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Incomputing, awireless intrusion prevention system(WIPS) is anetworkdevice that monitors theradio spectrumfor the presence of unauthorizedaccess points(intrusion detection), and can automatically take countermeasures(intrusion prevention).
The primary purpose of a WIPS is to prevent unauthorized network access tolocal... | https://en.wikipedia.org/wiki/Wireless_intrusion_prevention_system |
This is a technical featurecomparison of differentdisk encryption software.
TrueCrypt License Version 3.0 (legacy code only)
Different modes of operation supported by the software. Note that an encrypted volume can only use one mode of operation. | https://en.wikipedia.org/wiki/Comparison_of_disk_encryption_software |
Digital forensics(sometimes known asdigital forensic science) is a branch offorensic scienceencompassing the recovery, investigation, examination, and analysis of material found in digital devices, often in relation to mobile devices andcomputer crime.[1][2]The term "digital forensics" was originally used as a synonym ... | https://en.wikipedia.org/wiki/Digital_forensics |
Hardware-based full disk encryption(FDE) is available from manyhard disk drive(HDD/SSD) vendors, including:Hitachi, Integral Memory, iStorage Limited,Micron,Seagate Technology,Samsung,Toshiba,Viasat UK, andWestern Digital. Thesymmetric encryption keyis maintained independently from the computer'sCPU, thus allowing the... | https://en.wikipedia.org/wiki/Disk_encryption_hardware |
Disk encryption softwareis acomputer securitysoftware that protects the confidentiality of data stored on computer media (e.g., ahard disk,floppy disk, orUSB device) by usingdisk encryption.
Compared to access controls commonly enforced by anoperating system(OS), encryption passively protects data confidentiality even... | https://en.wikipedia.org/wiki/Disk_encryption_software |
Disk encryptionis a special case ofdata at restprotection when the storage medium is a sector-addressable device (e.g., a hard disk). This article presents cryptographic aspects of the problem. For an overview, seedisk encryption. For discussion of different software packages and hardware devices devoted to this proble... | https://en.wikipedia.org/wiki/Disk_encryption_theory |
Filesystem-level encryption,[1]often calledfile-based encryption,FBE, orfile/folder encryption, is a form ofdisk encryptionwhere individual files or directories areencryptedby thefile systemitself.
This is in contrast to thefull disk encryptionwhere the entire partition or disk, in which the file system resides, is en... | https://en.wikipedia.org/wiki/Filesystem-level_encryption |
Hardware-based full disk encryption(FDE) is available from manyhard disk drive(HDD/SSD) vendors, including:Hitachi, Integral Memory, iStorage Limited,Micron,Seagate Technology,Samsung,Toshiba,Viasat UK, andWestern Digital. Thesymmetric encryption keyis maintained independently from the computer'sCPU, thus allowing the... | https://en.wikipedia.org/wiki/Hardware-based_full_disk_encryption |
In re Boucher(case citation: No. 2:06-mJ-91, 2009 WL 424718) is afederalcriminalcaseinVermont, which was the first to directly address the question of whether investigators can compel a suspect to reveal theirencryptionpassphraseorpassword, despite theU.S. Constitution'sFifth Amendmentprotection againstself-incriminati... | https://en.wikipedia.org/wiki/In_re_Boucher |
Single sign-on(SSO) is an authentication scheme that allows a user to log in with a single ID to any of several related, yet independent, software systems.
True single sign-on allows the user to log in once and access services without re-entering authentication factors.
It should not be confused with same-sign on (Di... | https://en.wikipedia.org/wiki/Single_sign-on |
CCM mode(counter with cipher block chaining message authentication code;counter withCBC-MAC) is amode of operationfor cryptographicblock ciphers. It is anauthenticated encryptionalgorithm designed to provide bothauthenticationandconfidentiality. CCM mode is only defined for block ciphers with a block length of 128 bi... | https://en.wikipedia.org/wiki/CCM_mode |
Incryptography,CWC Mode(Carter–Wegman +CTRmode) is anAEAD block cipher mode of operationthat provides both encryption and built-in message integrity, similar to CCM and OCB modes. It combines the use of CTR mode with a 128-bit block cipher for encryption with an efficient polynomialCarter–Wegman MACwith a tag length of... | https://en.wikipedia.org/wiki/CWC_mode |
Offset codebook mode(OCB mode) is anauthenticated encryptionmode of operationfor cryptographicblock ciphers.[1][2]OCB mode was designed byPhillip Rogaway, who creditsMihir Bellare,John Black, and Ted Krovetz with assistance and comments on the designs. It is based on theintegrity-aware parallelizeable mode(IAPM) of aut... | https://en.wikipedia.org/wiki/OCB_mode |
EAX mode(encrypt-then-authenticate-then-translate[1]) is amode of operationfor cryptographic block ciphers. It is an Authenticated Encryption with Associated Data (AEAD) algorithm designed to simultaneously provide bothauthenticationandprivacyof the message (authenticated encryption) with a two-pass scheme, one pass f... | https://en.wikipedia.org/wiki/EAX_mode |
ChaCha20-Poly1305is anauthenticated encryption with associated data (AEAD)algorithm, that combines theChaCha20stream cipher with thePoly1305message authentication code.[1]It has fast software performance, and without hardware acceleration, is usually faster thanAES-GCM.[1]: §B
The two building blocks of the constructi... | https://en.wikipedia.org/wiki/ChaCha20-Poly1305 |
A new mode calledSophie Germain Counter Mode (SGCM)has been proposed as a variant of theGalois/Counter Modeof operation for block ciphers. Instead of the binary field GF(2128), it uses modular arithmetic in GF(p) wherepis asafe prime2128+ 12451with correspondingSophie Germain primep− 1/2= 2127+ 6225.[1]SGCM does prev... | https://en.wikipedia.org/wiki/Sophie_Germain_Counter_Mode |
Incryptography,signcryptionis a public-key primitive that simultaneously performs the functions of bothdigital signatureandencryption.
Encryption and digital signature are two fundamental cryptographic tools that can guarantee theconfidentiality,integrity, andnon-repudiation. Until 1997, they were viewed as important ... | https://en.wikipedia.org/wiki/Signcryption |
Incomputer scienceandcryptography,Whirlpool(sometimes styledWHIRLPOOL) is acryptographic hash function. It was designed byVincent Rijmen(co-creator of theAdvanced Encryption Standard) andPaulo S. L. M. Barreto, who first described it in 2000.
The hash has been recommended by theNESSIEproject. It has also been adopted... | https://en.wikipedia.org/wiki/Whirlpool_(cryptography) |
Incryptography,Square(sometimes writtenSQUARE) is ablock cipherinvented byJoan DaemenandVincent Rijmen. The design, published in 1997, is a forerunner toRijndael, which has been adopted as theAdvanced Encryption Standard. Square was introduced together with a new form ofcryptanalysisdiscovered byLars Knudsen, called t... | https://en.wikipedia.org/wiki/Square_(cipher) |
Incryptography, acipher block chaining message authentication code(CBC-MAC) is a technique for constructing amessage authentication code (MAC)from ablock cipher. The message is encrypted with some block cipher algorithm incipher block chaining (CBC) modeto create a chain of blocks such that each block depends on the p... | https://en.wikipedia.org/wiki/CBC-MAC |
One-key MAC(OMAC) is a family ofmessage authentication codesconstructed from ablock ciphermuch like theCBC-MACalgorithm. It may be used to provide assurance of the authenticity and, hence, the integrity of data. Two versions are defined:
OMAC is free for all uses: it is not covered by any patents.[4]
The core of the ... | https://en.wikipedia.org/wiki/One-key_MAC |
PMAC, which stands forparallelizable MAC, is amessage authentication codealgorithm. It was created byPhillip Rogaway.
PMAC is a method of taking ablock cipherand creating an efficient message authentication code that is reducible in security to the underlying block cipher.
PMAC is similar in functionality to theOMACa... | https://en.wikipedia.org/wiki/PMAC_(cryptography) |
Cicada 3301is the name given to eight sets ofpuzzlesposted under the name "3301" online between 2012 and 2014. The first puzzle started on January 4, 2012,[1]on4chan[2]and ran for nearly a month. A second round of puzzles began one year later on January 4, 2013, and then a third round following the confirmation of a fr... | https://en.wikipedia.org/wiki/Cicada_3301 |
Inherent viceis the tendency in physical objects to deteriorate because of the fundamental instability of the components of which they are made, as opposed to deterioration caused by external forces.[1][2]All objects have some kind of inherent vice as a result of the baseline law ofentropy.
The term is broadly used in... | https://en.wikipedia.org/wiki/Inherent_vice |
Acryptographickeyis calledephemeralif it is generated for each execution of a key establishment process.[1]In some cases ephemeral keys are used more than once, within a single session (e.g., in broadcast applications) where the sender generates only one ephemeral key pair per message and theprivate keyis combined sepa... | https://en.wikipedia.org/wiki/Ephemeral_key |
Random number generationis a process by which, often by means of arandom number generator(RNG), a sequence ofnumbersorsymbolsis generated that cannot be reasonably predicted better than byrandomchance. This means that the particular outcome sequence will contain some patterns detectable in hindsight but impossible to f... | https://en.wikipedia.org/wiki/Random_number_generator |
Incryptography,forward secrecy(FS), also known asperfect forward secrecy(PFS), is a feature of specifickey-agreement protocolsthat gives assurances thatsession keyswill not be compromised even if long-term secrets used in the session key exchange are compromised, limiting damage.[1][2][3]ForTLS, the long-term secret is... | https://en.wikipedia.org/wiki/Perfect_forward_secrecy |
40-track modeis asteganographictechnique that allows for hidden data on a 3.5 inchfloppy diskette.
A 3.5 inch 1.44MB mini-floppy diskette contains 80 tracks, 18 sectors per track, and 512 bytes per sector. A 3.5 inch 720k diskette contains 80 tracks, 9 sectors per track, and 512 bytes per sector. This technique refers... | https://en.wikipedia.org/wiki/40-track_mode |
Anacrosticis apoemor other word composition in which thefirstletter (or syllable, or word) of each new line (orparagraph, or other recurring feature in the text) spells out a word, message or the alphabet.[1]The term comes from the Frenchacrostichefrom post-classicalLatinacrostichis, fromKoine Greekἀκροστιχίς, fromAnci... | https://en.wikipedia.org/wiki/Acrostic |
TheBible code(Hebrew:הצופן התנ"כי,hatzofen hatanachi), also known as theTorah code, is a purported set ofencodedwords within a Hebrew text of theTorahthat, according to proponents, has predicted significant historical events. The statistical likelihood of the Bible code arising by chance has been thoroughly researched,... | https://en.wikipedia.org/wiki/Bible_code |
BPCS-steganography (Bit-Plane Complexity Segmentation steganography)is a type ofdigital steganography.
Digital steganography can hide confidential data (i.e. secret files) very securely by embedding them into some media data called "vessel data." The vessel data is also referred to as "carrier, cover, or dummy data". ... | https://en.wikipedia.org/wiki/BPCS-Steganography |
Hacktivismois an offshoot ofCult of the Dead Cow(cDc), whose beliefs includeaccess to informationas a basichuman right. It was founded in 1999.
The group's beliefs are described fully in The Hacktivismo Declaration, which seeks to apply theUniversal Declaration of Human Rightsand theInternational Covenant on Civil and... | https://en.wikipedia.org/wiki/Hacktivismo#Camera.2FShy |
Awarrant canaryis a method by which acommunications service provideraims to implicitly inform its users that the provider has been served with a governmentsubpoenadespite legal prohibitions on revealing the existence of the subpoena. The warrant canary typically informs users that there hasnotbeen a court-issued subpoe... | https://en.wikipedia.org/wiki/Warrant_canary |
Incryptographyandsteganography, plausiblydeniable encryptiondescribesencryptiontechniques where the existence of an encrypted file or message is deniable in the sense that an adversary cannot prove that theplaintextdata exists.[1]
The users mayconvincingly denythat a given piece of data is encrypted, or that they are ... | https://en.wikipedia.org/wiki/Deniable_encryption |
Adigital watermarkis a kind of marker covertly embedded in a noise-tolerantsignalsuch as audio, video or image data.[1]It is typically used to identify ownership of the copyright of such a signal. Digital watermarking is the process of hiding digital information in acarrier signal; the hidden information should,[2]but ... | https://en.wikipedia.org/wiki/Digital_watermarking |
Invisible ink, also known assecurity inkorsympathetic ink, is a substance used for writing, which is invisible either on application or soon thereafter, and can later be made visible by some means, such asheatorultravioletlight. Invisible ink is one form ofsteganography.
One of the earliest writers to mention an invis... | https://en.wikipedia.org/wiki/Invisible_ink |
Incryptography, amusic cipheris analgorithmfor theencryptionof a plaintext into musical symbols or sounds. Music-based ciphers are related to, but not the same asmusical cryptograms. The latter were systems used by composers to create musicalthemesormotifsto represent names based on similarities between letters of the ... | https://en.wikipedia.org/wiki/Music_cipher#Musical_Steganagraphy |
ThePolybius square, also known as thePolybius checkerboard, is a device invented by theancient GreeksCleoxenus and Democleitus, and made famous by thehistorianand scholarPolybius.[1]The device is used forfractionatingplaintextcharacters so that they can be represented by a smaller set of symbols, which is useful fortel... | https://en.wikipedia.org/wiki/Polybius_square |
Steganographic file systemsare a kind offile systemfirst proposed byRoss Anderson,Roger Needham, andAdi Shamir. Their paper proposed two main methods of hiding data: in a series of fixed size files originally consisting of random bits on top of which 'vectors' could be superimposed in such a way as to allow levels of ... | https://en.wikipedia.org/wiki/Steganographic_file_system |
Asteganographysoftware tool allows a user to embed hidden data inside a carrier file, such as an image or video, and later extract that data.
It is not necessary to conceal the message in the original file at all. Thus, it is not necessary to modify the original file and thus, it is difficult to detect anything. If a ... | https://en.wikipedia.org/wiki/Steganography_tools |
Anaudio watermarkis a unique electronic identifier embedded in an audio signal, typically used to identify ownership of copyright. It is similar to awatermarkon a photograph.
Digital watermarkingis the process of embedding information into a signal (e.g. audio, video or pictures) in a way that is difficult to remove. ... | https://en.wikipedia.org/wiki/Audio_watermark |
Security printingis the field of theprintingindustry that deals with the printing of items such asbanknotes,cheques,passports,tamper-evidentlabels,security tapes, productauthentication,stock certificates,postage stamps, andidentity cards. The main goal of security printing is to preventforgery, tampering, orcounterfeit... | https://en.wikipedia.org/wiki/Security_printing |
TheClandestine HUMINTpage adheres to the functions within the discipline, includingespionageand active counterintelligence.
The page deals withClandestine HUMINT operational techniques, also known as "tradecraft". It applies to clandestine operations for espionage, and a clandestine phase beforedirect action(DA) orunc... | https://en.wikipedia.org/wiki/Clandestine_HUMINT_operational_techniques |
TheUnited States Geospatial Intelligence Foundation(USGIF) is a 501(c)(3)non-profiteducational foundation inVirginiadedicated to promoting thegeospatial intelligencetradecraftand developing a strongerGEOINTCommunity with government, industry, academia, professional organizations, and individuals who develop and apply g... | https://en.wikipedia.org/wiki/United_States_Geospatial_Intelligence_Foundation |
k-anonymityis a property possessed by certainanonymized data. The termk-anonymity was first introduced byPierangela SamaratiandLatanya Sweeneyin a paper published in 1998,[1]although the concept dates to a 1986 paper by Tore Dalenius.[2]
k-anonymity is an attempt to solve the problem "Given person-specific field-struc... | https://en.wikipedia.org/wiki/K-anonymity |
Secure multi-party computation(also known assecure computation,multi-party computation(MPC) orprivacy-preserving computation) is a subfield of cryptography with the goal of creating methods for parties to jointly compute a function over their inputs while keeping those inputs private.[1]Unlike traditional cryptographic... | https://en.wikipedia.org/wiki/Secure_multi-party_computation |
Incryptography, aprivate information retrieval (PIR)protocol is a protocol that allows a user to retrieve an item from a server in possession of adatabasewithout revealing which item is retrieved. PIR is a weaker version of 1-out-of-noblivious transfer, where it is also required that the user should not get information... | https://en.wikipedia.org/wiki/Private_information_retrieval |
Incryptography, theZimmermann–Sassaman key-signing protocolis a protocol to speed up thepublic key fingerprintverification part of akey signing party. It requires somework before the event.
The protocol was invented during a key signing party withLen Sassaman,Werner Koch,Phil Zimmermann, and others.
The Sassaman-Effi... | https://en.wikipedia.org/wiki/Zimmermann%E2%80%93Sassaman_key-signing_protocol |
CryptoParty(Crypto-Party) is agrassrootsglobal endeavour[1]to introduce the basics of practical cryptography such as theTor anonymity network,I2P,Freenet,key signing parties,disk encryptionandvirtual private networksto the general public.[2][3]The project primarily consists of a series of free public workshops.
As a s... | https://en.wikipedia.org/wiki/CryptoParty |
Afriend-to-friend(orF2F) computer network is a type ofpeer-to-peer networkin which users only make direct connections with people they know.Passwordsordigital signaturescan be used forauthentication.
Unlike other kinds ofprivate P2P, users in a friend-to-friend network cannot find out who else is participating beyond ... | https://en.wikipedia.org/wiki/Friend-to-friend |
Self-sovereign identity(SSI) is an approach todigital identitythat gives individuals control over the information they use to prove who they are towebsites, services, andapplicationsacross the web. Without SSI, individuals with persistent accounts (identities) across theinternetmust rely on a number of large identity p... | https://en.wikipedia.org/wiki/Self-sovereign_identity |
Avirtual communityis asocial networkof individuals who connect through specificsocial media, potentially crossing geographical and political boundaries in order to pursue mutual interests or goals. Some of the most pervasive virtual communities areonline communitiesoperating undersocial networking services.
Howard Rhe... | https://en.wikipedia.org/wiki/Virtual_community |
In computer security, achain of trustis established by validating each component ofhardwareandsoftwarefrom the end entity up to the root certificate. It is intended to ensure that only trusted software and hardware can be used while still retaining flexibility.
A chain of trust is designed to allow multiple users to ... | https://en.wikipedia.org/wiki/Chain_of_trust |
Incryptographicsystems with hierarchical structure, atrust anchoris an authoritative entity for which trust is assumed and not derived.[1]
In theX.509architecture, aroot certificatewould be the trust anchor from which the wholechain of trustis derived. The trust anchor must be in the possession of the trusting party b... | https://en.wikipedia.org/wiki/Root_of_trust |
Anambigramis acalligraphiccomposition ofglyphs(letters, numbers, symbols or other shapes) that can yield different meanings depending on the orientation of observation.[2][3]Most ambigrams are visualpalindromesthat rely on some kind ofsymmetry, and they can often be interpreted asvisual puns.[4]The term was coined byDo... | https://en.wikipedia.org/wiki/Ambigram |
Anagrammatic poetryispoetrywith the constrained form that either each line or each verse is ananagramof all other lines or verses in the poem.
A poet that specializes in anagrams is an anagrammarian.[1]
Writing anagrammatic poetry is a form of aconstrained writingsimilar to writingpangramsor longalliterations.
Thisp... | https://en.wikipedia.org/wiki/Anagrammatic_poem |
Anagrams(also published under names includingAnagram,SnatchandWord Making and Taking) is atile-basedword gamethat involvesrearrangingletter tiles to form words.
The game pieces are a set of tiles with letters on one side. Tiles are shuffled face-down then turned over one by one, players forming words by combining them... | https://en.wikipedia.org/wiki/Anagrams_(game) |
Ananadrome[1][2][3][4][a]is a word or phrase whose letters can be reversed to spell a different word or phrase. For example,dessertsis an anadrome ofstressed. An anadrome is therefore a special type ofanagram. The English language is replete with such words.
The wordanadromecomes from Greekanádromos(ἀνάδρομος), "runni... | https://en.wikipedia.org/wiki/Ananym |
Ablanagram(portmanteauof blank andanagram) is a word which is ananagramof another but for the substitution of a single letter. The term has its origin in competitiveScrabble, where a blank tile on a player's rack may be used to form any of several possible words in conjunction with the player's other tiles.
Many seve... | https://en.wikipedia.org/wiki/Blanagram |
Constrained writingis aliterary techniquein which the writer is bound by some condition that forbids certain things or imposes a pattern.[1]
Constraints are very common inpoetry, which often requires the writer to use a particular verse form.
Constraints on writing are common and can serve a variety of purposes. For ... | https://en.wikipedia.org/wiki/Constrained_writing |
Aheterogram(fromhetero-, meaning 'different', +-gram, meaning 'written') is a word, phrase, or sentence in which noletterof the alphabet occurs more than once. The termsisogramandnonpattern wordhave also been used to mean the same thing.[1][2][3]
It is not clear who coined or popularized the term "heterogram". The con... | https://en.wikipedia.org/wiki/Isogram |
Aletter bankis a relative of theanagramwhere all the letters of one word (the "bank") can be used as many times as desired (minimum of once each) to make a new word or phrase. For example, IMPS is a bank of MISSISSIPPI and SPROUT is a bank ofSUPPORT OUR TROOPS. As a convention, the bank should have no repeat letters wi... | https://en.wikipedia.org/wiki/Letter_bank |
These aregeographic anagrams and anadromes.Anagramsare rearrangements of the letters of another name or word.Anadromes(also called reversals or ananyms) are other names or words spelled backwards. Technically, a reversal is also an anagram, but the two are derived by different methods, so they are listed separately.
P... | https://en.wikipedia.org/wiki/List_of_geographic_anagrams_and_ananyms |
In the biologicalnomenclature codes, ananagramcan be used to name a newtaxon.
Wordplaysare one source of inspiration allowing organisms to receivescientific names.[1]In thebinomial nomenclature, as scientists have latitude in naminggeneraandspecies, a taxon name can therefore be an anagram, provided it remains pronoun... | https://en.wikipedia.org/wiki/List_of_taxa_named_by_anagrams |
London Underground anagram mapis aparodymap of theLondon Undergroundwith the station and line names replaced withanagrams. The anagram map was circulated on the web in February 2006.
The map was featured on thousands ofblogsbefore aTransport for Londonlawyer requested that the map be removed. It inspired some people ... | https://en.wikipedia.org/wiki/London_Underground_anagram_map |
Apalindrome(/ˈpæl.ɪn.droʊm/) is a word,number, phrase, or other sequence of symbols that reads the same backwards as forwards, such asmadamorracecar, the date "22/02/2022" and the sentence: "A man, a plan, a canal –Panama". The 19-letterFinnishwordsaippuakivikauppias(asoapstonevendor) is the longest single-word palind... | https://en.wikipedia.org/wiki/Palindrome |
Apangramorholoalphabetic sentenceis asentenceusing every letter of a givenalphabetat least once. Pangrams have been used to displaytypefaces, test equipment, and develop skills inhandwriting,calligraphy, andtyping.
The best-known English pangram is "The quick brown fox jumps over the lazy dog".[1]It has been used sinc... | https://en.wikipedia.org/wiki/Pangram |
Arebus(/ˈriːbəs/REE-bəss) is apuzzledevice that combines the use of illustrated pictures with individual letters to depict words or phrases. For example: the word "been" might be depicted by a rebus showing an illustrated bumblebee next to a plus sign (+) and the letter "n".
It was a favourite form ofheraldicexpressio... | https://en.wikipedia.org/wiki/Rebus |
TheSator Square(orRotas-Sator SquareorTemplar Magic Square) is a two-dimensionalacrosticclass ofword squarecontaining a five-wordLatinpalindrome.[1]The earliest squares were found at Roman-era sites, all in ROTAS-form (where the top line is "ROTAS", not "SATOR"), with the earliest discovery atPompeii(and also likely pr... | https://en.wikipedia.org/wiki/Sator_Square |
Aspoonerismis an occurrence of speech in which correspondingconsonants,vowels, ormorphemesare switched (seemetathesis) between two words of a phrase.[1][a]These are named after the Oxford don and priestWilliam Archibald Spooner, who reportedly commonly spoke in this way.[2]
Examples include saying "blushing crow" inst... | https://en.wikipedia.org/wiki/Spoonerism |
Atautonymis ascientific nameof a species in which both parts of the name have the same spelling, such asRattus rattus. The first part of the name is the name of the genus and the second part is referred to as thespecific epithetin theInternational Code of Nomenclature for algae, fungi, and plantsand thespecific namein... | https://en.wikipedia.org/wiki/Tautonym |
Word playorwordplay[1](also:play-on-words) is aliterary techniqueand a form ofwitin which words used become the main subject of the work, primarily for the purpose of intended effect oramusement. Examples of word play includepuns, phonetic mix-ups such asspoonerisms, obscure words and meanings, cleverrhetoricalexcursio... | https://en.wikipedia.org/wiki/Word_play |
In mathematics,arithmetic geometryis roughly the application of techniques fromalgebraic geometryto problems innumber theory.[1]Arithmetic geometry is centered aroundDiophantine geometry, the study ofrational pointsofalgebraic varieties.[2][3]
In more abstract terms, arithmetic geometry can be defined as the study ofs... | https://en.wikipedia.org/wiki/Arithmetic_geometry |
Arithmetic topologyis an area ofmathematicsthat is a combination ofalgebraic number theoryandtopology. It establishes an analogy betweennumber fieldsand closed, orientable3-manifolds.
The following are some of the analogies used by mathematicians between number fields and 3-manifolds:[1]
Expanding on the last two exa... | https://en.wikipedia.org/wiki/Arithmetic_topology |
Themathematicaldisciplines ofcombinatoricsanddynamical systemsinteract in a number of ways. Theergodic theoryof dynamical systems has recently been used to prove combinatorial theorems about number theory which has given rise to the field ofarithmetic combinatorics. Alsodynamical systems theoryis heavily involved in th... | https://en.wikipedia.org/wiki/Combinatorics_and_dynamical_systems |
Inarithmetic dynamics, anarboreal Galois representationis acontinuousgroup homomorphismbetween theabsolute Galois groupof a field and theautomorphism groupof an infinite, regular, rootedtree.
The study of arboreal Galois representations of goes back to the works of Odoni in 1980s.
LetK{\displaystyle K}be afieldandKse... | https://en.wikipedia.org/wiki/Arboreal_Galois_representation |
Inmathematics, theEnriques–Kodaira classificationgroupscompactcomplex surfacesinto ten classes, each parametrized by amoduli space. For most of the classes the moduli spaces are well understood, but for the class of surfaces of general type the moduli spaces seem too complicated to describe explicitly, though some comp... | https://en.wikipedia.org/wiki/Enriques%E2%80%93Kodaira_classification |
Inalgebraic geometry, theNéron model(orNéron minimal model, orminimal model)
for anabelian varietyAKdefined over the field of fractionsKof a Dedekind domainRis the "push-forward" ofAKfrom Spec(K) to Spec(R), in other words the "best possible" group schemeARdefined overRcorresponding toAK.
They were introduced byAndré... | https://en.wikipedia.org/wiki/N%C3%A9ron_minimal_model |
The following tables provide acomparison ofnumerical analysissoftware.
[Note 1]
[Note 2]
[Note 3]
Was:Inria
(Andrey Ivashov)
Theoperating systemsthe software can run on natively (withoutemulation).
Colors indicate features available as
Theoperating systemsthe software can run on natively (withoutemulation). | https://en.wikipedia.org/wiki/Comparison_of_numerical-analysis_software |
The following tables compare general and technical information for manystatistical analysissoftware packages.
University of Amsterdam
Support for variousANOVAmethods
Support for variousregressionmethods.
Support for varioustime series analysismethods.
Support for variousstatisticalchartsanddiagrams. | https://en.wikipedia.org/wiki/Comparison_of_statistical_packages |
This is a list ofnumerical libraries, which arelibrariesused insoftware developmentfor performingnumericalcalculations. It is not a complete listing but is instead a list of numerical libraries with articles on Wikipedia, with few exceptions.
The choice of a typical library depends on a range of requirements such as:... | https://en.wikipedia.org/wiki/List_of_numerical_libraries |
The following is a list ofstatistical software. | https://en.wikipedia.org/wiki/List_of_statistical_software |
Mathematical softwareissoftwareused tomodel, analyze or calculate numeric, symbolic or geometric data.[1]
Numerical analysisandsymbolic computationhad been in most important place of the subject, but other kind of them is also growing now. A useful mathematical knowledge of such asalgorismwhich exist before theinventi... | https://en.wikipedia.org/wiki/Mathematical_software |
Web-based simulation(WBS) is the invocation ofcomputer simulationservices over theWorld Wide Web, specifically through aweb browser.[1][2][3][4]Increasingly, the web is being looked upon as an environment for providingmodeling and simulationapplications, and as such, is an emerging area of investigation within the simu... | https://en.wikipedia.org/wiki/Web-based_simulation |
Inmathematics,localization of a categoryconsists of adding to acategoryinversemorphismsfor some collection of morphisms, constraining them to becomeisomorphisms. This is formally similar to the process oflocalization of a ring; it in general makes objects isomorphic that were not so before. Inhomotopy theory, for examp... | https://en.wikipedia.org/wiki/Abelian_varieties_up_to_isogeny |
Inarithmetic geometry, theSelmer group, named in honor of the work ofErnst Sejersted Selmer(1951) byJohn William Scott Cassels(1962), is agroupconstructed from anisogenyofabelian varieties.
The Selmer group of an abelian varietyAwith respect to anisogenyf:A→Bof abelian varieties can be defined in terms ofGalois cohomo... | https://en.wikipedia.org/wiki/Selmer_group |
Inmathematics,Siegel modular formsare a major type ofautomorphic form. These generalize conventionalellipticmodular formswhich are closely related toelliptic curves. The complex manifolds constructed in the theory of Siegel modular forms areSiegel modular varieties, which are basic models for what amoduli spacefor abel... | https://en.wikipedia.org/wiki/Siegel_modular_form |
Inmathematics, arigidcollectionCofmathematical objects(for instance sets or functions) is one in which everyc∈Cis uniquely determined by less information aboutcthan one would expect.
The above statement does not define amathematical property; instead, it describes in what sense the adjective "rigid" is typically used i... | https://en.wikipedia.org/wiki/Rigidity_(mathematics) |
Local rigiditytheorems in the theory of discrete subgroups ofLie groupsare results which show that small deformations of certain such subgroups are always trivial. It is different fromMostow rigidityand weaker (but holds more frequently) thansuperrigidity.
The first such theorem was proven byAtle Selbergfor co-compact... | https://en.wikipedia.org/wiki/Local_rigidity |
Given atopological spaceand agroupactingon it, the images of a single point under the group action form anorbitof the action. Afundamental domainorfundamental regionis a subset of the space which contains exactly one point from each of these orbits. It serves as a geometric realization for the abstract set of represent... | https://en.wikipedia.org/wiki/Fundamental_domain |
Inmathematics, ahomothety(orhomothecy, orhomogeneous dilation) is atransformationof anaffine spacedetermined by a pointScalled itscenterand a nonzero numberkcalled itsratio, which sends pointXto a pointX′by the rule,[1]
Using position vectors:
In case ofS=O{\displaystyle S=O}(Origin):
which is auniform scalingand sh... | https://en.wikipedia.org/wiki/Homothetic_transformation |
Abelian varietiesare a natural generalization ofelliptic curvesto higher dimensions. However, unlike the case of elliptic curves, there is no well-behaved stack playing the role of amoduli stackfor higher-dimensional abelian varieties.[1]One can solve this problem by constructing a moduli stack of abelian varieties eq... | https://en.wikipedia.org/wiki/Moduli_of_abelian_varieties |
Innumber theory, aShimura varietyis a higher-dimensional analogue of amodular curvethat arises as a quotientvarietyof aHermitian symmetric spaceby acongruence subgroupof areductive algebraic groupdefined overQ. Shimura varieties are notalgebraic varietiesbut are families of algebraic varieties.Shimura curvesare the one... | https://en.wikipedia.org/wiki/Shimura_variety |
Innumber theoryandalgebraic geometry, amodular curveY(Γ) is aRiemann surface, or the correspondingalgebraic curve, constructed as aquotientof the complexupper half-planeHby theactionof acongruence subgroupΓ of themodular groupof integral 2×2 matrices SL(2,Z). The term modular curve can also be used to refer to thecompa... | https://en.wikipedia.org/wiki/Modular_curve |
Inmathematics,elliptic cohomologyis acohomology theoryin the sense ofalgebraic topology. It is related toelliptic curvesandmodular forms.
Historically, elliptic cohomology arose from the study ofelliptic genera. It was known by Atiyah and Hirzebruch that ifS1{\displaystyle S^{1}}acts smoothly and non-trivially on a sp... | https://en.wikipedia.org/wiki/Elliptic_cohomology |
Inmathematics, theMordell–Weil theoremstates that for anabelian varietyA{\displaystyle A}over anumber fieldK{\displaystyle K}, the groupA(K){\displaystyle A(K)}ofK-rational pointsofA{\displaystyle A}is afinitely-generated abelian group, called theMordell–Weil group. The case withA{\displaystyle A}anelliptic curveE{\dis... | https://en.wikipedia.org/wiki/Mordell%E2%80%93Weil_theorem |
Inmathematics, more specificallyalgebra,abstract algebraormodern algebrais the study ofalgebraic structures, which aresetswith specificoperationsacting on their elements.[1]Algebraic structures includegroups,rings,fields,modules,vector spaces,lattices, andalgebras over a field. The termabstract algebrawas coined in the... | https://en.wikipedia.org/wiki/Abstract_algebra |
Innumber theory, given aprime numberp,[note 1]thep-adic numbersform an extension of therational numberswhich is distinct from thereal numbers, though with some similar properties;p-adic numbers can be written in a form similar to (possiblyinfinite)decimals, but with digits based on a prime numberprather than ten, and e... | https://en.wikipedia.org/wiki/P-adic_number |
Inalgebraic geometry, astable curveis analgebraic curvethat is asymptotically stable in the sense ofgeometric invariant theory.
This is equivalent to the condition that it is acompleteconnected curve whose only singularities are ordinarydouble pointsand whoseautomorphism groupis finite.
The condition that the automo... | https://en.wikipedia.org/wiki/Semistable_curve |
Incryptography,Curve448orCurve448-Goldilocksis anelliptic curvepotentially offering 224 bits of security and designed for use with theelliptic-curve Diffie–Hellman(ECDH) key agreement scheme.
Developed by Mike Hamburg ofRambusCryptography Research, Curve448 allows fast performance compared with other proposed curves w... | https://en.wikipedia.org/wiki/Curve448 |
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