AI Chat To Pdf

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Sayre's paradox

Sayre's paradox is a dilemma encountered in the design of automated handwriting recognition systems. A standard statement of the paradox is that a cursively written word cannot be recognized without being segmented and cannot be segmented without being recognized. The paradox was first articulated in a 1973 publication by Kenneth M. Sayre, after whom it was named. == Nature of the problem == It is relatively easy to design automated systems capable of recognizing words inscribed in a printed format. Such words are segmented into letters by the very act of writing them on the page. Given templates matching typical letter shapes in a given language, individual letters can be identified with a high degree of probability. In cases of ambiguity, probable letter sequences can be compared with a selection of properly spelled words in that language (called a lexicon). If necessary, syntactic features of the language can be applied to render a generally accurate identification of the words in question. Printed-character recognition systems of this sort are commonly used in processing standardized government forms, in sorting mail by zip code, and so forth. In cursive writing, however, letters comprising a given word typically flow sequentially without gaps between them. Unlike a sequence of printed letters, cursively connected letters are not segmented in advance. Here is where Sayre's Paradox comes into play. Unless the word is already segmented into letters, template-matching techniques like those described above cannot be applied. That is, segmentation is a prerequisite for word recognition. But there are no reliable techniques for segmenting a word into letters unless the word itself has been identified. Word recognition requires letter segmentation, and letter segmentation requires word recognition. There is no way a cursive writing recognition system employing standard template-matching techniques can do both simultaneously. Advantages to be gained by use of automated cursive writing recognition systems include routing mail with handwritten addresses, reading handwritten bank checks, and automated digitalization of hand-written documents. These are practical incentives for finding ways of circumventing Sayre's Paradox. == Avoiding the paradox == One way of ameliorating the adverse effects of the paradox is to normalize the word inscriptions to be recognized. Normalization amounts to eliminating idiosyncrasies in the penmanship of the writer, such as unusual slope of the letters and unusual slant of the cursive line. This procedure can increase the probability of a correct match with a letter template, resulting in an incremental improvement in the success rate of the system. Since improvement of this sort still depends on accurate segmentation, however, it remains subject to the limitations of Sayre's Paradox. Researchers have come to realize that the only way to circumvent the paradox is by use of procedures that do not rely on accurate segmentation. == Directions of current research == Segmentation is accurate to the extent that it matches distinctions among letters in the actual inscriptions presented to the system for recognition (the input data). This is sometimes referred to as “explicit segmentation”. “Implicit segmentation,” by contrast, is division of the cursive line into more parts than the number of actual letters in the cursive line itself. Processing these “implicit parts” to achieve eventual word identification requires specific statistical procedures involving hidden Markov models (HMM). A Markov model is a statistical representation of a random process, which is to say a process in which future states are independent of states occurring before the present. In such a process, a given state is dependent only on the conditional probability of its following the state immediately before it. An example is a series of outcomes from successive casts of a die. An HMM is a Markov model, individual states of which are not fully known. Conditional probabilities between states are still determinate, but the identities of individual states are not fully disclosed. Recognition proceeds by matching HMMs of words to be recognized with previously prepared HMMs of words in the lexicon. The best match in a given case is taken to indicate the identity of the handwritten word in question. As with systems based on explicit segmentation, automated recognition systems based on implicit segmentation are judged more or less successful according to the percentage of correct identifications they accomplish. Instead of explicit segmentation techniques, most automated handwriting recognition systems today employ implicit segmentation in conjunction with HMM-based matching procedures. The constraints epitomized by Sayre's Paradox are largely responsible for this shift in approach.
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Opinion Space

Developed at UC Berkeley, "Opinion Space" (also known as The Collective Discovery Engine) is a social media technology designed to help communities generate and exchange ideas about important issues and policies. Version 1.0 was launched on April 4, 2009, at UC Berkeley, and explored the question "Do you think legalizing marijuana is a good idea?" It has since undergone 4 different iterations, and been used in partnership with various organizations including The Occupy movement (Version 4.0, 5/24/2013) and the African Robots Network (Version 4.0, 5/25/2013). Opinion Space has also been used in collaboration with the United States State Department and the University of California's Berkeley Center for New Media (Version 2.0, 12/1/2009 and Version 3.0, 2/25/2012) to gain public perspective on foreign policy issues. Then U.S. Secretary of State Hillary Rodham Clinton explained, "Opinion Space will harness the power of connection technologies to provide a unique forum for international dialogue. This is...an opportunity to extend our engagement beyond the halls of government directly to the people of the world" (2010). The website uses data visualization and statistical analysis to present and develop public opinion and ideas. Opinion Space is a self-organizing system that uses an intuitive graphical "map" that displays patterns, trends, and insights as they emerge and employs the wisdom of crowds to identify and highlight the most insightful ideas. The system uses a game model that incorporates techniques from deliberative polling, collaborative filtering, and multidimensional visualization.
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Social media use in education

Social media in education is the use of social media to enhance education. Social media are "a group of Internet-based applications...that allow the creation and exchange of user-generated content". It is also known as the read/write web. As time went on and technology evolved, social media has been an integral part of people's lives, including students, scholars, and teachers. However, social media are controversial because, in addition to providing new means of connection, critics claim that they damage self-esteem, shorten attention spans, and increase mental health issues. A 2016 dissertation presented surveys that focused on the impact of social media. It reported that 54.6% of students believed that social media affected their studies positively (38% agree, 16.6% strongly agree). About 40% disagreed, and 4.7% of students strongly disagreed. 53% of female students reported that social media negatively impacted their studies. Among male students, 40% agreed that social media had a negative impact on studies, while 59% disagreed. A 2023 article dives deep into the rewards system of the brain in response to social media. This study compares the social rewards system in our brain to those from social media. From ages 10-12, most are receiving a cell phone, social rewards in the brain start to feel more satisfying. Leading to adulthood, the effects of social rewards are less likely to feel reliant on feedback from peers. Equivalent to a more mature prefrontal cortex, this enables a better management of their emotional reaction to these social rewards, meaning a more balanced and controlled reaction. == History == A survey from Cambridge International of nearly 20,000 teachers and students (ages 12–19) from 100 countries found that 48% of students use a desktop computer in class, 42% uses phones, 33% use interactive whiteboards and 20% use tablets. Desktop computers are more used than tablets. Teachers were abandoning the "no phones at school" rule. A 2024 research survey through Common Sense Education reported 54% of age 8-12 and 69% of ages 13-18 social media is an extensive distraction from homework. === United States === The long-running technology boom accelerated after the millennium. As of 2018, 95% of US teenage students had access to a smartphone and 45% said they were online almost constantly. In the early days of social media, access to technology was a significant issue as many students did not own not compatible devices and school budgets were often insufficient to purchase devices for student use. Despite backlash, Missouri passed a law that prohibited teachers from communicating privately with students over social media in 2011. Supporters were concerned that online communication between underage students and faculty could lead to inappropriate relationships. Some schools adopted a "Bring Your Own Device" (BYOD) policy, allowing students to bring Internet-accessing devices, such as phones or tablets to class. During the pandemic, the federal government offered funds that allowed more schools to purchase devices. Over time, more students acquired phones with social media access. Personal devices increased student satisfaction, but reduced teachers' ability to control device use in their classrooms. A 2018 Pew Research study reported that 95% of teenagers had a phone and used social media consistently. === Canada === The Peel District School Board (PDSB) in Ontario accepted the use of social media in the classroom. In 2013, the PDSB introduced BYOD and unblocked many social media sites. That was later replaced by a policy that dealt specifically with social media. == Uses == === Classroom === In the classroom, social media offers a way to systematically distribute and gather information from students. Teachers can supply documents, and audio/video media to students for immediate or later use. One study on higher education reported that devices and social media: created opportunities for interaction provided occasions for collaboration sped up information access offered more ways to learn situated learning. Frustrations included anti-technology instructors, device challenges, and devices as a distraction. Social media in classrooms can have a negative effect. A Yale University publication reported that students who used laptops in class for non-academic reasons had poorer performance. Students spent most of their time on social media, shopping, and other personal activities. Social media has helped many educators mentor their students more effectively. === Outside of class === Social media offer a venue for video calls, stories, feeds, and game playing that can enhance the learning process. Teachers can utilize social media to communicate with their students. Social media can provide students with resources that they can utilize in essays, projects, and presentations. Students can easily access comments made by teachers and peers and offer feedback to teachers. Social media can offer students the opportunity to collaborate by sharing information without requiring face to face meetings. Social media can allow students to more easily connect with experts, to go beyond course materials. Instructors in a 2010 study reported that online technologies (social media) can help students become comfortable having discussions outside the classroom better than traditional means. Teachers may face some risk when using social media outside the classroom, without appropriate work rules. Studies explores how college students' engagement with social media platforms influences their communication preferences and habits, particularly in relation to using school email for academic purposes. === Professional development === Social media can aid professional development, as teachers become students, enhancing knowledge transfer, skill master, and collaboration. === Non-academic uses === Schools can use social media to make public announcements. Teachers and administrators can communicate other important information to parents and students and to receive feedback from them. Families can keep up with school events and policies. === Ecology education === The potential of using social media in ecological, nature and forest education include: virtual nature groups can help promote good habits in forest tourism and recreation (nature ethics), by entering general rules in the regulations by administrators, e.g. "DO NOT PICK UP PLANTS UNKNOWN TO US", which is to protects rare species from pointless picking. social media activity motivates people to learn about nature in the field, allows them to gain knowledge, dispels popular myths, enables contact with scientists and practitioners, promotes valuable literature, websites, and at the same time reveals distortions and substantive errors in popular news services. contact is not only virtual. Despite financial barriers and distance, Internet users organize nature conventions. Such meetings are an opportunity not only to make friends, but also to learn about nature together and have fun. the possibility of contact between scientists and nature lovers via Facebook has become a source of cooperation in species inventory, e.g. the online campaign of the NATRIX Herpetological Society, which consists not only of collecting reports of observations of the smooth snake by Internet users, but also of drawing attention to the biology and threats to this species. Social media has become a place where ecology education quickly reaches people of different ages and social statuses. The nature groups that have been created, in which nature lovers, biologists, foresters and scientists participate, can have a real impact on the state of knowledge and data collection through citizen science. == Apps and services == Social media can allow students to participate in their field by working with organizations outside the classroom. By offering easier access to peers outside the classroom, students can broaden their perspectives and find support resources. Social media aided learning outside of the classroom through collaboration and innovation. One specific study, "Exploring education-related use of social media," called this "audience connectors". Audience connectors bring students together while studying with WhatsApp and Facebook. This study reported that "60 percent [of students in the study] agreed that technology changes education for the better." While social media can promote a beneficial education platform, downsides exist. Students may become skilled at "lifting material from the internet" rather than enhancing their personal understanding. Another downside is student attention spans decline. A concern raised by the students of this study showed how many use spell-check as a crutch and will see a trend of points taken off when spell-check is not an option. Apps like X allowed teachers to make classroom accounts where students can learn about social media in a controlled context. Teachers can post assignments on th
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Intent-based network

Intent-Based Networking (IBN) is an approach to network management that shifts the focus from manually configuring individual devices to specifying desired outcomes or business objectives, referred to as "intents". == Description == Rather than relying on low-level commands to configure the network, administrators define these high-level intents, and the network dynamically adjusts itself to meet these requirements. IBN simplifies the management of complex networks by ensuring that the network infrastructure aligns with the desired operational goals. For example, an implementer can explicitly state a network purpose with a policy such as "Allow hosts A and B to communicate with X bandwidth capacity" without the need to understand the detailed mechanisms of the underlying devices (e.g. switches), topology or routing configurations. == Architecture == Advances in Natural Language Understanding (NLU) systems, along with neural network-based algorithms like BERT, RoBERTa, GLUE, and ERNIE, have enabled the conversion of user queries into structured representations that can be processed by automated services. This capability is crucial for managing the increasing complexity of network services. Intent-Based Networking (IBN) leverages these advancements to simplify network management by abstracting network services, reducing operational complexity, and lowering costs. A proposed three-layered architecture integrates intent-based automation into network management systems. In the business layer, intents are based on Key Performance Indicators (KPIs) and Service Level Agreements (SLAs), reflecting business objectives. The intent layer evaluates and re-plans actions dynamically, where a Knowledge module abstracts and reasons about intents, while an Agent interfaces with network objects to execute actions. The data layer observes network objects, updates topology information, and interacts with the Knowledge and Agent modules to ensure accurate and timely responses to network changes. At the bottom, the network layer contains the physical infrastructure, transforming network data into a usable format for the intent layer to act upon.
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Pandorabots

Pandorabots, Inc. is an artificial intelligence company that runs a web service for building and deploying chatbots. Pandorabots implements and supports development of the Artificial Intelligence Markup Language and makes portions of its code accessible for free. The Pandorabots Platform is "one of the oldest and largest chatbot hosting services in the world", allowing creation of virtual agents to hold human-like text or voice chats with consumers. The platform is written in Allegro Common LISP. == Use Cases == Common use cases include advertising, virtual assistance, e-learning, entertainment and education. The platform has also been used by academics and universities use the platform for teaching and research.
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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.
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Information Networking Institute

Information Networking Institute (INI) is an academic department within the College of Engineering at Carnegie Mellon University. The institute was established in 1989 as the nation's first research and education center devoted to information networking. The INI also partners with research and outreach entities to extend educational and training programs to a broad audience of people using information networking as part of their daily lives. The INI is the educational partner of Carnegie Mellon CyLab, a university-wide, multidisciplinary research center involving more than 50 faculty and 100 graduate students. == Center of Academic Excellence Designations == Through the work of the INI and CyLab, Carnegie Mellon University has been designated by the National Security Agency and the Department of Homeland Security as a National Center of Academic Excellence in Information Assurance/Cyber Defense Education (CAE-IA/CD) and a National Center of Academic Excellence in Information Assurance/Cyber Defense Research (CAE-R). It has also been designated by the NSA and the U.S. Cyber Command as a National Center of Academic Excellence in Cyber Operations (CAE-Cyber Ops). Through these designations, the INI and CyLab participate in the: Federal CyberCorps Scholarship for Service (SFS) Program - Students pursuing graduate degrees in information security (MSIS or MSISPM) are eligible for scholarships under the SFS program. Information Assurance Scholarship Program (IASP) - Students pursuing graduate degrees in information security and seeking careers with the Department of Defense may be eligible for scholarships under the IASP. Capacity Building Program for Faculty from Historically Black and Hispanic Serving Institutions - The INI and CyLab developed a month-long, in-residence summer program to help build information assurance education and research capacity at colleges and universities designated as Minority Serving Institutions – specifically, Historically Black Colleges and Universities (HBCUs) and Hispanic Serving Institutions (HSIs). This program is supported through a grant from the National Science Foundation. == Faculty and researchers == Faculty involved in teaching and advising in the INI programs are conducting research in all aspects of information networking and information security. Affiliated research centers are: Carnegie Mellon CyLab SEI's CERT Division == Alumni == The INI has graduated over 1,400 alumni who currently occupy positions in a variety of sectors across industry, government and academia.
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Embedded analytics

Embedded analytics enables organisations to integrate analytics capabilities into their own, often software as a service, applications, portals, or websites. This differs from embedded software and web analytics (also commonly known as product analytics). This integration typically provides contextual insights, quickly, easily and conveniently accessible since these insights should be present on the web page right next to the other, operational, parts of the host application. Insights are provided through interactive data visualisations, such as charts, diagrams, filters, gauges, maps and tables often in combination as dashboards embedded within the system. This setup enables easier, in-depth data analysis without the need to switch and log in between multiple applications. Embedded analytics is also known as customer facing analytics. Embedded analytics is the integration of analytic capabilities into a host, typically browser-based, business-to-business, software as a service, application. These analytic capabilities would typically be relevant and contextual to the use-case of the host application. == History == The term "embedded analytics" was first used by Howard Dresner: consultant, author, former Gartner analyst and inventor of the term "business intelligence" said Howard Dresner while he was working for Hyperion Solutions, a company that Oracle bought in 2007. Oracle started then to use the term "embedded analytics" at their press release for Oracle Rapid Planning on 2009 . == Considerations with embedded analytics == When evaluating embedding analytics, consideration would normally be given to integration at various levels, these would likely include: security integration, data integration, application logic integration, business rules integration, and user experience integration. This is in contrast to traditional BI, which expects users to leave their workflow applications to look at data insights in a separate set of tools. This immediacy makes embedded analytics much more intuitive and likely to be valued by users. A December 2016 report from Nucleus Research found that using BI tools, which require toggling between applications, can take up as much as 1–2 hours of an employee's time each week, whereas embedded analytics eliminate the need to toggle between apps.
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Co-occurrence matrix

A co-occurrence matrix or co-occurrence distribution (also referred to as : gray-level co-occurrence matrices GLCMs) is a matrix that is defined over an image to be the distribution of co-occurring pixel values (grayscale values, or colors) at a given offset. It is used as an approach to texture analysis with various applications especially in medical image analysis. == Method == Given a grey-level image I {\displaystyle I} , co-occurrence matrix computes how often pairs of pixels with a specific value and offset occur in the image. The offset, ( Δ x , Δ y ) {\displaystyle (\Delta x,\Delta y)} , is a position operator that can be applied to any pixel in the image (ignoring edge effects): for instance, ( 1 , 2 ) {\displaystyle (1,2)} could indicate "one down, two right". An image with p {\displaystyle p} different pixel values will produce a p × p {\displaystyle p\times p} co-occurrence matrix, for the given offset. The ( i , j ) th {\displaystyle (i,j)^{\text{th}}} value of the co-occurrence matrix gives the number of times in the image that the i th {\displaystyle i^{\text{th}}} and j th {\displaystyle j^{\text{th}}} pixel values occur in the relation given by the offset. For an image with p {\displaystyle p} different pixel values, the p × p {\displaystyle p\times p} co-occurrence matrix C is defined over an n × m {\displaystyle n\times m} image I {\displaystyle I} , parameterized by an offset ( Δ x , Δ y ) {\displaystyle (\Delta x,\Delta y)} , as: C Δ x , Δ y ( i , j ) = ∑ x = 1 n ∑ y = 1 m { 1 , if I ( x , y ) = i and I ( x + Δ x , y + Δ y ) = j 0 , otherwise {\displaystyle C_{\Delta x,\Delta y}(i,j)=\sum _{x=1}^{n}\sum _{y=1}^{m}{\begin{cases}1,&{\text{if }}I(x,y)=i{\text{ and }}I(x+\Delta x,y+\Delta y)=j\\0,&{\text{otherwise}}\end{cases}}} where: i {\displaystyle i} and j {\displaystyle j} are the pixel values; x {\displaystyle x} and y {\displaystyle y} are the spatial positions in the image I; the offsets ( Δ x , Δ y ) {\displaystyle (\Delta x,\Delta y)} define the spatial relation for which this matrix is calculated; and I ( x , y ) {\displaystyle I(x,y)} indicates the pixel value at pixel ( x , y ) {\displaystyle (x,y)} . The 'value' of the image originally referred to the grayscale value of the specified pixel, but could be anything, from a binary on/off value to 32-bit color and beyond. (Note that 32-bit color will yield a 232 × 232 co-occurrence matrix!) Co-occurrence matrices can also be parameterized in terms of a distance, d {\displaystyle d} , and an angle, θ {\displaystyle \theta } , instead of an offset ( Δ x , Δ y ) {\displaystyle (\Delta x,\Delta y)} . Any matrix or pair of matrices can be used to generate a co-occurrence matrix, though their most common application has been in measuring texture in images, so the typical definition, as above, assumes that the matrix is an image. It is also possible to define the matrix across two different images. Such a matrix can then be used for color mapping. == Aliases == Co-occurrence matrices are also referred to as: GLCMs (gray-level co-occurrence matrices) GLCHs (gray-level co-occurrence histograms) spatial dependence matrices == Application to image analysis == Whether considering the intensity or grayscale values of the image or various dimensions of color, the co-occurrence matrix can measure the texture of the image. Because co-occurrence matrices are typically large and sparse, various metrics of the matrix are often taken to get a more useful set of features. Features generated using this technique are usually called Haralick features, after Robert Haralick. Texture analysis is often concerned with detecting aspects of an image that are rotationally invariant. To approximate this, the co-occurrence matrices corresponding to the same relation, but rotated at various regular angles (e.g. 0, 45, 90, and 135 degrees), are often calculated and summed. Texture measures like the co-occurrence matrix, wavelet transforms, and model fitting have found application in medical image analysis in particular. == Other applications == Co-occurrence matrices are also used for words processing in natural language processing (NLP).
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Tumblr

Tumblr ( TUM-blər) is a microblogging and social media platform founded by David Karp in 2007 and operated by American company Tumblr, Inc., a subsidiary of Automattic. The service allows users to post multimedia and other content to a short-form blog. It has attracted significant attention and controversy for hosting a wide range of progressive user-generated content. == History == === Beginnings (2006–2012) === Development of Tumblr began in 2006 during a two-week gap between contracts at David Karp's software consulting company, Davidville. Karp had been interested in tumblelogs (short-form blogs, hence the name Tumblr) for some time and was waiting for one of the established blogging platforms to introduce their own tumblelogging platform. As none had done so after a year of waiting, Karp and developer Marco Arment began working on their own platform. Tumblr was launched in February 2007, and within two weeks had gained 75,000 users. Arment left the company in September 2010 to work on Instapaper. In June 2012, Tumblr featured its first major brand advertising campaign in collaboration with Adidas, who launched an official soccer Tumblr blog and bought ad placements on the user dashboard. This launch came only two months after Tumblr announced it would be moving towards paid advertising on its site. === Ownership by Yahoo! (2013–2018) === On May 20, 2013, it was announced that Yahoo and Tumblr had reached an agreement for Yahoo! Inc. to acquire Tumblr for $1.1 billion in cash. Many of Tumblr's users were unhappy with the news, causing some to start a petition, achieving nearly 170,000 signatures. David Karp remained CEO and the deal was finalized on June 20, 2013. Advertising sales goals were not met and in 2016 Yahoo wrote down $712 million of Tumblr's value. Verizon Communications acquired Yahoo in June 2017, and placed Yahoo and Tumblr under its Oath subsidiary. Karp announced in November 2017 that he would be leaving Tumblr by the end of the year. Jeff D'Onofrio, Tumblr's president and COO, took over leading the company. The site, along with the rest of the Oath division (renamed Verizon Media Group in 2019), continued to struggle under Verizon. In March 2019, Similarweb estimated Tumblr had lost 30% of its user traffic since December 2018, when the site had introduced a stricter content policy with heavier restrictions on adult content (which had been a notable draw to the service). In May 2019, it was reported that Verizon was considering selling the site due to its continued struggles since the purchase (as it had done with another Yahoo property, Flickr, via its sale to SmugMug). Following this news, Pornhub's vice president publicly expressed interest in purchasing Tumblr, with a promise to reinstate the previous adult content policies. === Automattic (2019–present) === On August 12, 2019, Verizon Media announced that it would sell Tumblr to Automattic, the operator of blog service WordPress.com and corporate backer of the open source blog software of the same name. The sale was for an undisclosed amount, but Axios reported that the sale price was less than $3 million, less than 0.3% of Yahoo's original purchase price. Automattic CEO Matt Mullenweg stated that the site will operate as a complementary service to WordPress.com, and that there were no plans to reverse the content policy decisions made during Verizon ownership. In November 2022, Mullenweg stated that Tumblr will add support for the decentralized social networking protocol ActivityPub. In November 2023, most of Tumblr's product development and marketing teams were transferred to other groups within Automattic. Mullenweg stated that focus would shift to core functionality and streamlining existing features. In February 2024, Automattic announced that it would begin selling user data from Tumblr and WordPress.com to Midjourney and OpenAI. Tumblr users are opted-in by default, with an option to opt out. In August 2024, Automattic announced that it would migrate Tumblr's backend to an architecture derived from WordPress, in order to ease development and code sharing between the platforms. The company stated that this migration would not impact the service's user experience and content, and that users "won't even notice a difference from the outside". In January 2025, Mullenweg stated that the migration, once completed, would also "unlock" ActivityPub access for Tumblr, including native support for the company's official ActivityPub plugin for WordPress. In April 2025, Automattic announced layoffs for 16% of its workforce, reducing a large portion of Tumblr staff. On March 16, 2026, Tumblr implemented a change to how notes were assigned to reblogs, making it more similar to sites like Twitter and Bluesky. The change was rolled back the next day after heavy user backlash. == Features == === Blog management === Dashboard: The dashboard is the primary tool for the typical Tumblr user. It is a live feed of recent posts from blogs that they follow. Through the dashboard, users are able to comment, reblog, and like posts from other blogs that appear on their dashboard. The dashboard allows the user to upload text posts, images, videos, quotes, or links to their blog with a click of a button displayed at the top of the dashboard. Users are also able to connect their blogs to their Twitter and Facebook accounts, so that whenever they make a post, it will also be sent as a tweet and a status update. As of June 2022, users can also turn off reblogs on specific posts through the dashboard. Queue: Users are able to set up a schedule to delay posts that they make. They can spread their posts over several hours or even days. Tags: Users can help their audience find posts about certain topics by adding tags. If someone were to upload a picture to their blog and wanted their viewers to find pictures, they would add the tag #picture, and their viewers could use that word to search for posts with the tag #picture. HTML editing: Tumblr allows users to edit their blog's theme using HTML to control the appearance of their blog. Custom themes are able to be shared and used by other users, or sold. Custom domains: Tumblr allows users to use custom domains for their blogs. Users must purchase a domain from Tumblr Domains, an in-house registrar that provides domains that can only be used with Tumblr unless removed from the user's blog and transferred to another registrar. Blogs previously were able to be linked with any domain/subdomain from any registrar, however following the introduction of the Tumblr Domains service, now requires you to purchase a domain directly from Tumblr to be used with a blog. Users who kept their blogs connected to a domain after the introduction got to keep their custom domain, as long as they do not disconnect it from Tumblr or let the domain expire. === Tags === The tagging system on the website operates on a hybrid tagging system, involving both self-tagging (user write their own tags on their posts) and an auto-manual function (the website will recommend popular tags and ones that the user has used before.) Only the first 20 tags added to any post will be indexed by the site. The tags are prefaced by a hashtag and separated by commas, and spaces and special characters are allowed, but only up to 140 characters total per tag. There are two main types used by Tumblr users: descriptive tagging, and opinion or commentary tagging. Descriptive tags are usually introduced by the original poster, and describe what is in the post (e.g. #art, #sky). These are important for the original poster to use, so their post will be indexed and searchable by others wishing to view that subject of content. Tags used as a form of communication are unique to Tumblr, and are typically more personal, expressing opinions, reactions, meta-commentary, background information, and more. Instead of adding onto the reblogged post (with their comments becoming an addition to each subsequent reblog from them) a user may add their comments in the tags, not changing the content or appearance of the original post in any way. Not all users choose to use tags this way, but those who do use tags for commentary may prefer it over adding a comment on the actual post. === Mobile === With Tumblr's 2009 acquisition of Tumblerette, an iOS application created by Jeff Rock and Garrett Ross, the service launched its official iPhone app. The site became available to BlackBerry smartphones on April 17, 2010, via a Mobelux application in BlackBerry World. In June 2012, Tumblr released a new version of its iOS app, Tumblr 3.0, allowing support for Spotify integration, hi-res images and offline access. An app for Android is also available. A Windows Phone app was released on April 23, 2013. An app for Google Glass was released on May 16, 2013. === Inbox and messaging === Tumblr blogs have the option to allow users to submit questions, either as themselves or anonymously, to the blog for a response. Tumblr
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Social media optimization

Social media optimization (SMO) is the use of online platforms to generate income or publicity to increase the awareness of a brand, event, product or service. Types of social media involved include RSS feeds, blogging sites, social bookmarking sites, social news websites, video sharing websites such as YouTube and social networking sites such as Facebook, Instagram, TikTok and X (Twitter). SMO is similar to search engine optimization (SEO) in that the goal is to drive web traffic, and draw attention to a company or creator. SMO's focal point is on gaining organic links to social media content. In contrast, SEO's core is about reaching the top of the search engine hierarchy. In general, social media optimization refers to optimizing a website and its content to encourage more users to use and share links to the website across social media and networking sites. SMO is used to strategically create online content ranging from well-written text to eye-catching digital photos or video clips that encourages and entices people to engage with a website. Users share this content, via its weblink, with social media contacts and friends. Common examples of social media engagement are "liking and commenting on posts, retweeting, embedding, sharing, and promoting content". Social media optimization is also an effective way of implementing online reputation management (ORM), meaning that if someone posts bad reviews of a business, an SMO strategy can ensure that the negative feedback is not the first link to come up in a list of search engine results. In the 2010s, with social media sites overtaking TV as a source for news for young people, news organizations have become increasingly reliant on social media platforms for generating web traffic. Publishers such as The Economist employ large social media teams to optimize their online posts and maximize traffic, while other major publishers now use advanced artificial intelligence (AI) technology to generate higher volumes of web traffic. == Relationship with search engine optimization == Social media optimization is an increasingly important factor in search engine optimization, which is the process of designing a website in a way so that it has as high a ranking as possible on search engines. Search engines are increasingly utilizing the recommendations of users of social networks such as Reddit, Facebook, Tumblr, Twitter, YouTube, LinkedIn, Pinterest and Instagram to rank pages in the search engine result pages. The implication is that when a webpage is shared or "liked" by a user on a social network, it counts as a "vote" for that webpage's quality. Thus, search engines can use such votes accordingly to properly ranked websites in search engine results pages. Furthermore, since it is more difficult to tip the scales or influence the search engines in this way, search engines are putting more stock into social search. This, coupled with increasingly personalized search based on interests and location, has significantly increased the importance of a social media presence in search engine optimization. Due to personalized search results, location-based social media presences on websites such as Yelp, Google Places, Foursquare, and Yahoo! Local have become increasingly important. While social media optimization is related to search engine marketing, it differs in several ways. Primarily, SMO focuses on driving web traffic from sources other than search engines, though improved search engine ranking is also a benefit of successful social media optimization. Further, SMO is helpful to target particular geographic regions in order to target and reach potential customers. This helps in lead generation (finding new customers) and contributes to high conversion rates (i.e., converting previously uninterested individuals into people who are interested in a brand or organization). == Relationship with viral marketing == Social media optimization is in many ways connected to the technique of viral marketing or "viral seeding" where word of mouth is created through the use of networking in social bookmarking, video and photo sharing websites. An effective SMO campaign can harness the power of viral marketing; for example, 80% of activity on Pinterest is generated through "repinning." Furthermore, by following social trends and utilizing alternative social networks, websites can retain existing followers while also attracting new ones. This allows businesses to build an online following and presence, all linking back to the company's website for increased traffic. For example, with an effective social bookmarking campaign, not only can website traffic be increased, but a site's rankings can also be increased. In a similar way, the engagement with blogs creates a similar result by sharing content through the use of RSS in the blogosphere. Social media optimization is considered an integral part of an online reputation management (ORM) or search engine reputation management (SERM) strategy for organizations or individuals who care about their online presence. SMO is one of six key influencers that affect Social Commerce Construct (SCC). Online activities such as consumers' evaluations and advices on products and services constitute part of what creates a Social Commerce Construct (SCC). Social media optimization is not limited to marketing and brand building. Increasingly, smart businesses are integrating social media participation as part of their knowledge management strategy (i.e., product/service development, recruiting, employee engagement and turnover, brand building, customer satisfaction and relations, business development and more). Additionally, social media optimization can be implemented to foster a community of the associated site, allowing for a healthy business-to-consumer (B2C) relationship. == Origins and implementation == According to technologist Danny Sullivan, the term "social media optimization" was first used and described by marketer Rohit Bhargava on his marketing blog in August 2006. In the same post, Bhargava established the five important rules of social media optimization. Bhargava believed that by following his rules, anyone could influence the levels of traffic and engagement on their site, increase popularity, and ensure that it ranks highly in search engine results. An additional 11 SMO rules have since been added to the list by other marketing contributors. The 16 rules of SMO, according to one source, are as follows: Increase your linkability Make tagging and bookmarking easy Reward inbound links Help your content to "travel" via sharing Encourage the mashup, where users are allowed to remix content Be a user resource, even if it doesn't help you (e.g., provide resources and information for users) Reward helpful and valuable users Participate (join the online conversation) Know how to target your audience Create new, quality content ("web scraping" of existing online content is ignored by good search engines) Be "real" in the tone and style of the posts Don't forget your roots; be humble Don't be afraid to experiment, innovate, try new things and "stay fresh" Develop an SMO strategy Choose your SMO tactics wisely Make SMO a key part of your marketing process and develop company best practices Bhargava's initial five rules were more specifically designed to SMO, while the list is now much broader and addresses everything that can be done across different social media platforms. According to author and CEO of TopRank Online Marketing, Lee Odden, a Social Media Strategy is also necessary to ensure optimization. This is a similar concept to Bhargava's list of rules for SMO. The Social Media Strategy may consider: Objectives e.g. creating brand awareness and using social media for external communications. Listening e.g. monitoring conversations relating to customers and business objectives. Audience e.g. finding out who the customers are, what they do, who they are influenced by, and what they frequently talk about. It is important to work out what customers want in exchange for their online engagement and attention. Participation and content e.g. establishing a presence and community online and engaging with users by sharing useful and interesting information. Measurement e.g. keeping a record of likes and comments on posts, and the number of sales to monitor growth and determine which tactics are most useful in optimizing social media. According to Lon Safko and David K. Brake in The Social Media Bible, it is also important to act like a publisher by maintaining an effective organizational strategy, to have an original concept and unique "edge" that differentiates one's approach from competitors, and to experiment with new ideas if things do not work the first time. If a business is blog-based, an effective method of SMO is using widgets that allow users to share content to their personal social media platforms. This will ultimately reach a wider target audience and drive mor
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Media engagement framework

The media engagement framework is a planning framework used by marketing professionals to understand the behavior of social media marketing-based audiences. The construct was introduced in the book, ROI of Social Media. Powell’s background in marketing ROI and Groves' experience and understanding of the applications of social media in business led to a collaboration. Dimos joined as a brand strategist for Litmus Group, a global management consulting firm. The media engagement framework consists of the definitions of personas (Individuals, Consumers and Influencers), referenced by the competitive set or constraint that applies to that persona and the measurement framework that might be applied to those personas. It is referenced at the center of the marketing process diagram, surrounded by the marketing functions of strategy, tactics, metrics and ROI. The marketing process diagram describes how the media engagement framework can apply to any strategic marketing activity but was developed to establish a completely integrated framework describing how both traditional and social media marketing activities can be planned, executed, measured and improved. == Application == The media engagement framework provides a strategic planning construct in which measurements and metrics play a crucial role. Applying the media engagement framework aids in the development and management of an effective online marketing presence leveraging social media to engage a market or audience. By first personifying the audience, the marketer is able to identify the limiting aspect of the engagements possible with that audience segment and then, understand the type of engagement metrics to apply. Each persona makes decisions differently about how he/she acts in the social media universe. A framework metric can be applied for each of these personas: Endorsement funnel for influencers Community engagement funnel for individuals Purchase funnel for consumers Individuals, influencers and consumers make decisions based on alternatives available to them and constraints put on them. To engage with an individual brands must realize they are competing against the time an individual spends on line. If they find something else more engaging, they will engage with that activity. Brands compete against other brands for the purchases of consumers acting in the category. Lastly, influencers have only so many endorsements they can make and therefore brands compete with other endorsers for the endorsement of an influencer. Creating engaging content by keeping target audience in mind like create content that audience find it funny, interesting, and relatable will encourage audience to share it on social networks. Which will be beneficial for you brand, getting more people to know about your business and brand. Contact Digilord to create engaging content for your brand. Use of listening tools (Google Alerts, Twitter Search, SocialMention.com, Veooz.com, Alterian SM2, Radian6, Sysomos, Buzzient etc.) can be employed within the model to help identify the members of the audience segment and to support the formation of other social engagement planning and management tools.
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Normal distributions transform

The normal distributions transform (NDT) is a point cloud registration algorithm introduced by Peter Biber and Wolfgang Straßer in 2003, while working at University of Tübingen. The algorithm registers two point clouds by first associating a piecewise normal distribution to the first point cloud, that gives the probability of sampling a point belonging to the cloud at a given spatial coordinate, and then finding a transform that maps the second point cloud to the first by maximising the likelihood of the second point cloud on such distribution as a function of the transform parameters. Originally introduced for 2D point cloud map matching in simultaneous localization and mapping (SLAM) and relative position tracking, the algorithm was extended to 3D point clouds and has wide applications in computer vision and robotics. NDT is very fast and accurate, making it suitable for application to large scale data, but it is also sensitive to initialisation, requiring a sufficiently accurate initial guess, and for this reason it is typically used in a coarse-to-fine alignment strategy. == Formulation == The NDT function associated to a point cloud is constructed by partitioning the space in regular cells. For each cell, it is possible to define the mean q = 1 n ∑ i x i {\displaystyle \textstyle \mathbf {q} ={\frac {1}{n}}\sum _{i}\mathbf {x_{i}} } and covariance S = 1 n ∑ i ( x i − q ) ( x i − q ) ⊤ {\displaystyle \textstyle \mathbf {S} ={\frac {1}{n}}\sum _{i}\left(\mathbf {x} _{i}-\mathbf {q} \right)\left(\mathbf {x} _{i}-\mathbf {q} \right)^{\top }} of the n {\displaystyle n} points of the cloud x 1 , … , x n {\displaystyle \mathbf {x} _{1},\dots ,\mathbf {x} _{n}} that fall within the cell. The probability density of sampling a point at a given spatial location x {\displaystyle \mathbf {x} } within the cell is then given by the normal distribution e − 1 2 ( x − q ) ⊤ S − 1 ( x − q ) {\displaystyle e^{-{\frac {1}{2}}\left(\mathbf {x} -\mathbf {q} \right)^{\top }\mathbf {S} ^{-1}\left(\mathbf {x} -\mathbf {q} \right)}} . Two point clouds can be mapped by a Euclidean transformation f {\displaystyle f} with rotation matrix R {\displaystyle \mathbf {R} } and translation vector t {\displaystyle \mathbf {t} } f R , t ( x ) = R x + t {\displaystyle f_{\mathbf {R} ,\mathbf {t} }(\mathbf {x} )=\mathbf {R} \mathbf {x} +\mathbf {t} } that maps from the second cloud to the first, parametrised by the rotation angles and translation components. The algorithm registers the two point clouds by optimising the parameters of the transformation that maps the second cloud to the first, with respect to a loss function based on the NDT of the first point cloud, solving the following problem arg ⁡ min R , t { − ∑ i NDT ⁡ ( f R , t ( x i ) ) } {\displaystyle \arg \min _{\mathbf {R} ,\mathbf {t} }\left\{-\sum _{i}\operatorname {NDT} \left(f_{\mathbf {R} ,\mathbf {t} }\left(\mathbf {x_{i}} \right)\right)\right\}} where the loss function represents the negated likelihood, obtained by applying the transformation to all points in the second cloud and summing the value of the NDT at each transformed point f R , t ( x ) {\displaystyle f_{\mathbf {R} ,\mathbf {t} }(\mathbf {x} )} . The loss is piecewise continuous and differentiable, and can be optimised with gradient-based methods (in the original formulation, the authors use Newton's method). In order to reduce the effect of cell discretisation, a technique consists of partitioning the space into multiple overlapping grids, shifted by half cell size along the spatial directions, and computing the likelihood at a given location as the sum of the NDTs induced by each grid.
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Server-Gated Cryptography

Server-Gated Cryptography (SGC), also known as International Step-Up by Netscape, is a defunct mechanism that was used to step up from 40-bit or 56-bit to 128-bit cipher suites with SSL. It was created in response to United States federal legislation on the export of strong cryptography in the 1990s. The legislation had limited encryption to weak algorithms and shorter key lengths in software exported outside of the United States of America. When the legislation added an exception for financial transactions, SGC was created as an extension to SSL with the certificates being restricted to financial organisations. In 1999, this list was expanded to include online merchants, healthcare organizations, and insurance companies. This legislation changed in January 2000, resulting in vendors no longer shipping export-grade browsers and SGC certificates becoming available without restriction. Internet Explorer supported SGC starting with patched versions of Internet Explorer 3. SGC became obsolete when Internet Explorer 5.01 SP1 and Internet Explorer 5.5 started supporting strong encryption without the need for a separate high encryption pack (except on Windows 2000, which needs its own high encryption pack that was included in Service Pack 2 and later). "Export-grade" browsers are unusable on the modern Web due to many servers disabling export cipher suites. Additionally, these browsers are incapable of using SHA-2 family signature hash algorithms like SHA-256. Certification authorities are trying to phase out the new issuance of certificates with the older SHA-1 signature hash algorithm. The continuing use of SGC facilitates the use of obsolete, insecure Web browsers with HTTPS. However, while certificates that use the SHA-1 signature hash algorithm remain available, some certificate authorities continue to issue SGC certificates (often charging a premium for them) although they are obsolete. The reason certificate authorities can charge a premium for SGC certificates is that browsers only allowed a limited number of roots to support SGC. When an SSL handshake takes place, the software (e.g. a web browser) would list the ciphers that it supports. Although the weaker exported browsers would only include weaker ciphers in its initial SSL handshake, the browser also contained stronger cryptography algorithms. There are two protocols involved to activate them. Netscape Communicator 4 used International Step-Up, which used the now obsolete insecure renegotiation to change to a stronger cipher suite. Microsoft used SGC, which sends a new Client Hello message listing the stronger cipher suites on the same connection after the certificate is determined to be SGC capable, and also supported Netscape Step-Up for compatibility (though this support in the NT 4.0 SP6 and IE 5.01 version had a bug where changing MAC algorithms during Step-Up did not work properly).
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Trace zero cryptography

First proposed by Gerhard Frey in 1998, trace zero cryptography refers to the use of trace zero varieties (TZV) for cryptographic purpose. Trace zero varieties are subgroups of the divisor class group on a low genus hyperelliptic curve defined over a finite field. These groups can be used to establish asymmetric cryptography using the discrete logarithm problem as cryptographic primitive. Trace zero varieties feature a better scalar multiplication performance than elliptic curves. This allows fast arithmetic in these groups, which can speed up the calculations with a factor 3 compared with elliptic curves and hence speed up the cryptosystem. Another advantage is that for groups of cryptographically relevant size, the order of the group can simply be calculated using the characteristic polynomial of the Frobenius endomorphism. This is not the case, for example, in elliptic curve cryptography when the group of points of an elliptic curve over a prime field is used for cryptographic purpose. However, to represent an element of the trace zero variety more bits are needed compared with elements of elliptic or hyperelliptic curves. Another disadvantage is the fact that it is possible to reduce the security of the TZV of 1/6th of the bit length using cover attack. == Mathematical background == A hyperelliptic curve C of genus g over a prime field F q {\displaystyle \mathbb {F} _{q}} where q = pn (p prime) of odd characteristic is defined as C : y 2 + h ( x ) y = f ( x ) , {\displaystyle C:~y^{2}+h(x)y=f(x),} where f monic, deg(f) = 2g + 1 and deg(h) ≤ g. The curve has at least one F q {\displaystyle \mathbb {F} _{q}} -rational Weierstraßpoint. The Jacobian variety J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} of C is for all finite extension F q n {\displaystyle \mathbb {F} _{q^{n}}} isomorphic to the ideal class group Cl ⁡ ( C / F q n ) {\displaystyle \operatorname {Cl} (C/\mathbb {F} _{q^{n}})} . With the Mumford's representation it is possible to represent the elements of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} with a pair of polynomials [u, v], where u, v ∈ F q n [ x ] {\displaystyle \mathbb {F} _{q^{n}}[x]} . The Frobenius endomorphism σ is used on an element [u, v] of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} to raise the power of each coefficient of that element to q: σ([u, v]) = [uq(x), vq(x)]. The characteristic polynomial of this endomorphism has the following form: χ ( T ) = T 2 g + a 1 T 2 g − 1 + ⋯ + a g T g + ⋯ + a 1 q g − 1 T + q g , {\displaystyle \chi (T)=T^{2g}+a_{1}T^{2g-1}+\cdots +a_{g}T^{g}+\cdots +a_{1}q^{g-1}T+q^{g},} where ai in Z {\displaystyle \mathbb {Z} } With the Hasse–Weil theorem it is possible to receive the group order of any extension field F q n {\displaystyle \mathbb {F} _{q^{n}}} by using the complex roots τi of χ(T): | J C ( F q n ) | = ∏ i = 1 2 g ( 1 − τ i n ) {\displaystyle |J_{C}(\mathbb {F} _{q^{n}})|=\prod _{i=1}^{2g}(1-\tau _{i}^{n})} Let D be an element of the J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} of C, then it is possible to define an endomorphism of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} , the so-called trace of D: Tr ⁡ ( D ) = ∑ i = 0 n − 1 σ i ( D ) = D + σ ( D ) + ⋯ + σ n − 1 ( D ) {\displaystyle \operatorname {Tr} (D)=\sum _{i=0}^{n-1}\sigma ^{i}(D)=D+\sigma (D)+\cdots +\sigma ^{n-1}(D)} Based on this endomorphism one can reduce the Jacobian variety to a subgroup G with the property, that every element is of trace zero: G = { D ∈ J C ( F q n ) | Tr ( D ) = 0 } , ( 0 neutral element in J C ( F q n ) {\displaystyle G=\{D\in J_{C}(\mathbb {F} _{q^{n}})~|~{\text{Tr}}(D)={\textbf {0}}\},~~~({\textbf {0}}{\text{ neutral element in }}J_{C}(\mathbb {F} _{q^{n}})} G is the kernel of the trace endomorphism and thus G is a group, the so-called trace zero (sub)variety (TZV) of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} . The intersection of G and J C ( F q ) {\displaystyle J_{C}(\mathbb {F} _{q})} is produced by the n-torsion elements of J C ( F q ) {\displaystyle J_{C}(\mathbb {F} _{q})} . If the greatest common divisor gcd ( n , | J C ( F q ) | ) = 1 {\displaystyle \gcd(n,|J_{C}(\mathbb {F} _{q})|)=1} the intersection is empty and one can compute the group order of G: | G | = | J C ( F q n ) | | J C ( F q ) | = ∏ i = 1 2 g ( 1 − τ i n ) ∏ i = 1 2 g ( 1 − τ i ) {\displaystyle |G|={\dfrac {|J_{C}(\mathbb {F} _{q^{n}})|}{|J_{C}(\mathbb {F} _{q})|}}={\dfrac {\prod _{i=1}^{2g}(1-\tau _{i}^{n})}{\prod _{i=1}^{2g}(1-\tau _{i})}}} The actual group used in cryptographic applications is a subgroup G0 of G of a large prime order l. This group may be G itself. There exist three different cases of cryptographical relevance for TZV: g = 1, n = 3 g = 1, n = 5 g = 2, n = 3 == Arithmetic == The arithmetic used in the TZV group G0 based on the arithmetic for the whole group J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} , But it is possible to use the Frobenius endomorphism σ to speed up the scalar multiplication. This can be archived if G0 is generated by D of order l then σ(D) = sD, for some integers s. For the given cases of TZV s can be computed as follows, where ai come from the characteristic polynomial of the Frobenius endomorphism : For g = 1, n = 3: s = q − 1 1 − a 1 mod ℓ {\displaystyle s={\dfrac {q-1}{1-a_{1}}}{\bmod {\ell }}} For g = 1, n = 5: s = q 2 − q − a 1 2 q + a 1 q + 1 q − 2 a 1 q + a 1 3 − a 1 2 + a 1 − 1 mod ℓ {\displaystyle s={\dfrac {q^{2}-q-a_{1}^{2}q+a_{1}q+1}{q-2a_{1}q+a_{1}^{3}-a_{1}^{2}+a_{1}-1}}{\bmod {\ell }}} For g = 2, n = 3: s = − q 2 − a 2 + a 1 a 1 q − a 2 + 1 mod ℓ {\displaystyle s=-{\dfrac {q^{2}-a_{2}+a_{1}}{a_{1}q-a_{2}+1}}{\bmod {\ell }}} Knowing this, it is possible to replace any scalar multiplication mD (|m| ≤ l/2) with: m 0 D + m 1 σ ( D ) + ⋯ + m n − 1 σ n − 1 ( D ) , where m i = O ( ℓ 1 / ( n − 1 ) ) = O ( q g ) {\displaystyle m_{0}D+m_{1}\sigma (D)+\cdots +m_{n-1}\sigma ^{n-1}(D),~~~~{\text{where }}m_{i}=O(\ell ^{1/(n-1)})=O(q^{g})} With this trick the multiple scalar product can be reduced to about 1/(n − 1)th of doublings necessary for calculating mD, if the implied constants are small enough. == Security == The security of cryptographic systems based on trace zero subvarieties according to the results of the papers comparable to the security of hyper-elliptic curves of low genus g' over F p ′ {\displaystyle \mathbb {F} _{p'}} , where p' ~ (n − 1)(g/g' ) for |G| ~128 bits. For the cases where n = 3, g = 2 and n = 5, g = 1 it is possible to reduce the security for at most 6 bits, where |G| ~ 2256, because one can not be sure that G is contained in a Jacobian of a curve of genus 6. The security of curves of genus 4 for similar fields are far less secure. == Cover attack on a trace zero crypto-system == The attack published in shows, that the DLP in trace zero groups of genus 2 over finite fields of characteristic diverse than 2 or 3 and a field extension of degree 3 can be transformed into a DLP in a class group of degree 0 with genus of at most 6 over the base field. In this new class group the DLP can be attacked with the index calculus methods. This leads to a reduction of the bit length 1/6th.
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