Semantic integration is the process of interrelating information from diverse sources, for example calendars and to do lists, email archives, presence information (physical, psychological, and social), documents of all sorts, contacts (including social graphs), search results, and advertising and marketing relevance derived from them. In this regard, semantics focuses on the organization of and action upon information by acting as an intermediary between heterogeneous data sources, which may conflict not only by structure but also context or value. == Applications and methods == In enterprise application integration (EAI), semantic integration can facilitate or even automate the communication between computer systems using metadata publishing. Metadata publishing potentially offers the ability to automatically link ontologies. One approach to (semi-)automated ontology mapping requires the definition of a semantic distance or its inverse, semantic similarity and appropriate rules. Other approaches include so-called lexical methods, as well as methodologies that rely on exploiting the structures of the ontologies. For explicitly stating similarity/equality, there exist special properties or relationships in most ontology languages. OWL, for example has "owl:equivalentClass", "owl:equivalentProperty" and "owl:sameAs". Eventually system designs may see the advent of composable architectures where published semantic-based interfaces are joined together to enable new and meaningful capabilities. These could predominately be described by means of design-time declarative specifications, that could ultimately be rendered and executed at run-time. Semantic integration can also be used to facilitate design-time activities of interface design and mapping. In this model, semantics are only explicitly applied to design and the run-time systems work at the syntax level. This "early semantic binding" approach can improve overall system performance while retaining the benefits of semantic driven design. == Semantic integration situations == From the industry use case, it has been observed that the semantic mappings were performed only within the scope of the ontology class or the datatype property. These identified semantic integrations are (1) integration of ontology class instances into another ontology class without any constraint, (2) integration of selected instances in one ontology class into another ontology class by the range constraint of the property value and (3) integration of ontology class instances into another ontology class with the value transformation of the instance property. Each of them requires a particular mapping relationship, which is respectively: (1) equivalent or subsumption mapping relationship, (2) conditional mapping relationship that constraints the value of property (data range) and (3) transformation mapping relationship that transforms the value of property (unit transformation). Each identified mapping relationship can be defined as either (1) direct mapping type, (2) data range mapping type or (3) unit transformation mapping type. == KG vs. RDB approaches == In the case of integrating supplemental data source, KG(Knowledge graph) formally represents the meaning involved in information by describing concepts, relationships between things, and categories of things. These embedded semantics with the data offer significant advantages such as reasoning over data and dealing with heterogeneous data sources. The rules can be applied on KG more efficiently using graph query. For example, the graph query does the data inference through the connected relations, instead of repeated full search of the tables in relational database. KG facilitates the integration of new heterogeneous data by just adding new relationships between existing information and new entities. This facilitation is emphasized for the integration with existing popular linked open data source such as Wikidata.org. SQL query is tightly coupled and rigidly constrained by datatype within the specific database and can join tables and extract data from tables, and the result is generally a table, and a query can join tables by any columns which match by datatype. SPARQL query is the standard query language and protocol for Linked Open Data on the web and loosely coupled with the database so that it facilitates the reusability and can extract data through the relations free from the datatype, and not only extract but also generate additional knowledge graph with more sophisticated operations(logic: transitive/symmetric/inverseOf/functional). The inference based query (query on the existing asserted facts without the generation of new facts by logic) can be fast comparing to the reasoning based query (query on the existing plus the generated/discovered facts based on logic). The information integration of heterogeneous data sources in traditional database is intricate, which requires the redesign of the database table such as changing the structure and/or addition of new data. In the case of semantic query, SPARQL query reflects the relationships between entities in a way that aligned with human's understanding of the domain, so the semantic intention of the query can be seen on the query itself. Unlike SPARQL, SQL query, which reflects the specific structure of the database and derived from matching the relevant primary and foreign keys of tables, loses the semantics of the query by missing the relationships between entities. Below is the example that compares SPARQL and SQL queries for medications that treats "TB of vertebra". SELECT ?medication WHERE { ?diagnosis a example:Diagnosis . ?diagnosis example:name “TB of vertebra” . ?medication example:canTreat ?diagnosis . } SELECT DRUG.medID FROM DIAGNOSIS, DRUG, DRUG_DIAGNOSIS WHERE DIAGNOSIS.diagnosisID=DRUG_DIAGNOSIS.diagnosisID AND DRUG.medID=DRUG_DIAGNOSIS.medID AND DIAGNOSIS.name=”TB of vertebra” == Examples == The Pacific Symposium on Biocomputing has been a venue for the popularization of the ontology mapping task in the biomedical domain, and a number of papers on the subject can be found in its proceedings.
Kounta (software company)
Kounta is an Australian software company founded in 2012. The company's flagship product, Kounta, comprises a cloud based point of sale mobile app. == History == Kounta was founded in 2012 by entrepreneur Nick Cloete. The company is headquartered in Sydney, Australia. In 2012, the company launched its flagship product, Kounta, a hospitality-focused point of sale (POS) mobile app for iPad, Android, Mac, and Windows. The app was initially a web-based application, and later developed into an online cash register and inventory management system that allows businesses to take payments from customers via mobile devices. The app has been made available for iPad, iPhone, and Android devices; as well as iOS, Windows, and other peripherals. In 2012, Kounta partnered with Epson, providing a cloud-based POS platform for Epson printers. In 2013, the company formed a partnership with PayPal, integrating cashless and cardless transaction options via PayPal's mobile app. In 2014, MYOB (company) made an undisclosed investment towards Kounta. This partnership led to the development of MYOB Kounta, a co-branded application merging Kounta's POS with MYOB's application software. MYOB Kounta launched in October of the same year. In 2016, Kounta announced a partnership with the Commonwealth Bank of Australia to include the Kounta app onto "Albert", the bank's EFTPOS tablet, which allowed the Commonwealth Bank of Australia to become the first bank to manage all customers operations from a single device and mobile application. == Technology == The Kounta POS is a software-as-a-service (SaaS) that runs as an application in web browsers as well as natively on iOS and Android operating systems. Kounta also incorporates an Open API, making it possible for other software providers to integrate complementary apps, further extending the software's use. Traditional IT tasks, such as data backup and encryption, hardware maintenance, and server upgrades are handled by Kounta's data center. Kounta is made accessible via paid monthly subscription licenses. == Acquisition by Lightspeed == In October 2019, Kounta was acquired by Lightspeed, an advanced commerce platform for retail, hospitality, and golf businesses based in Montreal, Canada. Lightspeed acquired Kounta for $35.3 million USD.
Social influence bias
The social influence bias is an asymmetric herding effect on online social media platforms which makes users overcompensate for negative ratings but amplify positive ones. Driven by the desire to be accepted within a specific group, it surrounds the idea that people alter certain behaviors to be like those of the people within a group. Therefore, it is a subgroup term for various types of cognitive biases. Some social influence bias types include the bandwagon effect, authority bias, groupthinking effect, social comparison bias, social media bias and more. Understanding these biases helps us understand the term overall. However, the composition of the term "social influence bias" requires critical examination to understand the way that it affects individuals' and groups' lives. The term "influence" has 2 different types of stigma. For one, it surrounds the idea that people show their true inner selves when "under the influence". On the other end, it also proposes the idea that people are not their own selves when "under the influence". These tend to be constructions made by people, which also tend to fit the situation based on their own perspectives. So, even in social terms, it requires both sides to be examined to understand whether we truly are affected by context, or we remain to be and behave in terms of our own selves. The term "influence" doesn't necessarily say that there lies greater strength in our inner self's desires and decisions, nor does it say that external factors have the greater power. In a similar manner, both social and non-social judgments are to be associated with anxiety, but the same can't necessarily be said in the case of social conformity. So, the gray areas within this topic beg the question, "What does social influence bias say about us, and does it affect us all in the same way?" == Social media bias == Media bias is reflected in search systems in social media. Kulshrestha and her team found through research in 2018 that the top-ranked results returned by these search engines can influence users' perceptions when they conduct searches for events or people, which is particularly reflected in political bias and polarizing topics. Fueled by confirmation bias, online echo chambers allow users to be steeped within their own ideology. Because social media is tailored to your interests and your selected friends, it is an easy outlet for political echo chambers. Social media bias is also reflected in hostile media effect. Social media has a place in disseminating news in modern society, where viewers are exposed to other people's comments while reading news articles. In their 2020 study, Gearhart and her team showed that viewers' perceptions of bias increased and perceptions of credibility decreased after seeing comments with which they held different opinions. == In research context == In observational data, how social influence affects collected judgment is challenging to fully understand. Positive social influence can accumulate and result in a rating bubble, while negative social influence is neutralized by crowd correction. This phenomenon was first described in a paper written by Lev Muchnik, Sinan Aral and Sean J. Taylor in 2014, then the question was revisited by Cicognani et al., whose experiment reinforced Munchnik's and his co-authors' results. == Relevance == Online customer reviews are trusted sources of information in various contexts such as online marketplaces, dining, accommodation, movies, or digital products. However, these online ratings are not immune to herd behavior, which means that subsequent reviews are not independent from each other. As on many such sites, preceding opinions are visible to a new reviewer, he or she can be heavily influenced by the antecedent evaluations in his or her decision about the certain product, service or online content. This form of herding behavior inspired Muchnik, Aral and Taylor to conduct their experiment on influence in social contexts. == Experimental design == Muchnik, Aral, and Taylor designed a large-scale randomized experiment to measure social influence on user reviews. The experiment was conducted on social news aggregation website like Reddit. The study lasted for 5 months, the authors randomly assigned 101 281 comments to one of the following treatment groups: up-treated (4049), down-treated (1942), or control (the proportions reflect the observed ratio of up-and down-votes. Comments which fell to the first group were given an up-vote upon the creation of the comment, the second group got a down-vote upon creation, the comments in the control group remained untouched. A vote is equivalent to a single rating (+1 or -1). As other users are unable to trace a user’s votes, they were unaware of the experiment. Due to randomization, comments in the control and the treatment group were not different in terms of expected rating. The treated comments were viewed more than 10 million times and rated 308 515 times by successive users. == Results == The up-vote treatment increased the probability of up-voting by the first viewer by 32% over the control group, while the probability of down-voting did not change compared to the control group, which means that users did not correct the random positive rating. The upward bias remained inplace for the observed 5-month period. The accumulating herding effect increased the comment’s mean rating by 25% compared to the control group comments. Positively manipulated comments did receive higher ratings at all parts of the distribution, which means that they were also more likely to collect extremely high scores. The negative manipulation created an asymmetric herd effect: although the probability of subsequent down-votes was increased by the negative treatment, the probability of up-voting also grew for these comments. The community performed a correction which neutralized the negative treatment and resulted non-different final mean ratings from the control group. The authors also compared the final mean scores of comments across the most active topic categories on the website. The observed positive herding effect was present in the "politics," "culture and society," and "business" subreddits, but was not applicable for "economics," "IT," "fun," and "general news".- == Implications == The skewed nature of online ratings makes review outcomes different to what it would be without the social influence bias. In a 2009 experiment by Hu, Zhang and Pavlou showed that the distribution of reviews of a certain product made by unconnected individuals is approximately normal, however, the rating of the same product on Amazon followed a J-Shaped distribution with twice as much five-star ratings than others. Cicognani, Figini and Magnani came to similar conclusions after their experiment conducted on a tourism services website: positive preceding ratings influenced raters' behavior more than mediocre ones. Positive crowd correction makes community-based opinions upward-biased.
Data storage
Data storage is the recording (storing) of information (data) in a storage medium. Handwriting, phonographic recording, magnetic tape, and optical discs are all examples of storage media. Biological molecules such as RNA and DNA are considered by some as data storage. Recording may be accomplished with virtually any form of energy. Electronic data storage requires electrical power to store and retrieve data. Data stored in a digital, machine-readable medium is called digital data. Computer data storage is one of the core functions of a general-purpose computer. Electronic documents can be stored in much less space than paper documents. Barcodes and magnetic ink character recognition (MICR) are two ways of recording machine-readable data on paper. == Recording media == A recording medium is physical material that holds information. Newly created information is distributed and can be stored in four storage media–print, film, magnetic, and optical–and seen or heard in four information flows–telephone, radio, TV, and the Internet as well as being observed directly. Digital information is stored on electronic media in many different recording formats. With electronic media, the data and the recording media are sometimes referred to as "software" despite the more common use of the word to describe computer software. With (traditional art) static media, art materials such as crayons may be considered both equipment and medium as the wax, charcoal or chalk material from the equipment becomes part of the surface of the medium. Some recording media may be temporary, either by design or by nature. Volatile organic compounds may be used to purposely make data expire over time or to reduce environmental impact. Data such as smoke signals or skywriting are temporary by nature. Depending on the volatility, a gas (e.g., atmosphere, smoke) or a liquid surface such as a lake would be considered a temporary recording medium, if it could be considered a recording medium at all. == Global capacity, digitization, and trends == A 2003 UC Berkeley report estimated that about five exabytes of new information were produced in 2002 and that 92% of this data was stored on magnetic media (primarily hard disk drives). This was about twice the data produced in 1999. The amount of data transmitted over telecommunications systems in 2002 was nearly 18 exabytes—three and a half times more than was recorded on non-volatile storage. Telephone calls constituted 98% of the telecommunicated information in 2002. The researchers' highest estimate for the growth rate of newly stored information (uncompressed) was more than 30% per year. In a more limited study, the International Data Corporation estimated that the total amount of digital data in 2007 was 281 exabytes and that the total amount of digital data produced exceeded the global storage capacity for the first time. A 2011 article in Science estimated that the year 2002 was the beginning of the digital age for information storage: an age in which more information is stored on digital storage devices than on analog storage devices. In 1986, approximately 1% of the world's capacity to store information was in digital format; this grew to 3% by 1993, to 25% by 2000, and to 94% by 2007. These figures correspond to less than three compressed exabytes in 1986, and 295 compressed exabytes in 2007. The quantity of digital storage doubled roughly every three to four years. It is estimated that around 120 zettabytes of data will be generated in 2023, an increase of 60x from 2010, and that it will increase to 181 zettabytes generated in 2025. == Mass storage ==
Group key
In cryptography, a group key is a cryptographic key that is shared between a group of users. Typically, group keys are distributed by sending them to individual users, either physically, or encrypted individually for each user using either that user's pre-distributed private key. A common use of group keys is to allow a group of users to decrypt a broadcast message that is intended for that entire group of users, and no one else. For example, in the Second World War, group keys (known as "iodoforms", a term invented by a classically educated non-chemist, and nothing to do with the chemical of the same name) were sent to groups of agents by the Special Operations Executive. These group keys allowed all the agents in a particular group to receive a single coded message. In present-day applications, group keys are commonly used in conditional access systems, where the key is the common key used to decrypt the broadcast signal, and the group in question is the group of all paying subscribers. In this case, the group key is typically distributed to the subscribers' receivers using a combination of a physically distributed secure cryptoprocessor in the form of a smartcard and encrypted over-the-air messages.
Cloudflare
Cloudflare, Inc., is an American technology company headquartered in San Francisco, California, that provides a range of internet services, including content delivery network (CDN) services, cloud cybersecurity, DDoS mitigation, and ICANN-accredited domain registration. The company's services act primarily as a reverse proxy between website visitors and a customer's hosting provider, improving performance and protecting against malicious traffic. Cloudflare was founded in 2009 by Matthew Prince, Lee Holloway, and Michelle Zatlyn. The company went public on the New York Stock Exchange in 2019 under the ticker symbol NET. Cloudflare has since expanded its offerings to include edge computing through its Workers platform, a public DNS resolver (1.1.1.1), and a VPN-like service known as WARP. In recent years, the company has integrated artificial intelligence into its infrastructure, acquiring companies such as Replicate and launching tools to manage AI bots and scrapers. According to W3Techs, Cloudflare is used by approximately 21.3% of all websites on the Internet as of January 2026. The company has been the subject of controversy regarding its policy of content neutrality. While Cloudflare executives have historically advocated for remaining a neutral infrastructure provider, the company has terminated services for specific high-profile websites associated with hate speech and violence, including The Daily Stormer, 8chan, and Kiwi Farms, following significant public pressure. Cloudflare has also faced criticism and litigation regarding copyright infringement by websites using its services, notably losing a lawsuit against Japanese publishers in 2025. The company experienced significant global outages in late 2025 which disrupted services for major platforms internationally. == History == Cloudflare was founded on July 26, 2009, by Matthew Prince, Lee Holloway, and Michelle Zatlyn. Prince and Holloway had previously collaborated on Project Honey Pot, a product of Unspam Technologies that partly inspired the basis of Cloudflare. In 2009, the company was venture-capital funded. On August 15, 2019, Cloudflare submitted its S-1 filing for an initial public offering on the New York Stock Exchange under the stock ticker NET. It opened for public trading on September 13, 2019, at $15 per share. According to the company, the name 'Cloudflare' was chosen, over the initial 'WebWall', because it best described what they were trying to do: build a "firewall in the cloud." In 2020, Cloudflare co-founder and COO Michelle Zatlyn was named president. Cloudflare has acquired web-services and security companies, including StopTheHacker (February 2014), CryptoSeal (June 2014), Eager Platform Co. (December 2016), Neumob (November 2017), S2 Systems (January 2020), Linc (December 2020), Zaraz (December 2021), Vectrix (February 2022), Area 1 Security (February 2022), Nefeli Networks (March 2024), BastionZero (May 2024), and Kivera (October 2024). Replicate (November 2025), and Human Native (January 2026). Since at least 2017, Cloudflare has used a wall of lava lamps at its San Francisco headquarters as a source of randomness for encryption keys, alongside double pendulums at its London offices and a Geiger counter at its Singapore offices. The lava lamp installation implements the Lavarand method, where a camera transforms the unpredictable shapes of the "lava" blobs into a digital image. In Q4 2022, Cloudflare provided paid services to 162,086 customers. In October 2024, Cloudflare won a lawsuit against patent troll Sable Networks. Sable paid Cloudflare $225,000, granted it a royalty-free license to its patent portfolio, and dedicated its patents to the public by abandoning its patent rights. In November 2025, it was announced Cloudflare had agreed to acquire Replicate, a San Francisco–based platform that enables software developers to run, fine-tune, and deploy open-source machine-learning models via an API without managing infrastructure. In January 2026, Cloudflare released an analysis regarding BGP routing leaks observed from the Venezuelan state-owned ISP CANTV (AS8048), which occurred on January 2 coincides with the arrest of Nicolás Maduro. While some security researchers had speculated that the outages were linked to U.S. cyber operations, Cloudflare's data indicated that the anomalies were consistent with a pattern of "insufficient routing export and import policies" by the ISP rather than malicious external interference. In January 2026, Cloudflare acquired Human Native, an AI data marketplace that brokers transactions between developers and content creators, for an undisclosed amount. On January 16, 2026, Cloudflare acquired The Astro Technology Company, the developers behind the open-source web framework Astro. In May 2026, Cloudflare announced the elimination of approximately 1,100 positions, around 20 percent of its workforce, in a restructuring the company attributed to the rapid adoption of artificial intelligence tools. The announcement coincided with the company's first-quarter 2026 earnings, which reported a record $639.8 million in quarterly revenue, a 34 percent year-over-year increase. CEO Matthew Prince stated the cuts were not driven by performance concerns but reflected roles made obsolete by AI, and that Cloudflare expected to employ more people by the end of 2027 than at any point during 2026. == Products == Cloudflare provides network and security products for consumers and businesses, utilizing edge computing, reverse proxies for web traffic, data center interconnects, and a content distribution network to serve content across its network of servers. It supports transport layer protocols TCP, UDP, QUIC, and many application layer protocols such as DNS over HTTPS, SMTP, and HTTP/2 with support for HTTP/2 Server Push. As of 2023, Cloudflare handles an average of 45 million HTTP requests per second. As of 2024, Cloudflare servers are powered by AMD EPYC 9684X processors. Cloudflare also provides analysis and reports on large-scale outages, including Verizon's October 2024 outage. === Artificial intelligence === In 2023, Cloudflare launched "Workers AI", a framework allowing for use of Nvidia GPU's within Cloudflare's network. In 2024, Cloudflare launched a tool that prevents bots from scraping websites. To build automatic bot detector models, the company analyzed "AI" bots and crawler traffic. The company also launched an "AI" assistant to generate charts based on queries by leveraging "Workers AI". Cloudflare announced plans in September 2024 to launch a marketplace where website owners can sell "AI" model providers access to scrape their site's content. In March 2025, Cloudflare announced a new feature called "AI Labyrinth", which combats unauthorized "AI" data scraping by serving fake "AI"-generated content to LLM bots. In July, the company rolled out a permission-based setting to allow websites to automatically block online bots from scraping data and content. Cloudflare released AutoRAG into beta in 2025. AutoRAG (retrieval augmented generation) creates a vector database of a website's unstructured content to identify relationships between concepts. It is part of an initiative with Microsoft, alongside their NLWeb standard, to make websites easier for people and automated systems to query. Cloudflare and GoDaddy partnered in April 2026 to enable AI Crawl Control features on GoDaddy hosted websites. This would allow site owners to decide how AI bot crawlers interact with their content. === DDoS mitigation === Cloudflare provides free and paid DDoS mitigation services that protect customers from distributed denial of service (DDoS) attacks. Cloudflare received media attention in June 2011 for providing DDoS mitigation for the website of LulzSec, a black hat hacking group. In March 2013, The Spamhaus Project was targeted by a DDoS attack that Cloudflare reported exceeded 300 gigabits per second (Gbit/s). Patrick Gilmore, of Akamai, stated that at the time it was "the largest publicly announced DDoS attack in the history of the Internet". While trying to defend Spamhaus against the DDoS attacks, Cloudflare ended up being attacked as well; Google and other companies eventually came to Spamhaus' defense and helped it to absorb the unprecedented amount of attack traffic. In 2014, Cloudflare began providing free DDoS mitigation for artists, activists, journalists, and human rights groups under the name "Project Galileo". In 2017, it extended the service to electoral infrastructure and political campaigns under the name "Athenian Project". By 2025, more than 2,900 users and organizations were participating in Project Galileo, including 31 US states. In February 2014, Cloudflare claimed to have mitigated an NTP reflection attack against an unnamed European customer, which it stated peaked at 400 Gbit/s. In November 2014, it reported a 500 Gbit/s DDoS attack in Hong Kong. In July 2021, the company claimed to have absorbed a DDoS atta
Hybrid argument (cryptography)
In cryptography, the hybrid argument is a proof technique used to show that two distributions are computationally indistinguishable. == History == Hybrid arguments had their origin in a papers by Andrew Yao in 1982 and Shafi Goldwasser and Silvio Micali in 1983. == Formal description == Formally, to show two distributions D1 and D2 are computationally indistinguishable, we can define a sequence of hybrid distributions D1 := H0, H1, ..., Ht =: D2 where t is polynomial in the security parameter n. Define the advantage of any probabilistic efficient (polynomial-bounded time) algorithm A as A d v H i , H i + 1 d i s t ( A ) := | Pr [ x ← $ H i : A ( x ) = 1 ] − Pr [ x ← $ H i + 1 : A ( x ) = 1 ] | , {\displaystyle {\mathsf {Adv}}_{H_{i},H_{i+1}}^{\mathsf {dist}}(\mathbf {A} ):=\left|\Pr[x{\stackrel {\$}{\gets }}H_{i}:\mathbf {A} (x)=1]-\Pr[x{\stackrel {\$}{\gets }}H_{i+1}:\mathbf {A} (x)=1]\right|,} where the dollar symbol ($) denotes that we sample an element from the distribution at random. By triangle inequality, it is clear that for any probabilistic polynomial time algorithm A, A d v D 1 , D 2 d i s t ( A ) ≤ ∑ i = 0 t − 1 A d v H i , H i + 1 d i s t ( A ) . {\displaystyle {\mathsf {Adv}}_{D_{1},D_{2}}^{\mathsf {dist}}(\mathbf {A} )\leq \sum _{i=0}^{t-1}{\mathsf {Adv}}_{H_{i},H_{i+1}}^{\mathsf {dist}}(\mathbf {A} ).} Thus there must exist some k s.t. 0 ≤ k < t(n) and A d v H k , H k + 1 d i s t ( A ) ≥ A d v D 1 , D 2 d i s t ( A ) / t ( n ) . {\displaystyle {\mathsf {Adv}}_{H_{k},H_{k+1}}^{\mathsf {dist}}(\mathbf {A} )\geq {\mathsf {Adv}}_{D_{1},D_{2}}^{\mathsf {dist}}(\mathbf {A} )/t(n).} Since t is polynomial-bounded, for any such algorithm A, if we can show that it has a fixed negligible advantage function ε(n) between distributions Hi and Hi+1 for every i, so in particular, ϵ ( n ) ≥ A d v H k , H k + 1 d i s t ( A ) ≥ A d v D 1 , D 2 d i s t ( A ) / t ( n ) , {\displaystyle \epsilon (n)\geq {\mathsf {Adv}}_{H_{k},H_{k+1}}^{\mathsf {dist}}(\mathbf {A} )\geq {\mathsf {Adv}}_{D_{1},D_{2}}^{\mathsf {dist}}(\mathbf {A} )/t(n),} then it immediately follows that its advantage to distinguish the distributions D1 = H0 and D2 = Ht must also be negligible. == Applications == The hybrid argument is extensively used in cryptography. Some simple proofs using hybrid arguments are: If one cannot efficiently predict the next bit of the output of some number generator, then this generator is a pseudorandom number generator (PRG). We can securely expand a PRG with 1-bit output into a PRG with n-bit output.