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Implementation is the realization of an application, execution of a plan, idea, model, design, specification, standard, algorithm, policy, or the administration or management of a process or objective.
== Industry-specific definitions ==
=== Information technology ===
In the information technology industry, implem... | Wikipedia/Implementation_(computer_science) |
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all limiting values of points. For example, the open interval (0,1... | Wikipedia/Compact_(topology) |
Linear or point-projection perspective (from Latin perspicere 'to see through') is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by the eye. Perspect... | Wikipedia/Perspective_(graphical) |
In mathematics and logic, an axiomatic system is a set of formal statements (i.e. axioms) used to logically derive other statements such as lemmas or theorems. A proof within an axiom system is a sequence of deductive steps that establishes a new statement as a consequence of the axioms. An axiom system is called compl... | Wikipedia/Axiomatic_method |
In algebraic geometry, a complex algebraic variety is an algebraic variety (in the scheme sense or otherwise) over the field of complex numbers.
== Chow's theorem ==
Chow's theorem states that a projective complex analytic variety, i.e., a closed analytic subvariety of the complex projective space
... | Wikipedia/Complex_algebraic_varieties |
In mathematics, the idea of descent extends the intuitive idea of 'gluing' in topology. Since the topologists' glue is the use of equivalence relations on topological spaces, the theory starts with some ideas on identification.
== Descent of vector bundles ==
The case of the construction of vector bundles from data o... | Wikipedia/Descent_theory |
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and returns another function (in the style of a higher-order function in computer scien... | Wikipedia/Symbol_of_a_differential_operator |
In algebraic geometry, a projective variety is an algebraic variety that is a closed subvariety of a projective space. That is, it is the zero-locus in
P
n
{\displaystyle \mathbb {P} ^{n}}
of some f... | Wikipedia/Projective_algebraic_variety |
In algebraic geometry, an affine variety or affine algebraic variety is a certain kind of algebraic variety that can be described as a subset of an affine space.
More formally, an affine algebraic set is the set of the common zeros over an algebraically closed field k of some family of polynomials in the polynomial rin... | Wikipedia/Ring_of_regular_functions |
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not generally hold for real anal... | Wikipedia/Analytic_functions |
In mathematics, an algebraic cycle on an algebraic variety V is a formal linear combination of subvarieties of V. These are the part of the algebraic topology of V that is directly accessible by algebraic methods. Understanding the algebraic cycles on a variety can give profound insights into the structure of the var... | Wikipedia/Algebraic_cycle |
In number theory and algebraic geometry, the Tate conjecture is a 1963 conjecture of John Tate that would describe the algebraic cycles on a variety in terms of a more computable invariant, the Galois representation on étale cohomology. The conjecture is a central problem in the theory of algebraic cycles. It can be co... | Wikipedia/Tate_conjecture |
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point t... | Wikipedia/Displacement_(physics) |
In physics, a body force is a force that acts throughout the volume of a body. Forces due to gravity, electric fields and magnetic fields are examples of body forces. Body forces contrast with contact forces or surface forces which are exerted to the surface of an object.
Fictitious forces such as the centrifugal force... | Wikipedia/Body_force |
In mechanics, compression is the application of balanced inward ("pushing") forces to different points on a material or structure, that is, forces with no net sum or torque directed so as to reduce its size in one or more directions. It is contrasted with tension or traction, the application of balanced outward ("pulli... | Wikipedia/Compression_(physics) |
In physics and engineering, a constitutive equation or constitutive relation is a relation between two or more physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance or field, and approximates its response to external stimuli, usually as applie... | Wikipedia/Constitutive_equations |
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measurement (such as metres and grams) and tracking these dimensions as calculations or compari... | Wikipedia/Dimension_(physics) |
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra
A
{\displaystyle A}
over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, that is,... | Wikipedia/Banach_*-algebra |
In mathematics, transform theory is the study of transforms, which relate a function in one domain to another function in a second domain. The essence of transform theory is that by a suitable choice of basis for a vector space a problem may be simplified—or diagonalized as in spectral theory.
Main examples of transfor... | Wikipedia/Transform_theory |
In mathematics, the Wiener algebra, named after Norbert Wiener and usually denoted by A(T), is the space of absolutely convergent Fourier series. Here T denotes the circle group.
== Banach algebra structure ==
The norm of a function f ∈ A(T) is given by
‖
f
‖
=
... | Wikipedia/Wiener_algebra |
Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The idea is to write the solution of the differential equation as a sum of certain "basis functions" (for example, as a Fourier series which is a sum of sinusoids) and the... | Wikipedia/Spectral_method |
In mathematics, an AW*-algebra is an algebraic generalization of a W*-algebra. They were introduced by Irving Kaplansky in 1951. As operator algebras, von Neumann algebras, among all C*-algebras, are typically handled using one of two means: they are the dual space of some Banach space, and they are determined to a lar... | Wikipedia/AW*-algebra |
In mathematics, the multiplier algebra, denoted by M(A), of a C*-algebra A is a unital C*-algebra that is the largest unital C*-algebra that contains A as an ideal in a "non-degenerate" way. It is the noncommutative generalization of Stone–Čech compactification. Multiplier algebras were introduced by Busby (1968).
For ... | Wikipedia/Corona_algebra |
In mathematics, particularly in functional analysis and ring theory, an approximate identity is a net in a Banach algebra or ring (generally without an identity) that acts as a substitute for an identity element.
== Definition ==
A right approximate identity in a Banach algebra A is a net
{
... | Wikipedia/Σ-unital_algebra |
In the mathematical field of functional analysis, a nuclear C*-algebra is a C*-algebra A such that for every C*-algebra B the injective and projective C*-cross norms coincides on the algebraic tensor product A⊗B and the completion of A⊗B with respect to this norm is a C*-algebra. This property was first studied by Take... | Wikipedia/Nuclear_C*-algebra |
In mathematics, a projectionless C*-algebra is a C*-algebra with no nontrivial projections. For a unital C*-algebra, the projections 0 and 1 are trivial. While for a non-unital C*-algebra, only 0 is considered trivial. The problem of whether simple infinite-dimensional C*-algebras with this property exist was posed in... | Wikipedia/Projectionless_C*-algebra |
Superstrong approximation is a generalisation of strong approximation in algebraic groups G, to provide spectral gap results. The spectrum in question is that of the Laplacian matrix associated to a family of quotients of a discrete group Γ; and the gap is that between the first and second eigenvalues (normalisation so... | Wikipedia/Superstrong_approximation |
In functional analysis, a uniform algebra A on a compact Hausdorff topological space X is a closed (with respect to the uniform norm) subalgebra of the C*-algebra C(X) (the continuous complex-valued functions on X) with the following properties:
the constant functions are contained in A
for every x, y
... | Wikipedia/Uniform_algebra |
In algebraic geometry, a correspondence between algebraic varieties V and W is a subset R of V×W, that is closed in the Zariski topology. In set theory, a subset of a Cartesian product of two sets is called a binary relation or correspondence; thus, a correspondence here is a relation that is defined by algebraic equat... | Wikipedia/Correspondence_(algebraic_geometry) |
In applied mathematics, proto-value functions (PVFs) are automatically learned basis functions that are useful in approximating task-specific value functions, providing a compact representation of the powers of transition matrices. They provide a novel framework for solving the credit assignment problem. The framewor... | Wikipedia/Proto-value_function |
In mathematics, specifically in functional and complex analysis, the disk algebra A(D) (also spelled disc algebra) is the set of holomorphic functions
ƒ : D →
C
{\displaystyle \mathbb {C} }
(where D is the open unit disk in the complex plane
... | Wikipedia/Disk_algebra |
The spectrum of a linear operator
T
{\displaystyle T}
that operates on a Banach space
X
{\displaystyle X}
is a fundamental concept of functional analysis. The spectrum consists of all scalars
λ
... | Wikipedia/Decomposition_of_spectrum_(functional_analysis) |
The Schröder–Bernstein theorem from set theory has analogs in the context operator algebras. This article discusses such operator-algebraic results.
== For von Neumann algebras ==
Suppose M is a von Neumann algebra and E, F are projections in M. Let ~ denote the Murray-von Neumann equivalence relation on M. Define a ... | Wikipedia/Schröder–Bernstein_theorems_for_operator_algebras |
In functional analysis, a state of an operator system is a positive linear functional of norm 1. States in functional analysis generalize the notion of density matrices in quantum mechanics, which represent quantum states, both mixed states and pure states. Density matrices in turn generalize state vectors, which only ... | Wikipedia/State_(functional_analysis) |
In mathematics, the multiplier algebra, denoted by M(A), of a C*-algebra A is a unital C*-algebra that is the largest unital C*-algebra that contains A as an ideal in a "non-degenerate" way. It is the noncommutative generalization of Stone–Čech compactification. Multiplier algebras were introduced by Busby (1968).
For ... | Wikipedia/Multiplier_algebra |
In mathematics, specifically in functional analysis, a Banach algebra, A, is amenable if all bounded derivations from A into dual Banach A-bimodules are inner (that is of the form
a
↦
a
.
x
−
x
.
a
{\displaystyle a\... | Wikipedia/Amenable_Banach_algebra |
In functional analysis, a Banach function algebra on a compact Hausdorff space X is unital subalgebra, A, of the commutative C*-algebra C(X) of all continuous, complex-valued functions from X, together with a norm on A that makes it a Banach algebra.
A function algebra is said to vanish at a point p if f(p) = 0 for al... | Wikipedia/Banach_function_algebra |
In the mathematical field of spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are excellent spectral expanders. As Murty's survey paper notes, Ramanujan graphs "fuse diverse branches of pure mathematics, namely, number... | Wikipedia/Ramanujan_graph |
In functional analysis, compact operators are linear operators on Banach spaces that map bounded sets to relatively compact sets. In the case of a Hilbert space H, the compact operators are the closure of the finite rank operators in the uniform operator topology. In general, operators on infinite-dimensional spaces fe... | Wikipedia/Spectral_theory_of_compact_operators |
In general topology and related areas of mathematics, the disjoint union (also called the direct sum, free union, free sum, topological sum, or coproduct) of a family of topological spaces is a space formed by equipping the disjoint union of the underlying sets with a natural topology called the disjoint union topolog... | Wikipedia/Disjoint_union_(topology) |
In mathematics, the real rank of a C*-algebra is a noncommutative analogue of Lebesgue covering dimension. The notion was first introduced by Lawrence G. Brown and Gert K. Pedersen.
== Definition ==
The real rank of a unital C*-algebra A is the smallest non-negative integer n, denoted RR(A), such that for every (n + ... | Wikipedia/Real_rank_(C*-algebras) |
In mathematics, a topological space
X
{\displaystyle X}
is said to be a Baire space if countable unions of closed sets with empty interior also have empty interior.
According to the Baire category theorem, compact Hausdorff spaces and complete metric spaces are examples of Ba... | Wikipedia/Category_(topology) |
In mathematics, particularly in functional analysis, the spectrum of a bounded linear operator (or, more generally, an unbounded linear operator) is a generalisation of the set of eigenvalues of a matrix. Specifically, a complex number
λ
{\displaystyle \lambda }
is said to b... | Wikipedia/Continuous_spectrum_(functional_analysis) |
In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The direct sum of modules is the smallest module which contains the given modules as submodules with no "unnecessary" constraints, making it an example of a coproduct. Contrast with the direct product, which ... | Wikipedia/Direct_sum_of_algebras |
In functional analysis, every C*-algebra is isomorphic to a subalgebra of the C*-algebra
B
(
H
)
{\displaystyle {\mathcal {B}}(H)}
of bounded linear operators on some Hilbert space
H
... | Wikipedia/Spectral_theory_of_normal_C*-algebras |
In mathematics, the Dirichlet eigenvalues are the fundamental modes of vibration of an idealized drum with a given shape. The problem of whether one can hear the shape of a drum is: given the Dirichlet eigenvalues, what features of the shape of the drum can one deduce. Here a "drum" is thought of as an elastic membra... | Wikipedia/Dirichlet_eigenvalue |
In geometric measure theory the area formula relates the Hausdorff measure of the image of a Lipschitz map, while accounting for multiplicity, to the integral of the Jacobian of the map. It is one of the fundamental results of the field that has connections, for example, to rectifiability and Sard's theorem.
Definition... | Wikipedia/Area_formula_(geometric_measure_theory) |
The icosian calculus is a non-commutative algebraic structure discovered by the Irish mathematician William Rowan Hamilton in 1856.
In modern terms, he gave a group presentation of the icosahedral rotation group by generators and relations.
Hamilton's discovery derived from his attempts to find an algebra of "triplets"... | Wikipedia/Icosian_calculus |
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly deter... | Wikipedia/Algorithmically_insoluble |
Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. The word calculus is a Latin word, meaning originally "small pebble"; as such pebbles were u... | Wikipedia/Discrete_calculus |
In mathematics, the discrete exterior calculus (DEC) is the extension of the exterior calculus to discrete spaces including graphs, finite element meshes, and lately also general polygonal meshes (non-flat and non-convex). DEC methods have proved to be very powerful in improving and analyzing finite element methods: fo... | Wikipedia/Discrete_exterior_calculus |
Discrete Morse theory is a combinatorial adaptation of Morse theory developed by Robin Forman. The theory has various practical applications in diverse fields of applied mathematics and computer science, such as configuration spaces, homology computation, denoising, mesh compression, and topological data analysis.
==... | Wikipedia/Discrete_Morse_theory |
In mathematics, specifically in operator K-theory, the Baum–Connes conjecture suggests a link between the K-theory of the reduced C*-algebra of a group and the K-homology of the classifying space of proper actions of that group. The conjecture sets up a correspondence between different areas of mathematics, with the K... | Wikipedia/Baum–Connes_conjecture |
In mathematics, computational group theory is the study of
groups by means of computers. It is concerned
with designing and analysing algorithms and
data structures to compute information about groups. The subject
has attracted interest because for many interesting groups
(including most of the sporadic groups) it is i... | Wikipedia/Computational_group_theory |
Geometric and Functional Analysis (GAFA) is a mathematical journal published by Birkhäuser, an independent division of Springer-Verlag. The journal is published bi-monthly.
The journal publishes major results on a broad range of mathematical topics related to geometry and analysis.
GAFA is both an acronym and a part o... | Wikipedia/Geometric_and_Functional_Analysis |
In mathematics, especially in the area of modern algebra known as combinatorial group theory, Nielsen transformations are certain automorphisms of a free group which are a non-commutative analogue of row reduction and one of the main tools used in studying free groups (Fine, Rosenberger & Stille 1995).
Given a finite b... | Wikipedia/Nielsen_transformation |
In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties:
A ... | Wikipedia/C*-algebras |
In geometric group theory, a graph of groups is an object consisting of a collection of groups indexed by the vertices and edges of a graph, together with a family of monomorphisms of the edge groups into the vertex groups.
There is a unique group, called the fundamental group, canonically associated to each finite con... | Wikipedia/Graph_of_groups |
In mathematics, Out(Fn) is the outer automorphism group of a free group on n generators. These groups are at universal stage in geometric group theory, as they act on the set of presentations with
n
{\displaystyle n}
generators of any finitely generated group. Despite geometr... | Wikipedia/Outer_space_(group_theory) |
In geometric group theory and dynamical systems the iterated monodromy group of a covering map is a group describing the monodromy action of the fundamental group on all iterations of the covering. A single covering map between spaces is therefore used to create a tower of coverings, by placing the covering over itself... | Wikipedia/Iterated_monodromy_group |
The Novikov conjecture is one of the most important unsolved problems in topology. It is named for Sergei Novikov who originally posed the conjecture in 1965.
The Novikov conjecture concerns the homotopy invariance of certain polynomials in the Pontryagin classes of a manifold, arising from the fundamental group. Acco... | Wikipedia/Novikov_conjecture |
In mathematics, the ping-pong lemma, or table-tennis lemma, is any of several mathematical statements that ensure that several elements in a group acting on a set freely generates a free subgroup of that group.
== History ==
The ping-pong argument goes back to the late 19th century and is commonly attributed to Felix... | Wikipedia/Ping-pong_lemma |
In mathematics, a finite subdivision rule is a recursive way of dividing a polygon or other two-dimensional shape into smaller and smaller pieces. Subdivision rules in a sense are generalizations of regular geometric fractals. Instead of repeating exactly the same design over and over, they have slight variations in ea... | Wikipedia/Cannon's_conjecture |
In the mathematical subject of geometric group theory, the growth rate of a group with respect to a symmetric generating set describes how fast a group grows. Every element in the group can be written as a product of generators, and the growth rate counts the number of elements that can be written as a product of leng... | Wikipedia/Growth_rate_(group_theory) |
In group theory, Tietze transformations are used to transform a given presentation of a group into another, often simpler presentation of the same group. These transformations are named after Heinrich Tietze who introduced them in a paper in 1908.
A presentation is in terms of generators and relations; formally speaki... | Wikipedia/Tietze_transformation |
In cryptography, a random oracle is an oracle (a theoretical black box) that responds to every unique query with a (truly) random response chosen uniformly from its output domain. If a query is repeated, it responds the same way every time that query is submitted.
Stated differently, a random oracle is a mathematical ... | Wikipedia/Random_oracle_model |
In cryptography, a universal hashing message authentication code, or UMAC, is a message authentication code (MAC) calculated using universal hashing, which involves choosing a hash function from a class of hash functions according to some secret (random) process and applying it to the message. The resulting digest or f... | Wikipedia/UMAC_(cryptography) |
Skein is a cryptographic hash function and one of five finalists in the NIST hash function competition. Entered as a candidate to become the SHA-3 standard, the successor of SHA-1 and SHA-2, it ultimately lost to NIST hash candidate Keccak.
The name Skein refers to how the Skein function intertwines the input, similar ... | Wikipedia/Skein_(hash_function) |
In cryptography, Tiger is a cryptographic hash function designed by Ross Anderson and Eli Biham in 1995 for efficiency on 64-bit platforms. The size of a Tiger hash value is 192 bits. Truncated versions (known as Tiger/128 and Tiger/160) can be used for compatibility with protocols assuming a particular hash size. Unli... | Wikipedia/Tiger_(hash_function) |
Steganography ( STEG-ə-NOG-rə-fee) is the practice of representing information within another message or physical object, in such a manner that the presence of the concealed information would not be evident to an unsuspecting person's examination. In computing/electronic contexts, a computer file, message, image, or v... | Wikipedia/Steganography |
There are a number of standards related to cryptography. Standard algorithms and protocols provide a focus for study; standards for popular applications attract a large amount of cryptanalysis.
== Encryption standards ==
Data Encryption Standard (DES, now obsolete)
Advanced Encryption Standard (AES)
RSA the original ... | Wikipedia/Cryptography_standards |
In cryptography, a key derivation function (KDF) is a cryptographic algorithm that derives one or more secret keys from a secret value such as a master key, a password, or a passphrase using a pseudorandom function (which typically uses a cryptographic hash function or block cipher). KDFs can be used to stretch keys in... | Wikipedia/Key_derivation_function |
The following tables compare general and technical information for a number of cryptographic hash functions. See the individual functions' articles for further information. This article is not all-inclusive or necessarily up-to-date. An overview of hash function security/cryptanalysis can be found at hash function secu... | Wikipedia/Comparison_of_cryptographic_hash_functions |
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 (in French) Jacques Patarin following the idea of the Matsumoto and Imai system. It is based on polynomials over finite fields
... | Wikipedia/Hidden_Field_Equations |
In cryptography, a T-function is a bijective mapping that updates every bit of the state in a way that can be described as
x
i
′
=
x
i
+
f
... | Wikipedia/T-function |
Industrial espionage, also known as economic espionage, corporate spying, or corporate espionage, is a form of espionage conducted for commercial purposes instead of purely national security.
While political espionage is conducted or orchestrated by governments and is international in scope, industrial or corporate esp... | Wikipedia/Industrial_espionage |
Short integer solution (SIS) and ring-SIS problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based cryptography began in 1996 from a seminal work by Miklós Ajtai who presented a family of one-way functions based on SIS problem. He showed that it is secure in an ave... | Wikipedia/Short_integer_solution_problem |
In cryptography, the Cellular Message Encryption Algorithm (CMEA) is a block cipher which was used for securing mobile phones in the United States. CMEA is one of four cryptographic primitives specified in a Telecommunications Industry Association (TIA) standard, and is designed to encrypt the control channel, rather t... | Wikipedia/Cellular_Message_Encryption_Algorithm |
In cryptography, padding is any of a number of distinct practices which all include adding data to the beginning, middle, or end of a message prior to encryption. In classical cryptography, padding may include adding nonsense phrases to a message to obscure the fact that many messages end in predictable ways, e.g. sinc... | Wikipedia/Padding_(cryptography) |
The paranoiac-critical method is a surrealist technique developed by Salvador Dalí in the early 1930s. He employed it in the production of paintings and other artworks, especially those that involved optical illusions and other multiple images. The technique consists of the artist invoking a paranoid state (fear that t... | Wikipedia/Paranoiac-critical_method |
Cryptography is the practice and study of encrypting information, or in other words, securing information from unauthorized access. There are many different cryptography laws in different nations. Some countries prohibit the export of cryptography software and/or encryption algorithms or cryptoanalysis methods. Some co... | Wikipedia/Cryptography_law |
In the history of cryptography, a grille cipher was a technique for encrypting a plaintext by writing it onto a sheet of paper through a pierced sheet (of paper or cardboard or similar). The earliest known description is due to Jacopo Silvestri in 1526. His proposal was for a rectangular stencil allowing single letters... | Wikipedia/Grille_(cryptography) |
The Secure Hash Algorithms are a family of cryptographic hash functions published by the National Institute of Standards and Technology (NIST) as a U.S. Federal Information Processing Standard (FIPS), including:
SHA-0: A retronym applied to the original version of the 160-bit hash function published in 1993 under the ... | Wikipedia/Secure_Hash_Algorithms |
Kleptography is the study of stealing information securely and subliminally. The term was introduced by Adam Young and Moti Yung in the Proceedings of Advances in Cryptology – Crypto '96.
Kleptography is a subfield of cryptovirology and is a natural extension of the theory of subliminal channels that was pioneered by G... | Wikipedia/Kleptography |
A law enforcement agency (LEA) is any government agency responsible for law enforcement within a specific jurisdiction through the employment and deployment of law enforcement officers and their resources. The most common type of law enforcement agency is the police, but various other forms exist as well, including age... | Wikipedia/Law_enforcement_agency |
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys to provide equivalent security, compared to cryptosystems based on modular exponentiation in Galois fields, such as the RSA cryptosystem and ElGam... | Wikipedia/Elliptic_Curve_Cryptography |
In cryptography, a sponge function or sponge construction is any of a class of algorithms with finite internal state that take an input bit stream of any length and produce an output bit stream of any desired length. Sponge functions have both theoretical and practical uses. They can be used to model or implement many ... | Wikipedia/Sponge_function |
Introduced by Martin Hellman and Susan K. Langford in 1994, the differential-linear attack is a mix of both linear cryptanalysis and differential cryptanalysis.
The attack utilises a differential characteristic over part of the cipher with a probability of 1 (for a few rounds—this probability would be much lower for th... | Wikipedia/Differential-linear_attack |
Hash-based cryptography is the generic term for constructions of cryptographic primitives based on the security of hash functions. It is of interest as a type of post-quantum cryptography.
So far, hash-based cryptography is used to construct digital signatures schemes such as the Merkle signature scheme, zero knowledge... | Wikipedia/Hash-based_cryptography |
Materials MASINT is one of the six major disciplines generally accepted to make up the field of Measurement and Signature Intelligence (MASINT), with due regard that the MASINT subdisciplines may overlap, and MASINT, in turn, is complementary to more traditional intelligence collection and analysis disciplines such as ... | Wikipedia/Materials_MASINT |
Capstone is a United States government long-term project to develop cryptography standards for public and government use. Capstone was authorized by the Computer Security Act of 1987, driven by the National Institute of Standards and Technology (NIST) and the National Security Agency (NSA); the project began in 1993.
... | Wikipedia/Capstone_(cryptography) |
"Communication Theory of Secrecy Systems" is a paper published in 1949 by Claude Shannon discussing cryptography from the viewpoint of information theory. It is one of the foundational treatments (arguably the foundational treatment) of modern cryptography. His work has been described as a "turning point, and marked th... | Wikipedia/Communication_Theory_of_Secrecy_Systems |
Non-commutative cryptography is the area of cryptology where the cryptographic primitives, methods and systems are based on algebraic structures like semigroups, groups and rings which are non-commutative. One of the earliest applications of a non-commutative algebraic structure for cryptographic purposes was the use o... | Wikipedia/Non-commutative_cryptography |
In cryptography, a round or round function is a basic transformation that is repeated (iterated) multiple times inside the algorithm. Splitting a large algorithmic function into rounds simplifies both implementation and cryptanalysis.
For example, encryption using an oversimplified three-round cipher can be written as ... | Wikipedia/Round_(cryptography) |
In cryptography, a salt is random data fed as an additional input to a one-way function that hashes data, a password or passphrase. Salting helps defend against attacks that use precomputed tables (e.g. rainbow tables), by vastly growing the size of table needed for a successful attack. It also helps protect passwords ... | Wikipedia/Salt_(cryptography) |
Computer and network surveillance is the monitoring of computer activity and data stored locally on a computer or data being transferred over computer networks such as the Internet. This monitoring is often carried out covertly and may be completed by governments, corporations, criminal organizations, or individuals. I... | Wikipedia/Computer_and_network_surveillance |
Cryptography is the practice and study of encrypting information, or in other words, securing information from unauthorized access. There are many different cryptography laws in different nations. Some countries prohibit the export of cryptography software and/or encryption algorithms or cryptoanalysis methods. Some co... | Wikipedia/Cryptography_laws_in_different_nations |
Lattice-based cryptography is the generic term for constructions of cryptographic primitives that involve lattices, either in the construction itself or in the security proof. Lattice-based constructions support important standards of post-quantum cryptography. Unlike more widely used and known public-key schemes such... | Wikipedia/Lattice-based_cryptography |
Books on cryptography have been published sporadically and with variable quality for a long time. This is despite the paradox that secrecy is of the essence in sending confidential messages – see Kerckhoffs' principle.
In contrast, the revolutions in cryptography and secure communications since the 1970s are covered in... | Wikipedia/Books_on_cryptography |
Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in information input can affect the resultant difference at the output. In the case of a block ciphe... | Wikipedia/Differential_cryptanalysis |
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