en.wikipedia.org/wiki/Haj%C3%B3s_construction |
Mathematicscan be used to studySudokupuzzles to answer questions such as "How many filled Sudoku grids are there?", "What is the minimal number of clues in a valid puzzle?" and "In what ways can Sudoku grids be symmetric?" through the use ofcombinatoricsandgroup theory.
The analysis of Sudoku is generally divided betw... | https://en.wikipedia.org/wiki/Mathematics_of_Sudoku |
Ingraph theory, a part of mathematics, ak-partite graphis agraphwhoseverticesare (or can be)partitionedintokdifferentindependent sets. Equivalently, it is a graph that can becoloredwithkcolors, so that no two endpoints of an edge have the same color. Whenk= 2these are thebipartite graphs, and whenk= 3they are called th... | https://en.wikipedia.org/wiki/Multipartite_graph |
Ingraph theory, auniquely colorable graphis ak-chromaticgraphthat has only one possible (proper)k-coloringup topermutationof the colors. Equivalently, there is only one way topartitionitsverticesintokindependent setsand there is no way to partition them intok− 1independent sets.
Acomplete graphis uniquely colorable, ... | https://en.wikipedia.org/wiki/Uniquely_colorable_graph |
Incryptanalysis, thepiling-up lemmais a principle used inlinear cryptanalysisto constructlinear approximationsto the action ofblock ciphers. It was introduced byMitsuru Matsui(1993) as an analytical tool for linear cryptanalysis.[1]The lemma states that the bias (deviation of theexpected valuefrom 1/2) of alinear Boole... | https://en.wikipedia.org/wiki/Piling-up_lemma |
Incomplexity theoryandcomputability theory, anoracle machineis anabstract machineused to studydecision problems. It can be visualized as ablack box, called anoracle, which is able to solve certain problems in a single operation. The problem can be of anycomplexity class. Evenundecidable problems, such as thehalting pro... | https://en.wikipedia.org/wiki/Oracle_machine |
Computer and network surveillanceis the monitoring of computer activity and data stored locally on a computer or data being transferred overcomputer networkssuch as theInternet. This monitoring is often carried out covertly and may be completed by governments, corporations, criminal organizations, or individuals. It ma... | https://en.wikipedia.org/wiki/Computer_and_network_surveillance |
Incomputer security, acovert channelis a type ofattackthat creates a capability to transfer information objects between processes that are not supposed to be allowed to communicate by thecomputer security policy. The term, originated in 1973 byButler Lampson, is defined as channels "not intended forinformation transfe... | https://en.wikipedia.org/wiki/Covert_channel |
Incomputer science, an operation,functionorexpressionis said to have aside effectif it has any observable effect other than its primary effect of reading the value of its arguments and returning a value to the invoker of the operation. Example side effects include modifying anon-local variable, astatic local variableor... | https://en.wikipedia.org/wiki/Side_effect_(computer_science) |
Wire dataorwire imageis the information that passes over computer and telecommunication networks defining communications betweenclient and serverdevices. It is the result of decodingwire and transport protocolscontaining the bi-directional data payload. More precisely, wire data is the information that is communicated ... | https://en.wikipedia.org/wiki/Wire_data |
Theleftover hash lemmais alemmaincryptographyfirst stated byRussell Impagliazzo,Leonid Levin, andMichael Luby.[1]
Given a secretkeyXthat hasnuniform randombits, of which anadversarywas able to learn the values of somet<nbits of that key, the leftover hash lemma states that it is possible to produce a key of aboutn−tbi... | https://en.wikipedia.org/wiki/Leftover_hash_lemma |
Incryptography, asemantically securecryptosystemis one where only negligible information about theplaintextcan be feasibly extracted from theciphertext. Specifically, anyprobabilistic, polynomial-time algorithm(PPTA) that is given the ciphertext of a certain messagem{\displaystyle m}(taken from any distribution of mess... | https://en.wikipedia.org/wiki/Semantic_security |
TheClipper chipwas achipsetthat was developed and promoted by the United StatesNational Security Agency(NSA) as anencryptiondevice that secured "voice and data messages" with a built-inbackdoorthat was intended to "allow Federal, State, and local law enforcement officials the ability to decode intercepted voice and dat... | https://en.wikipedia.org/wiki/Clipper_chip |
Data Securities International, DSIwas a technology escrow administration company based inSan Francisco, California. Founded in 1982, the companyescrows source codeand other maintenance materials for licensees and stakeholders. In 1997,Iron Mountain Incorporatedacquired the company. In 2021, Iron Mountain sold DSI (now ... | https://en.wikipedia.org/wiki/Data_Securities_International |
Incryptography, arelated-key attackis any form ofcryptanalysiswhere the attacker can observe the operation of acipherunder several differentkeyswhose values are initially unknown, but where some mathematical relationship connecting the keys is known to the attacker. For example, the attacker might know that the last 80... | https://en.wikipedia.org/wiki/Related-key_attack |
Abackdooris a typically covert method of bypassing normalauthenticationor encryption in a computer, product, embedded device (e.g. ahome router), or its embodiment (e.g. part of acryptosystem,algorithm,chipset, or even a "homunculus computer"—a tiny computer-within-a-computer such as that found in Intel'sAMT technology... | https://en.wikipedia.org/wiki/Backdoor_(computing) |
Inmathematics, ahomogeneous distributionis adistributionSonEuclidean spaceRnorRn\ {0} that ishomogeneousin the sense that, roughly speaking,
for allt> 0.
More precisely, letμt:x↦x/t{\displaystyle \mu _{t}:x\mapsto x/t}be the scalar division operator onRn. A distributionSonRnorRn\ {0} is homogeneous of degreemprovide... | https://en.wikipedia.org/wiki/Homogeneous_distribution |
Incryptography,integral cryptanalysisis acryptanalytic attackthat is particularly applicable toblock ciphersbased onsubstitution–permutation networks. It was originally designed byLars Knudsenas a dedicated attack againstSquare, so it is commonly known as theSquare attack. It was also extended to a few other ciphers r... | https://en.wikipedia.org/wiki/Integral_cryptanalysis |
Incryptography,differential equations of addition(DEA) are one of the most basic equations related todifferential cryptanalysisthat mix additions over two different groups (e.g. addition modulo 232and addition over GF(2)) and where input and output differences are expressed as XORs.
Differential equations of addition... | https://en.wikipedia.org/wiki/Differential_equations_of_addition |
TheAND gateis a basic digitallogic gatethat implements thelogical conjunction(∧) frommathematical logic– AND gates behave according to theirtruth table. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If any of the inputs to the AND gate are not HIGH, a LOW (0) is outputted. The function... | https://en.wikipedia.org/wiki/AND_gate |
TheOR gateis a digitallogic gatethat implementslogical disjunction. The OR gate outputs "true" if any of its inputs is "true"; otherwise it outputs "false". The input and output states are normally represented by differentvoltagelevels.
Any OR gate can be constructed with two or more inputs. It outputs a 1 if any of t... | https://en.wikipedia.org/wiki/OR_gate |
In digital logic, aninverterorNOT gateis alogic gatewhich implementslogical negation. It outputs abitopposite of the bit that is put into it. The bits are typically implemented as two differingvoltagelevels.
The NOT gate outputs a zero when given a one, and a one when given a zero. Hence, it inverts its inputs. Colloq... | https://en.wikipedia.org/wiki/Inverter_(logic_gate) |
Indigital electronics, aNAND(NOT AND)gateis alogic gatewhich produces an output which is false only if all its inputs are true; thus its output iscomplementto that of anAND gate. A LOW (0) output results only if all the inputs to the gate are HIGH (1); if any input is LOW (0), a HIGH (1) output results. A NAND gate is ... | https://en.wikipedia.org/wiki/NAND_gate |
TheNOR(NOT OR)gateis a digitallogic gatethat implementslogical NOR- it behaves according to thetruth tableto the right. A HIGH output (1) results if both the inputs to the gate are LOW (0); if one or both input is HIGH (1), a LOW output (0) results. NOR is the result of thenegationof theORoperator. It can also in some ... | https://en.wikipedia.org/wiki/NOR_gate |
TheXNOR gate(sometimesENOR,EXNOR,NXOR,XANDand pronounced asExclusive NOR) is a digitallogic gatewhose function is thelogical complementof the Exclusive OR (XOR) gate.[1]It is equivalent to the logical connective (↔{\displaystyle \leftrightarrow }) frommathematical logic, also known as the material biconditional. The tw... | https://en.wikipedia.org/wiki/XNOR_gate |
TheIMPLY gateis a digitallogic gatethat implements alogical conditional.
IMPLY can be denoted in algebraic expressions with thelogic symbolright-facing arrow (→). Logically, it is equivalent tomaterial implication, and the logical expression ¬A v B.
There are two symbols for IMPLY gates: the traditional symbol and th... | https://en.wikipedia.org/wiki/IMPLY_gate |
Alogic gateis a device that performs aBoolean function, alogical operationperformed on one or morebinaryinputs that produces a single binary output. Depending on the context, the term may refer to anideal logic gate, one that has, for instance, zerorise timeand unlimitedfan-out, or it may refer to a non-ideal physical ... | https://en.wikipedia.org/wiki/Logic_gate |
Gauss's lemmainnumber theorygives a condition for an integer to be aquadratic residue. Although it is not useful computationally, it has theoretical significance, being involved in someproofs of quadratic reciprocity.
It made its first appearance inCarl Friedrich Gauss's third proof (1808)[1]: 458–462ofquadratic recip... | https://en.wikipedia.org/wiki/Gauss%27s_lemma_(number_theory) |
Innumber theory,Zolotarev's lemmastates that theLegendre symbol
for an integeramoduloan oddprime numberp, wherepdoes not dividea, can be computed as the sign of a permutation:
where ε denotes thesignature of a permutationand πais thepermutationof the nonzeroresidue classesmodpinduced bymultiplicationbya.
For example... | https://en.wikipedia.org/wiki/Zolotarev%27s_lemma |
Inmathematics, acharacter sumis a sum∑χ(n){\textstyle \sum \chi (n)}of values of aDirichlet characterχmoduloN, taken over a given range of values ofn. Such sums are basic in a number of questions, for example in the distribution ofquadratic residues, and in particular in the classical question of finding an upper bound... | https://en.wikipedia.org/wiki/Character_sum |
Innumber theory, thelaw of quadratic reciprocityis a theorem aboutmodular arithmeticthat gives conditions for the solvability ofquadratic equationsmoduloprime numbers. Due to its subtlety, it has many formulations, but the most standard statement is:
Law of quadratic reciprocity—Letpandqbe distinct odd prime numbers, ... | https://en.wikipedia.org/wiki/Law_of_quadratic_reciprocity |
Aquadratic residue codeis a type ofcyclic code.
Examples of quadratic
residue codes include the(7,4){\displaystyle (7,4)}Hamming codeoverGF(2){\displaystyle GF(2)}, the(23,12){\displaystyle (23,12)}binary Golay codeoverGF(2){\displaystyle GF(2)}and the(11,6){\displaystyle (11,6)}ternary Golay codeoverGF(3){\displaysty... | https://en.wikipedia.org/wiki/Quadratic_residue_code |
Manymathematical problemshave been stated but not yet solved. These problems come from manyareas of mathematics, such astheoretical physics,computer science,algebra,analysis,combinatorics,algebraic,differential,discreteandEuclidean geometries,graph theory,group theory,model theory,number theory,set theory,Ramsey theory... | https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics |
Incomputational complexity theory, theunique games conjecture(often referred to asUGC) is a conjecture made bySubhash Khotin 2002.[1][2][3]The conjecture postulates that the problem of determining the approximatevalueof a certain type of game, known as aunique game, hasNP-hardcomputational complexity. It has broad app... | https://en.wikipedia.org/wiki/Unique_games_conjecture |
This article is alist of notable unsolved problemsincomputer science. A problem in computer science is considered unsolved when no solution is known or when experts in the field disagree about proposed solutions.
The graph isomorphism problem involves determining whether two finite graphs are isomorphic, meaning there... | https://en.wikipedia.org/wiki/Unsolved_problems_in_computer_science |
Incomputer science,2-satisfiability,2-SATor just2SATis acomputational problemof assigning values to variables, each of which has two possible values, in order to satisfy a system ofconstraintson pairs of variables. It is a special case of the generalBoolean satisfiability problem, which can involve constraints on more ... | https://en.wikipedia.org/wiki/2-satisfiability |
Inlogicandcomputer science, theBoolean satisfiability problem(sometimes calledpropositional satisfiability problemand abbreviatedSATISFIABILITY,SATorB-SAT) asks whether there exists aninterpretationthatsatisfiesa givenBooleanformula. In other words, it asks whether the formula's variables can be consistently replaced b... | https://en.wikipedia.org/wiki/Boolean_satisfiability_problem |
Intheoretical computer science, thecircuit satisfiability problem(also known asCIRCUIT-SAT,CircuitSAT,CSAT, etc.) is thedecision problemof determining whether a givenBoolean circuithas an assignment of its inputs that makes the output true.[1]In other words, it asks whether the inputs to a given Boolean circuit can be ... | https://en.wikipedia.org/wiki/Circuit_satisfiability |
Incomputational complexity theory,Karp's 21 NP-complete problemsare a set ofcomputational problemswhich areNP-complete. In his 1972 paper, "Reducibility Among Combinatorial Problems",[1]Richard KarpusedStephen Cook's 1971 theorem that theboolean satisfiability problemis NP-complete[2](also called theCook–Levin theorem)... | https://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problems |
Inlogic, specifically indeductive reasoning, anargumentisvalidif and only ifit takes a form that makes it impossible for thepremisesto betrueand the conclusion nevertheless to befalse.[1]It is not required for a valid argument to have premises that are actually true,[2]but to have premises that, if they were true, woul... | https://en.wikipedia.org/wiki/Validity_(logic) |
Inartificial intelligenceandoperations research,constraint satisfactionis the process of finding a solution through
a set ofconstraintsthat impose conditions that thevariablesmustsatisfy.[1]A solution is therefore an assignment of values to the variables that satisfies all constraints—that is, a point in thefeasible r... | https://en.wikipedia.org/wiki/Constraint_satisfaction |
Lutz's resource-bounded measureis a generalisation ofLebesgue measuretocomplexity classes. It was originally developed byJack Lutz. Just as Lebesgue measure gives a method to quantify the size of subsets of theEuclidean spaceRn{\displaystyle \mathbb {R} ^{n}}, resource bounded measure gives a method to classify the siz... | https://en.wikipedia.org/wiki/Almost_complete |
Incomputational complexity theory, agadgetis a subunit of a problem instance that simulates the behavior of one of the fundamental units of a different computational problem. Gadgets are typically used to constructreductionsfrom one computational problem to another, as part of proofs ofNP-completenessor other types of ... | https://en.wikipedia.org/wiki/Gadget_(computer_science) |
Incomputational complexity, problems that are in thecomplexity classNPbut are neither in the classPnorNP-completeare calledNP-intermediate, and the class of such problems is calledNPI.Ladner's theorem, shown in 1975 byRichard E. Ladner,[1]is a result asserting that, ifP ≠ NP, then NPI is not empty; that is, NP contains... | https://en.wikipedia.org/wiki/Ladner%27s_theorem |
This is a list of some of the more commonly known problems that areNP-completewhen expressed asdecision problems. As there are thousands of such problems known, this list is in no way comprehensive. Many problems of this type can be found inGarey & Johnson (1979).
Graphsoccur frequently in everyday applications. Examp... | https://en.wikipedia.org/wiki/List_of_NP-complete_problems |
Incomputational complexity theory, a computational problemHis calledNP-hardif, for every problemLwhich can be solved innon-deterministic polynomial-time, there is apolynomial-time reductionfromLtoH. That is, assuming a solution forHtakes 1 unit time,H's solution can be used to solveLin polynomial time.[1][2]As a conse... | https://en.wikipedia.org/wiki/NP-hard |
TheP versus NP problemis a majorunsolved problemintheoretical computer science. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved.
Here, "quickly" means an algorithm exists that solves the task and runs inpolynomial time(as opposed to, say,exponential time), me... | https://en.wikipedia.org/wiki/P_%3D_NP_problem |
Incomputational complexity,strong NP-completenessis a property of computational problems that is a special case ofNP-completeness. A general computational problem may have numerical parameters. For example, the input to thebin packingproblem is a list of objects of specific sizes and a size for the bins that must cont... | https://en.wikipedia.org/wiki/Strongly_NP-complete |
Travelling Salesmanis a 2012 intellectualthrillerfilm about four mathematicians who solve theP versus NP problem, one of the most challengingmathematicalproblems in history. The title refers to thetravelling salesman problem, anoptimization problemthat acts like a key to solving other difficult mathematical problems. I... | https://en.wikipedia.org/wiki/Travelling_Salesman_(2012_film) |
Inmathematics,probabilistic metric spacesare a generalization ofmetric spaceswhere thedistanceno longer takes values in the non-negativereal numbersR≥0, but in distribution functions.[1]
LetD+be the set of allprobability distribution functionsFsuch thatF(0) = 0 (Fis a nondecreasing, leftcontinuous mappingfromRinto [0,... | https://en.wikipedia.org/wiki/Probabilistic_metric_space |
Arandomness extractor, often simply called an "extractor", is a function, which being applied to output from a weakentropy source, together with a short, uniformly random seed, generates a highlyrandomoutput that appearsindependentfrom the source anduniformly distributed.[1]Examples of weakly random sources includeradi... | https://en.wikipedia.org/wiki/Randomness_extractor |
Instatisticsand related fields, asimilarity measureorsimilarity functionorsimilarity metricis areal-valued functionthat quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such measures are in some sense the inverse ofdistance metrics: they take on large values f... | https://en.wikipedia.org/wiki/Similarity_measure |
ATuring machineis amathematical model of computationdescribing anabstract machine[1]that manipulates symbols on a strip of tape according to a table of rules.[2]Despite the model's simplicity, it is capable of implementing anycomputer algorithm.[3]
The machine operates on an infinite[4]memory tape divided intodiscrete... | https://en.wikipedia.org/wiki/Turing_machine |
The following articles containlists of problems: | https://en.wikipedia.org/wiki/Lists_of_problems |
List of unsolved problemsmay refer to several notableconjecturesoropen problemsin various academic fields: | https://en.wikipedia.org/wiki/List_of_unsolved_problems |
Incomputability theoryandcomputational complexity theory, areductionis analgorithmfor transforming oneprobleminto another problem. A sufficiently efficient reduction from one problem to another may be used to show that the second problem is at least as difficult as the first.
Intuitively, problemAisreducibleto problem... | https://en.wikipedia.org/wiki/Reduction_(complexity) |
Inphilosophy,unknowabilityis the possibility of inherently unaccessibleknowledge. It addresses theepistemologyof that which cannot be known. Some related concepts include the limits of knowledge,ignorabimus,unknown unknowns, thehalting problem, andchaos theory.
Nicholas Rescherprovides the most recent focused scholars... | https://en.wikipedia.org/wiki/Unknowability |
Inprobability theoryandinformation theory, themutual information(MI) of tworandom variablesis a measure of the mutualdependencebetween the two variables. More specifically, it quantifies the "amount of information" (inunitssuch asshannons(bits),natsorhartleys) obtained about one random variable by observing the other r... | https://en.wikipedia.org/wiki/Mutual_information |
Theconditional quantum entropyis anentropy measureused inquantum information theory. It is a generalization of theconditional entropyofclassical information theory. For a bipartite stateρAB{\displaystyle \rho ^{AB}}, the conditional entropy is writtenS(A|B)ρ{\displaystyle S(A|B)_{\rho }}, orH(A|B)ρ{\displaystyle H(A... | https://en.wikipedia.org/wiki/Conditional_quantum_entropy |
Inprobability theoryandinformation theory, thevariation of informationorshared information distanceis a measure of the distance between two clusterings (partitions of elements). It is closely related tomutual information; indeed, it is a simple linear expression involving the mutual information. Unlike the mutual inf... | https://en.wikipedia.org/wiki/Variation_of_information |
Ininformation theory, theentropy power inequality(EPI) is a result that relates to so-called "entropy power" ofrandom variables. It shows that the entropy power of suitablywell-behavedrandom variables is asuperadditivefunction. The entropy power inequality was proved in 1948 byClaude Shannonin his seminal paper "A Math... | https://en.wikipedia.org/wiki/Entropy_power_inequality |
Alikelihood function(often simply called thelikelihood) measures how well astatistical modelexplainsobserved databy calculating the probability of seeing that data under differentparametervalues of the model. It is constructed from thejoint probability distributionof therandom variablethat (presumably) generated the ob... | https://en.wikipedia.org/wiki/Likelihood_function |
Arandomness test(ortest for randomness), in data evaluation, is a test used to analyze the distribution of a set of data to see whether it can be described asrandom(patternless). Instochastic modeling, as in somecomputer simulations, the hoped-for randomness of potential input data can be verified, by a formal test fo... | https://en.wikipedia.org/wiki/Randomness_test |
Incryptography, anSP-network, orsubstitution–permutation network(SPN), is a series of linked mathematical operations used inblock cipheralgorithms such asAES (Rijndael),3-Way,Kalyna,Kuznyechik,PRESENT,SAFER,SHARK, andSquare.
Such a network takes a block of theplaintextand thekeyas inputs, and applies several alternati... | https://en.wikipedia.org/wiki/Substitution%E2%80%93permutation_network |
Thelifting schemeis a technique for both designingwaveletsand performing thediscrete wavelet transform(DWT). In an implementation, it is often worthwhile to merge these steps and design the wavelet filterswhileperforming the wavelet transform. This is then called thesecond-generation wavelet transform. The technique wa... | https://en.wikipedia.org/wiki/Lifting_scheme |
Incryptography,format-preserving encryption(FPE), refers to encrypting in such a way that the output (theciphertext) is in the same format as the input (theplaintext). The meaning of "format" varies. Typically only finite sets of characters are used; numeric, alphabetic or alphanumeric. For example:
For such finite d... | https://en.wikipedia.org/wiki/Format-preserving_encryption |
TheLai–Massey schemeis a cryptographic structure used in the design ofblock ciphers,[1][2]an alternative to theFeistel networkfor converting a non-invertible keyed round function to an invertible keyed cipher. It is used inIDEAandIDEA NXT. The scheme was originally introduced byXuejia Lai[3]with the assistance ofJames ... | https://en.wikipedia.org/wiki/Lai%E2%80%93Massey_scheme |
Competitive analysisis a method invented for analyzingonline algorithms, in which the performance of an online algorithm (which must satisfy an unpredictable sequence of requests, completing each request without being able to see the future) is compared to the performance of an optimaloffline algorithmthat can view the... | https://en.wikipedia.org/wiki/Competitive_analysis_(online_algorithm) |
Thek-server problemis a problem oftheoretical computer sciencein the category ofonline algorithms, one of two abstract problems onmetric spacesthat are central to the theory ofcompetitive analysis(the other beingmetrical task systems). In this problem, an online algorithm must control the movement of a set ofkservers, ... | https://en.wikipedia.org/wiki/K-server_problem |
Incomputer science, anonline algorithm[1]is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed to thealgorithm, without having the entire input available from the start. In contrast, anoffline algorithmis given the whole problem data from the beginning and is req... | https://en.wikipedia.org/wiki/Online_algorithm |
Buffer overflow protectionis any of various techniques used during software development to enhance the security of executable programs by detectingbuffer overflowsonstack-allocated variables, and preventing them from causing program misbehavior or from becoming serioussecurityvulnerabilities. A stack buffer overflow o... | https://en.wikipedia.org/wiki/Buffer_overflow_protection |
Aheap overflow,heap overrun, orheap smashingis a type ofbuffer overflowthat occurs in theheapdata area. Heap overflows are exploitable in a different manner to that ofstack-based overflows. Memory on the heap isdynamically allocatedatruntimeand typically contains program data. Exploitation is performed by corrupting th... | https://en.wikipedia.org/wiki/Heap_overflow |
Buffer overflow protectionis any of various techniques used during software development to enhance the security of executable programs by detectingbuffer overflowsonstack-allocated variables, and preventing them from causing program misbehavior or from becoming serioussecurityvulnerabilities. A stack buffer overflow o... | https://en.wikipedia.org/wiki/Stack-smashing_protection |
Uncontrolled format stringis a type ofcode injectionvulnerabilitydiscovered around 1989 that can be used insecurity exploits.[1]Originally thought harmless, format string exploits can be used tocrasha program or to execute harmful code. The problem stems from the use ofunchecked user inputas theformat stringparameter i... | https://en.wikipedia.org/wiki/Uncontrolled_format_string |
Intel MPX(Memory Protection Extensions) are a discontinued set of extensions to thex86instruction set architecture. Withcompiler,runtime libraryandoperating systemsupport, Intel MPX claimed to enhance security tosoftwareby checkingpointer referenceswhose normal compile-time intentions are maliciously exploited at runti... | https://en.wikipedia.org/wiki/Intel_MPX |
Microsoft Windows SDK, and its predecessorsPlatform SDK, and.NET Framework SDK, aresoftware development kits(SDKs) fromMicrosoftthat containdocumentation,header files,libraries, samples and tools required to develop applications forMicrosoft Windowsand.NET Framework.[1]These libraries are also distributed asWindows Sys... | https://en.wikipedia.org/wiki/Microsoft_Windows_SDK |
Valgrind(/ˈvælɡrɪnd/)[6]is aprogramming toolformemory debugging,memory leakdetection, andprofiling.
Valgrind was originally designed to be afreely licensedmemory debugging tool forLinuxonx86, but has since evolved to become a generic framework for creating dynamic analysis tools such as checkers and profilers.
Valgri... | https://en.wikipedia.org/wiki/Valgrind |
Thesoftware release life cycleis the process of developing, testing, and distributing a software product (e.g., anoperating system). It typically consists of several stages, such as pre-alpha, alpha, beta, and release candidate, before the final version, or "gold", is released to the public.
Pre-alpha refers to the ea... | https://en.wikipedia.org/wiki/Software_release_life_cycle |
Backportingis the action of taking parts from a newerversionof asoftware systemorsoftware componentandportingthem to an older version of the same software. It forms part of themaintenancestep in asoftware development process, and it is commonly used for fixingsecurity issuesin older versions of the software and also fo... | https://en.wikipedia.org/wiki/Backporting |
Dribbleware, in the context ofcomputer software, is a product for whichpatchesare often being released.[1]The term usually has negative connotations, and can refer to software which hasn't been tested properly prior to release, or for which planned features could not be implemented.
Dribbleware is not necessarily due ... | https://en.wikipedia.org/wiki/Dribbleware |
The computer toolpatchis aUnixprogramthat updatestext filesaccording to instructions contained in a separate file, called apatch file. The patch file (also called apatchfor short) is a text file that consists of a list of differences and is produced by running the relateddiffprogram with the original and updated file a... | https://en.wikipedia.org/wiki/Patch_(Unix) |
Insoftware engineering,portingis the process of adaptingsoftwarefor the purpose of achieving some form of execution in acomputing environmentthat is different from the one that a given program (meant for such execution) was originally designed for (e.g., differentCPU, operating system, or third partylibrary). The term ... | https://en.wikipedia.org/wiki/Porting |
Avulnerability database(VDB) is a platform aimed at collecting, maintaining, and disseminating information about discoveredcomputer security vulnerabilities. Thedatabasewill customarily describe the identified vulnerability, assess the potential impact on affected systems, and any workarounds or updates to mitigate the... | https://en.wikipedia.org/wiki/Vulnerability_database |
Delta encodingis a way of storing or transmittingdatain the form ofdifferences(deltas) between sequential data rather than complete files; more generally this is known asdata differencing. Delta encoding is sometimes calleddelta compression, particularly where archival histories of changes are required (e.g., inrevisio... | https://en.wikipedia.org/wiki/Delta_encoding |
System Modification Program/Extended(SMP/E), the proprietary version ofSystem Modification Program(SMP), "is a tool designed to manage the installation of software products on [a]z/OSsystem and to track the modifications" to those products.[1]: 1[2][3][4][5]
SMP/E manages multiple software versions, helps apply patche... | https://en.wikipedia.org/wiki/SMP/E |
Automatic bug-fixingis the automaticrepairofsoftware bugswithout the intervention of a human programmer.[1][2][3]It is also commonly referred to asautomatic patch generation,automatic bug repair, orautomatic program repair.[3]The typical goal of such techniques is to automatically generate correctpatchesto eliminate bu... | https://en.wikipedia.org/wiki/Automatic_bug_fixing |
Shavlik Technologieswas a privately held company founded in 1993 by Mark Shavlik, who also was one of the original developers ofWindows NTin the late 1980s and early 1990s atMicrosoft.[1]
The company providedsoftwareand services for networkvulnerability assessmentand for managing networksecurity patches. Mark Shavlik ... | https://en.wikipedia.org/wiki/Shavlik_Technologies |
Awhite hat(or awhite-hat hacker,a whitehat) is an ethicalsecurity hacker.[1][2]Ethical hacking is a term meant to imply a broader category than just penetration testing.[3][4]Under the owner's consent, white-hat hackers aim to identify any vulnerabilities or security issues the current system has.[5]The white hat is co... | https://en.wikipedia.org/wiki/White_hat_(computer_security) |
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