Electronic business (also known as online business or e-business) is any kind of business or commercial activity that includes sharing information across the internet. Commerce constitutes the exchange of products and services between businesses, groups, and individuals; and can be seen as one of the essential activities of any business. E-commerce focuses on the use of ICT to enable the external activities and relationships of the business with individuals, groups, and other organizations, while e-business does not only deal with online commercial operations of enterprises, but also deals with their other organizational matters such as human resource management and production. The term "e-business" was coined by IBM's marketing and Internet team in 1996. == Market participants == Electronic business can take place between a very large number of market participants; it can be between business and consumer, private individuals, public administrations, or any other organizations such as non-governmental organizations (NGOs). These various market participants can be divided into three main groups: Business (B) Consumer (C) Administration (A) All of them can be either buyers or service providers within the market. There are nine possible combinations for electronic business relationships. B2C and B2B belong to E-commerce, while A2B and A2A belong to the E-government sector which is also a part of the electronic business. == History == One of the founding pillars of electronic business was the development of the Electronic Data Interchange (EDI) electronic data interchange. This system replaced traditional mailing and faxing of documents with a digital transfer of data from one computer to another, without any human intervention. Michael Aldrich is considered the developer of the predecessor to online shopping. In 1979, the entrepreneur connected a television set to a transaction processing computer with a telephone line and called it "teleshopping", meaning shopping at distance. From the mid-nineties, major advancements were made in the commercial use of the Internet. Amazon, which launched in 1995, started as an online bookstore and grew to become nowadays the largest online retailer worldwide, selling food, toys, electronics, apparel and more. Other successful stories of online marketplaces include eBay or Etsy. In 1994, IBM, with its agency Ogilvy & Mather, began to use its foundation in IT solutions and expertise to market itself as a leader of conducting business on the Internet through the term "e-business." Then CEO Louis V. Gerstner, Jr. was prepared to invest $1 billion to market this new brand. After conducting worldwide market research in October 1997, IBM began with an eight-page piece in The Wall Street Journal that would introduce the concept of "e-business" and advertise IBM's expertise in the new field. IBM decided not to trademark the term "e-business" in the hopes that other companies would use the term and create an entirely new industry. However, this proved to be too successful and by 2000, to differentiate itself, IBM launched a $300 million campaign about its "e-business infrastructure" capabilities. Since that time, the terms, "e-business" and "e-commerce" have been loosely interchangeable and have become a part of the common vernacular. According to the U.S. Department Of Commerce, the estimated retail e-commerce sales in Q1 2020 were representing almost 12% of total U.S. retail sales, against 4% for Q1 2010. == Business model == The transformation toward e-business is complex and in order for it to succeed, there is a need to balance between strategy, an adapted business model (e-intermediary, marketplaces), right processes (sales, marketing) and technology (Supply Chain Management, Customer Relationship Management). When organizations go online, they have to decide which e-business models best suit their goals. A business model is defined as the organization of product, service and information flows, and the source of revenues and benefits for suppliers and customers. The concept of the e-business model is the same but used in online presence. === Revenue model === A key component of the business model is the revenue model or profit model, which is a framework for generating revenues. It identifies which revenue source to pursue, what value to offer, how to price the value, and who pays for the value. It is a key component of a company's business model. It primarily identifies what product or service will be created in order to generate revenues and the ways in which the product or service will be sold. Without a well-defined revenue model, that is, a clear plan of how to generate revenues, new businesses will more likely struggle due to costs that they will not be able to sustain. By having a revenue model, a business can focus on a target audience, fund development plans for a product or service, establish marketing plans, begin a line of credit and raise capital. ==== E-commerce ==== E-commerce (short for "electronic commerce") is trading in products or services using computer networks, such as the Internet. Electronic commerce draws on technologies such as mobile commerce, electronic funds transfer, supply chain management, Internet marketing, online transaction processing, electronic data interchange (EDI), inventory management systems, and automated data collection. Modern electronic commerce typically uses the World Wide Web for at least one part of the transaction's life cycle, although it may also use other technologies such as e-mail. == Concerns == While much has been written of the economic advantages of Internet-enabled commerce, there is also evidence that some aspects of the internet such as maps and location-aware services may serve to reinforce economic inequality and the digital divide. Electronic commerce may be responsible for consolidation and the decline of mom-and-pop, brick and mortar businesses resulting in increases in income inequality. === Security === E-business systems naturally have greater security risks than traditional business systems, therefore it is important for e-business systems to be fully protected against these risks. A far greater number of people have access to e-businesses through the internet than would have access to a traditional business. Customers, suppliers, employees, and numerous other people use any particular e-business system daily and expect their confidential information to stay secure. Hackers are one of the great threats to the security of e-businesses. Some common security concerns for e-Businesses include keeping business and customer information private and confidential, the authenticity of data, and data integrity. Some of the methods of protecting e-business security and keeping information secure include physical security measures as well as data storage, data transmission, anti-virus software, firewalls, and encryption to list a few. ==== Privacy and confidentiality ==== Confidentiality is the extent to which businesses makes personal information available to other businesses and individuals. With any business, confidential information must remain secure and only be accessible to the intended recipient. However, this becomes even more difficult when dealing with e-businesses specifically. To keep such information secure means protecting any electronic records and files from unauthorized access, as well as ensuring safe transmission and data storage of such information. Tools such as encryption and firewalls manage this specific concern within e-business. ==== Authenticity ==== E-business transactions pose greater challenges for establishing authenticity due to the ease with which electronic information may be altered and copied. Both parties in an e-business transaction want to have the assurance that the other party is who they claim to be, especially when a customer places an order and then submits a payment electronically. One common way to ensure this is to limit access to a network or trusted parties by using a virtual private network (VPN) technology. The establishment of authenticity is even greater when a combination of techniques are used, and such techniques involve checking "something you know" (i.e. password or PIN), "something you need" (i.e. credit card), or "something you are" (i.e. digital signatures or voice recognition methods). Many times in e-business, however, "something you are" is pretty strongly verified by checking the purchaser's "something you have" (i.e. credit card) and "something you know" (i.e. card number). ==== Data integrity ==== Data integrity answers the question "Can the information be changed or corrupted in any way?" This leads to the assurance that the message received is identical to the message sent. A business needs to be confident that data is not changed in transit, whether deliberately or by accident. To help with data integrity, firewalls protect stored data against unauthorized access, while
Webull
Webull Corporation, often stylized as simply Webull, is a U.S.-based financial services holding company headquartered in St. Petersburg, Florida. It owns and operates the Webull electronic trading platform for self-directed retail investors. Depending on jurisdiction, the Webull platform offers trading in stocks, exchange-traded funds (ETFs), options, margin, bonds, cryptocurrency and futures, as well as market-data tools. Webull began operations in 2016 under Hunan Fumi Information Technology, a China-based financial technology company founded by Wang Anquan. It launched U.S. brokerage services through Webull Financial LLC in 2018 and expanded during the retail-trading boom of 2020 and 2021. In April 2025, Webull became a publicly traded company on the Nasdaq through a merger with special-purpose acquisition company SK Growth Opportunities Corporation. The company's U.S. brokerage revenue relies substantially on payment for order flow, with options trading accounting for the larger share of its order-flow rebates in 2025. Webull has faced regulatory actions related to options customer approvals, complaint handling, suspicious activity reporting, social-media marketing and customer disclosures. It has also faced scrutiny from U.S. lawmakers and state officials over its historical and operational ties to China and the handling of U.S. customer data. == History == === Founding === Webull was founded in 2016 under Hunan Fumi Information Technology, a China-based financial technology company, by Wang Anquan, a former employee of Alibaba Group and Xiaomi. Hunan Fumi Information Technology received backing from Xiaomi, Shunwei Capital, and other investors in China. Fumi Technology was a Hunan-based fintech start-up incubated by Xiaomi and raised about CNY200 million (approximately US$30 million) in a Series B financing round in 2018. On May 24, 2017, Webull Financial LLC was established as a Delaware limited liability company. It began offering brokerage services in the United States in May 2018. Wang hired Anthony Denier as CEO of the U.S. brokerage that year and the two mapped out their strategy on napkins at a Mexican restaurant in New York City. Webull Corporation was incorporated in the Cayman Islands in September 2019 as the group's holding company. === Retail trading boom === In May 2020, the company received SEC approval to launch a robo-advisor on its platform. By August 2020, the platform had over 11 million registered users, and in October 2020, it had 750,000 daily active users. Webull introduced options trading in 2020 and later added cryptocurrency trading through a separate digital-asset business. In November 2020, Webull began supporting cryptocurrency transactions. In December 2020, Webull launched trading services in Hong Kong. During the GameStop short squeeze in January 2021, Webull gained attention as some retail traders looked for alternatives to Robinhood. On January 27, 2021, Webull recorded its highest-ever number of active daily users, at 952,000, and the Webull app was downloaded across the Apple App and Google Play stores an estimated 100,000 times. That week, approximately 1.2 million people downloaded the Webull mobile app, which the company reported as a 1,548% week-over-week increase. On January 28, 2021, Webull was directed by its clearing house to temporarily halt buy orders for stocks affected by the GameStop short squeeze. In June 2021, Webull was reported to be considering a U.S. initial public offering that could raise up to $400 million. === Restructuring and expansion === Webull restructured its China-related corporate arrangements in 2022 and later stated that Hunan Fumi was no longer affiliated with the group. In 2022 and 2023, Webull expanded in several non-U.S. markets, including Singapore, Australia, South Africa, Japan, the United Kingdom and Indonesia. In June 2023, Webull moved cryptocurrency trading to a separate app called Webull Pay. By the end of 2023, Webull had 4.3 million funded accounts and US$8.2 billion in customer assets. In January 2024, Anthony Denier was promoted to group president of Webull Corporation. In November 2024, Webull launched overnight, or extended-hours, trading, expanding the trading window of U.S. stocks for users inside and outside the United States. === SPAC merger and Nasdaq listing === On February 28, 2024, Webull agreed to go public through a business combination with SK Growth Opportunities Corporation (NASDAQ: SKGR), a special-purpose acquisition company, in a deal that valued the company at approximately US$7.3 billion. The proposed valuation drew scrutiny because of Webull's limited financial disclosure at announcement, reliance on payment for order flow and small expected public float. SK Growth shareholders approved the business combination on March 30, 2025, and the transaction closed on April 10, 2025. Webull's Class A ordinary shares and warrants began trading on the Nasdaq on April 11, 2025 under the ticker symbols BULL and BULLW (incentive warrants traded under BULLZ until their redemption in June 2025). The merger brought Webull to the public market but generated little cash for the company: after shareholder redemptions, Webull disclosed net proceeds of US$430,066 from the transaction. After the listing, Webull's shares experienced extreme volatility, rising as much as 500% to US$79.56 on April 14, 2025, after closing at US$13.25 on the prior trading day. The initial post-listing surge increased the value of Webull holdings owned by earlier investors, including RIT Capital Partners, which had first invested in Webull in 2021. In April 2026, after Webull's shares had fallen about 70% over the previous year, the company authorized a US$100 million share repurchase program. == Business model and financials == Webull provides a self-directed electronic trading platform available through mobile, desktop and web applications. Depending on jurisdiction, the platform offers trading in stocks, exchange-traded funds, options, margin, futures, fixed income products, cryptocurrency, cash management features and market data tools. In the United States, Webull Financial LLC is a registered broker-dealer and member of FINRA and the Securities Investor Protection Corporation, while Webull operates in other markets through locally licensed brokerage subsidiaries. Webull operates a commission-free or low-cost brokerage model for self-directed retail investors. In the United States, a substantial part of its trading-related revenue comes from payment for order flow, while in some non-U.S. markets the company more commonly charges commissions directly to customers. The platform is aimed at more active retail investors, including users seeking options tools, extended-hours trading and real-time market data. For 2025, Webull reported total revenue of US$571.0 million, up from US$390.2 million in 2024. Equity and option order-flow rebates accounted for US$304.1 million, or 53.3% of revenue, making order-flow rebates the company's largest reported revenue category. Interest-related income accounted for US$154.3 million, handling charge income for US$87.3 million and other revenue for US$25.3 million. Options were the larger component of the company's order-flow rebates in 2025, generating US$210.0 million compared with US$94.2 million from equities. Webull also generates revenue from interest-related activities, including margin financing, customer bank deposits, stock lending and corporate bank deposits. The company has stated that its interest-related income is affected by interest rates, customer cash balances, margin balances and demand for stock lending. The company had approximately 20 million registered users worldwide as of February 2024. As of December 31, 2025, it reported 26.8 million registered users, 5.0 million funded accounts and US$24.6 billion in customer assets. As of March 2025, Webull operated in Hong Kong, Singapore, Australia, South Africa, Japan, the United Kingdom, the United States, Indonesia, Canada, Brazil, Thailand, Malaysia and Mexico. == Marketing and sponsorships == Webull has used paid digital advertising, referral incentives, free-stock promotions, affiliate marketing and sports sponsorships to acquire customers and promote its brand. In its 2025 annual filing, the company reported marketing and branding expenses of US$152.3 million in 2023, US$138.7 million in 2024 and US$135.9 million in 2025. Webull said most of its advertising and promotion costs were related to paid search and paid social advertising, and that it had reduced free-stock promotions while shifting toward deposit- and asset-transfer-based incentives. In September 2021, BSE Global, the parent company of the Brooklyn Nets and New York Liberty, entered into a global multi-year agreement with Webull. Under the agreement, Webull became an official sponsor and online brokerage partner of the teams, with branding that included a jersey patch on Brooklyn Nets uniforms. Spo
Social news website
A social news website is a website that features user-posted stories. Such stories are ranked based on popularity, as voted on by other users of the site or by website administrators. Users typically comment online on the news posts and these comments may also be ranked in popularity. Since their emergence with the birth of Web 2.0, social news sites have been used to link many types of information, including news, humor, support, and discussion. All such websites allow the users to submit content and each site differs in how the content is moderated. On the Slashdot and Fark websites, administrators decide which articles are selected for the front page. On Reddit and Digg, the articles that get the most votes from the community of users will make it to the front page. Many social news websites also feature an online comment system, where users discuss the issues raised in an article. Some of these sites have also applied their voting system to the comments, so that the most popular comments are displayed first. Some social news websites also have a social networking service, in that users can set up a user profile and follow other users' online activity on the website. Like many other Web 2.0 tools, social news websites use the collective intelligence of all of the users to operate. Social news websites also "impl[y] the technical, economic, legal, and human enhancement of a universally distributed intelligence that will unleash a positive dynamic of recognition and skills mobilization". Social news websites help participants to share a collective vision and awareness of how their actions are integrated with those of other individuals. Social news websites provide a new and innovative way to participate in a community that is constantly being flooded with new information. These social news websites "include opportunities for peer-to-peer learning, a changed attitude toward intellectual property, the diversification of cultural expression, the development of skills valued in the modern workplace, and a more empowered conception of citizenship". These websites can help to shape and reshape democratic opinions and perspectives. Social news sites may mitigate the gatekeeping of mainstream news sources and allow the public to decide what counts as "news", which may facilitate a more participatory culture. Social news sites may also support democratic participation by allowing users from across geographic and national boundaries to access the same information, respond to fellow users' views and beliefs, and create a virtual sphere for users to contribute within. == Websites == === Active === ==== Fark ==== Fark, which started in 1997, features news on any topic. On Fark, users can submit articles to the administrators of the site. Each day, these administrators pick out 50 articles to display on the front page. ==== Slashdot ==== Slashdot, started in 1997, was one of the first social news websites. It focuses mainly on science and technology-related news. Users can submit stories and the editors pick out the best stories each day for the front page. Users can then post comments on the stories. The influx of web traffic that resulted from Slashdot linking to external websites led to the effect being called the Slashdot effect ==== Digg ==== Digg, started in December 2004, introduced the voting system. This system allows users to "digg" or "bury" articles. "Digging" is the equivalent of voting positively, so that popular articles are displayed first. "Burying" does not lower an article's score. However, if an article is buried enough times, it will be automatically deleted from the site. Digg offers a social networking service, as members can follow other members and build personal profiles with information about their interests. ==== Reddit ==== Reddit, started in June 2005, is a social news website where users can submit articles and comments and vote on these submissions. The submissions are organized into categories called "subreddits". Unlike Digg, with Reddit, users can directly affect an article's score. An "upvote" will increase the score and a "downvote" will decrease it. Articles with the highest scores are displayed on the front page. There is also a page for "controversial" articles, that have an almost equal number of upvotes and downvotes. Free speech debates have arisen due to the shutting down of obscene or potentially illegal "subreddits" (including /r/jailbait, a collection of sexually suggestive underage pictures.) Reddit introduced a system of user-created communities called "subreddits", which are essentially categories for a specific type of news. Comments on the featured posts are shown in a hierarchical fashion also based on votes. Users have the ability to earn "karma" for their participation and time on the website. ==== Hacker News ==== Hacker News, started in February 2007, is a social news site focusing on computer science and entrepreneurship, created by Paul Graham and run by his startup incubator, Y Combinator. === Defunct === ==== Newsvine ==== Newsvine, started in March 2006, was a social news website mostly focused on politics, both international and domestic. The Newsvine home page allowed users to customize "seeds" and story feeds. Users received articles via "The Wire" from sources including The Associated Press or The Huffington Post, and from "The Vine" a stream of content from other Newsvine users. The "Top of the Vine" displayed the most voted and commented on articles of the day, week, month, or year. Additionally, Newsvine allowed members to create their own "Customizable Column", which could highlight a user's content posted, recent comments, and information about the specific Newsvine member. ==== feedalizr ==== feedalizr was a cross-platform, desktop social media aggregator built using Adobe Integrated Runtime that consolidates the updates from social media and social networking websites. Users can then use this application to update those sites from their desktop and view a consolidated stream of information. ==== Voat ==== Voat, launched in April 2014 and discontinued in December of 2020, was also a social news website and is very similar to Reddit visually and functionally. The site's userbase included a large number of alt right users, many of whom migrated to Voat after being banned on Reddit. ==== Prismatic ==== Prismatic combined machine learning, user experience design, and interaction design to create a new way to discover, consume, and share media. Prismatic software used social network aggregation and machine learning algorithms to filter the content that aligns with the interests of a specific user. Prismatic integrated with Facebook, Twitter, and Pocket to gather information about user's interests and suggest the most relevant stories to read. ==== Artifact ==== Artifact was an iOS and Android app that used machine learning to personalize news recommendations to readers, and also had social features such as liking articles, commenting, and reputation scores for users.
Visual networking
Visual networking refers to an emerging class of user applications that combine digital video and social networking capabilities. It is based upon the premise that visual literacy, "the ability to interpret, negotiate and make meaning from information presented in the form of a moving image", is a powerful force in how humans communicate, entertain and learn. The duality of visual networking—subsuming entertainment and communications, professional and personal content, video and other digital media, data networks and social networks to create immersive experiences, when, where and how the user wants it. These applications have changed video content from long-form movies and broadcast television programming to a database of segments or "clips", and social network annotations. And the generation and distribution of content takes on a new dimension with Web 2.0 applications—participatory social-networks or communities that facilitate interactive creativity, collaboration and sharing between users. == History == The rise of visual networking is relatively recent phenomenon driven by the emergence of social networking capabilities and the ability to deliver interactive video over a broadband network. It is a natural evolution of the current social networking phenomena whereby social networking annotations are layered over broadband video to create highly interactive and immersive experiences between individuals and their content. Until early 2005 this was not considered viable due to the lack of web and broadband infrastructure designed to support the transmission of web video and the still nascent stage of social networks like MySpace and Facebook. The introduction of YouTube in February 2005 marked the first significant combination of broadband video and social network systems designed to allow users to share, rate and tag user generated and premium content. From 2006 to 2008 this trend continued to gain steam as individuals and businesses pursued new combinations of video and social networking across a wide range of entertainment, communication and learning applications. == Broadband video takes off == Video has largely been defined by its use as an entertainment medium. Since the commercial availability of the television in the late '30s video has become the dominant entertainment medium far eclipsing audio and text based entertainment both in terms of time and dollars spent. Within the past decade, video use has rapidly evolved across a broader range of devices, multiple locations and user applications. The popularization of the long-tail and user-generated video has further challenged people's ideas of what's possible with video. A key advantage of video relative to other media is its superior ability to communicate ideas and emotions economically. If a picture is worth a thousand words, then a video may be worth a thousand pictures. Video by its very nature is highly experiential, making communications more compelling, informative and memorable. == Social networking meets video == At the core of visual networking is the concept that people can participate in communities of content and communities of interest. A community of interest is defined as a community of people who share a common interest or passion. These people exchange ideas and thoughts about the given passion, but may know (or care) little about each other outside of this area. Participation in a community of interest can be compelling, entertaining and create a ‘sticky’ community where people return frequently and remain for extended periods. The unparalleled potential of the Internet to promote such connections is only now being fully recognized and exploited, through Web-based groups established for that purpose. Based on the six degrees of separation concept (the idea that any two people on the planet could make contact through a chain of no more than five intermediaries), social networking establishes interconnected Internet communities (sometimes known as personal networks) that help people make contacts that would be good for them to know, but that they would be unlikely to have met otherwise. == Transition from search to discovery == The phrase The Long Tail was, according to Chris Anderson, first coined by himself in October 2004. Anderson argued that products that are in low demand or have low sales volume can collectively make up a market share that rivals or exceeds the relatively few current bestsellers and blockbusters, if the store or distribution channel is large enough. The Long Tail also has implications for the producers of content; especially those whose products could not—for economic reasons—find a place in pre-Internet information distribution channels controlled by book publishers, record companies, movie studios, and television networks. Looked at from the producers' side, the Long Tail has made possible a flowering of creativity across all fields of human endeavor. One example of this is YouTube, where thousands of diverse videos—whose content, production value or lack of popularity make them inappropriate for traditional television—are easily accessible to a wide range of viewers. The benefit to the consumer is that they know have an almost infinite choice of content to select from able to create their own specific channels based upon their unique needs. A potential negative side effect of the long tail is the rapidly growing inventory of text, audio and video content. The storage and distribution systems of the past restricted the number of songs, video, and books making it easier to search for what was relevant to the individual. As the long-tail has grown, more and more relevant and irrelevant content passes an individual by without their knowledge. This is especially true for video because unlike text-based files which can searched and indexed for easy finding, video typically has only its title as a clue to what's in it. This lack of comprehensive meta-data has limited the applicability of traditional search models. Augmenting traditional search has been the emergence of content based discovery tools that make people aware of relevant content based upon their participation in communities of interest and/or communities of content. The idea is that users may or may not start out searching for something, but they soon begin reacting to things they find, exploring links on pages they stumble upon and taking cues from fellow surfers about where to go. Instead of the old, passive, lean-back style of watching video, viewers are actively seeking content through discovery. People interact with each other, posting comments on what they just saw. Many sites now allow people to vote on videos, ranking and rating them. Ranking is the result of one of a number of algorithms that measure how many people have watched something or how many sites link to it. == Early examples == YouTube is the best early example of a visual networking experience. YouTube is a video sharing website where users can upload, view and share video clips. Unregistered users can watch most videos on the site, while registered users are permitted to upload an unlimited number of videos. Few statistics are publicly available regarding the number of videos on YouTube. However, in July 2006, the company revealed that more than 100 million videos were being watched every day, and 2.5 billion videos were watched in June 2006. 50,000 videos were being added per day in May 2006, and this increased to 65,000 by July. In January 2008 alone, nearly 79 million users watched over 3 billion videos on YouTube. Telepresence refers to a set of technologies which allow a person to feel as if they were present, to give the appearance that they were present, or to have an effect, at a location other than their true location. Telepresence requires that the senses of the user, or users, are provided with such stimuli as to give the feeling of being in that other location. Additionally, the user(s) may be given the ability to affect the remote location. In this case, the user's position, movements, actions, voice, etc. may be sensed, transmitted and duplicated in the remote location to bring about this effect. Therefore, information may be traveling in both directions between the user and the remote location. Critical the creating an in-person experience is the presence of high-definition video perfectly synchronized with stereophonic sound. A minimum system usually includes visual feedback. Ideally, the entire field of view of the user is filled with a view of the remote location, and the viewpoint corresponds to the movement and orientation of the user's head. In this way, it differs from television or cinema, where the viewpoint is out of the control of the viewer. == Other applications == While still in its infancy, visual networking applications are beginning to emerge that span both consumer and business markets. === Mobile video === Proliferation of multi-function mobile devices, particularl
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.
Fabric computing
Fabric computing or unified computing involves constructing a computing fabric consisting of interconnected nodes that look like a weave or a fabric when seen collectively from a distance. Usually the phrase refers to a consolidated high-performance computing system consisting of loosely coupled storage, networking and parallel processing functions linked by high bandwidth interconnects (such as 10 Gigabit Ethernet and InfiniBand) but the term has also been used to describe platforms such as the Azure Services Platform and grid computing in general (where the common theme is interconnected nodes that appear as a single logical unit). The fundamental components of fabrics are "nodes" (processor(s), memory, and/or peripherals) and "links" (functional connections between nodes). While the term "fabric" has also been used in association with storage area networks and with switched fabric networking, the introduction of compute resources provides a complete "unified" computing system. Other terms used to describe such fabrics include "unified fabric", "data center fabric" and "unified data center fabric". Ian Foster, director of the Computation Institute at the Argonne National Laboratory and University of Chicago suggested in 2007 that grid computing "fabrics" were "poised to become the underpinning for next-generation enterprise IT architectures and be used by a much greater part of many organizations". == History == While the term has been in use since the mid to late 1990s the growth of cloud computing and Cisco's evangelism of unified data center fabrics followed by unified computing (an evolutionary data center architecture whereby blade servers are integrated or unified with supporting network and storage infrastructure) starting March 2009 has renewed interest in the technology. There have been mixed reactions to Cisco's architecture, particularly from rivals who claim that these proprietary systems will lock out other vendors. Analysts claim that this "ambitious new direction" is "a big risk" as companies such as IBM and HP who have previously partnered with Cisco on data center projects (accounting for $2–3bn of Cisco's annual revenue) are now competing with them. In 2007, Wombat Financial Software launched the "Wombat Data Fabric," the first commercial off-the-shelf software platform providing high performance / low-latency RDMA-based messaging across an Infiniband switch. == Key characteristics == The main advantages of fabrics are that massive concurrent processing combined with a huge, tightly coupled address space makes it possible to solve huge computing problems (such as those presented by delivery of cloud computing services); and that they are both scalable and able to be dynamically reconfigured. Challenges include a non-linearly degrading performance curve, whereby adding resources does not linearly increase performance which is a common problem with parallel computing and maintaining security. == Companies == As of 2015 companies offering unified or fabric computing systems include Avaya, Brocade, Cisco, Dell, Egenera, HPE, IBM, Liquid Computing Corporation, TIBCO, Unisys, and Xsigo Systems.
Cryptochannel
In telecommunications, a cryptochannel is a complete system of crypto-communications between two or more holders or parties. It includes: (a) the cryptographic aids prescribed; (b) the holders thereof; (c) the indicators or other means of identification; (d) the area or areas in which effective; (e) the special purpose, if any, for which provided; and (f) pertinent notes as to distribution, usage, etc. A cryptochannel is analogous to a radio circuit.