Enterprise information integration (EII) is the ability to support a unified view of data and information for an entire organization. The goal of EII is to get a large set of heterogeneous data sources to appear to a user or system as a single, homogeneous data source. In a data virtualization application of EII, there is a process of information integration, using data abstraction to provide a unified interface (known as uniform data access) for viewing all the data within an organization, and a single set of structures and naming conventions (known as uniform information representation) to represent this data. == Overview == Data within an enterprise can be stored in heterogeneous formats, including relational databases (which themselves come in a large number of varieties), text files, XML files, spreadsheets and a variety of proprietary storage methods, each with their own indexing and data access methods. Standardized data access APIs have emerged that offer a specific set of commands to retrieve and modify data from a generic data source. Many applications exist that implement these APIs' commands across various data sources, most notably relational databases. Such APIs include ODBC, JDBC, XQJ, OLE DB, and more recently ADO.NET. There are also standard formats for representing data within a file that are very important to information integration. The best-known of these is XML, which has emerged as a standard universal representation format. There are also more specific XML "grammars" defined for specific types of data such as Geography Markup Language for expressing geographical features and Directory Service Markup Language for holding directory-style information. In addition, non-XML standard formats exist such as iCalendar for representing calendar information and vCard for business card information. Enterprise Information Integration (EII) applies data integration commercially. Despite the theoretical problems described above, the private sector shows more concern with the problems of data integration as a viable product. EII emphasizes neither correctness nor tractability, but speed and simplicity. === Uniform data access === Uniform data access means connectivity and controllability across numerous target data sources. Necessary to fields such as EII and Electronic Data Interchange (EDI), it is most often used regarding analysis of disparate data types and data sources, which must be rendered into a uniform information representation, and generally must appear homogenous to the analysis tools—when the data being analyzed is typically heterogeneous and widely varying in size, type, and original representation. === Uniform information representation === Uniform information representation allows information from several realms or disciplines to be displayed and worked with as if it came from the same realm or discipline. It takes information from a number of sources, which may have used different methodologies and metrics in their data collection, and builds a single large collection of information, where some records may be more complete than others across all fields of data Uniform information representation is particularly important in EII and Electronic Data Interchange (EDI), where different departments of a large organization may have collected information for different purposes, with different labels and units, until one department realized that data already collected by those other departments could be re-purposed for their own needs—saving the enterprise the effort and cost of re-collecting the same information. === Combining disparate data sets === Each data source is disparate and as such is not designed to support EII. Therefore, data virtualization as well as data federation depends upon accidental data commonality to support combining data and information from disparate data sets. Because of this lack of data value commonality across data sources, the return set may be inaccurate, incomplete, and impossible to validate. One solution is to recast disparate databases to integrate these databases without the need for ETL. The recast databases support commonality constraints where referential integrity may be enforced between databases. The recast databases provide designed data access paths with data value commonality across databases. === Simplicity of deployment === Even if recognized as a solution to a problem, EII as of 2009 currently takes time to apply and offers complexities in deployment. Proposed schema-less solutions include "Lean Middleware". === Handling higher-order information === Analysts experience difficulty—even with a functioning information integration system—in determining whether the sources in the database will satisfy a given application. Answering these kinds of questions about a set of repositories requires semantic information like metadata and/or ontologies. == Applications == EII products enable loose coupling between homogeneous-data consuming client applications and services and heterogeneous-data stores. Such client applications and services include Desktop Productivity Tools (spreadsheets, word processors, presentation software, etc.), development environments and frameworks (Java EE, .NET, Mono, SOAP or RESTful Web services, etc.), business intelligence (BI), business activity monitoring (BAM) software, enterprise resource planning (ERP), Customer relationship management (CRM), business process management (BPM and/or BPEL) Software, and web content management (CMS). == Data access technologies == Service Data Objects (SDO) for Java, C++ and .Net clients and any type of data source XQuery and XQuery API for Java
Actionstep
Actionstep is a cloud-based legal practice management software for law firms and compliance-focused businesses. Actionstep is built to be a comprehensive practice management software with features for workflow automation as well as automatic document generation == History == Actionstep was created by Ted Jordan, CEO of Actionstep, in 2004. It was first used commercially in 2005 by a New Zealand construction franchise as well as a law firm. Actionstep soon expanded into central government and a wider range of small business users (mainly in New Zealand and Australia). After a few years the expanse of their legal client base prompted the company to add key legal specific features to the product with the aim of further expanding their legal market. Through Actionstep's tenure as a practice management software they have gradually expanded from their headquarters in New Zealand and offices located in the United Kingdom and the United States of America. In October 2020, private equity firm Serent Capital Partners purchased 84.25% stake in Actionstep. In April 2022, the company announced unlimited annual leave to its staff == Product == The premise of Actionstep is that it saves companies from having to purchase software tailored to their work flow and instead allows companies to modify the program without additional coding.{{Citation needed}} The founder and CEO Ted Jordan used cloud technology to allow the software to be continuously updated without the need to purchase or redesign new software. This theoretically allows businesses to remain current all the time and cut external I.T. costs.{{Citation needed}} Actionstep also integrates with software from other companies, such as Xero accounting, Microsoft Office & Office 365, Gmail, Google Drive, Dropbox, NetDocuments, QuickBooks, LawPay, BundleDocs, Box, HotDocs, Infotrack, GlobalX, PEXA, JOSEF and Zapier. Actionstep contains workflow automation features aimed at increasing office efficiency. These automated processes include automatic task assignment, information collection, document generation & automation, cataloguing, and matter generation. == Awards == Actionstep was named First International Best of SaaS Showplace Award Winner in 2009. Actionstep has also been a finalist in the ComputerWorld Excellence Awards (2007), and the Vero Excellence in Business Support (2010).
Social computing
Social computing is an area of computer science that is concerned with the intersection of social behavior and computational systems. It is based on creating or fostering existing social conventions and social contexts through the use of software and technology. Blogs, email, instant messaging, social network services, wikis, social bookmarking and other instances of what is often called social software illustrate ideas from social computing. The rise in social computing is attributed to the prevalence of personal devices and increased overall computing power. This enables a growing number of users to participate in sharing content and interact with another. == Definitions == Humans—and human behavior—are profoundly social. Humans tend to orient to one another and develop abilities to interact with each other and other species. This ranges from expression and gesture through spoken, written, and body language. Humans are influenced by the behavior of those around them and can rely on social context and cues to make decisions. An example of a behavior relying on social contexts is applauding at the end of the play. This is based on the context that the show ended, and other audience members are applauding. Social information provides a basis for inferences, planning, and coordinating activity. == Examples == Common tools include blogs, email, instant messaging, social networking sites, wikis, and social bookmarking platforms. These technologies enable users to generate content, share knowledge, and interact in real time. == Applications == The rise of social computing has highlighted opportunities for businesses. Businesses are interacting on social computing platforms and investing in facilities to support and research social computing.Business models can leverage the massive customer bases that accumulate through social computing channels. Some organizations have started their own blogs and networks (McAfee, 2006, Joe, 2005). Organizations from diverse industry sectors such as Google, Cisco, and Fox, have sought to acquire or invest in successful social computing enterprises. A business blog can serve as a source of information and promotion for the company. This allows the company to share content about the company and their initiatives. Businesses have also interacted with social computing to market themselves and interact with customers. A notable example is Wendy's with their X (formerly Twitter) account. The account was primarily used to promote business promotions and interact with users in a playful or meaningful way. E-commerce web sites have allowed users to leave reviews and feedback on purchases which has improved online shopping experience for sellers and consumers.As another example of social computing’s business applications, many e-commerce Web sites have adopted online product/vendor feedback/reputation systems. Such systems provide an asynchronous platform for the consumer community to share experiences collectively and influence their purchasing behavior. They also provide a vehicle for eliciting feedback information valuable to the vendors and e-commerce site operators.Consumers can use the feedback systems to make a more educated choice on a purchase by comparing reviews between products or vendors. Sellers can track consumer behaviors and trends regarding a product and adjust their supply according to the demand. == Challenges and criticism == Social computing raises several concerns related to privacy, data security, and algorithmic bias. The widespread collection and analysis of user-generated data can lead to ethical dilemmas, especially when users are unaware of how their information is used. Critics also highlight issues of digital labor, surveillance, and the spread of misinformation, which can influence public opinion and social dynamics. === Term appearance === The term appeared in the mid 1990s after technology advancements and development of the web. In 1994, the concept of social computing was first proposed by Schuler. He thought, "Social computing is a computing application, with software as the medium or focus of social relationships." === Premise === The premise of social computing is that it is possible to design digital systems that support useful functionality by making socially produced information available to their users. This information may be provided directly, as when systems show the number of users who have rated a review as helpful or not. Or the information may be provided after being filtered and aggregated, as is done when systems recommend a product based on what else people with similar purchase history have purchased. Alternatively, the information may be provided indirectly, as is the case with Google's page rank algorithms which orders search results based on the number of pages that (recursively) point to them. In all of these cases, information that is produced by a group of people is used to provide or enhance the functioning of a system. Social computing is concerned with systems of this sort and the mechanisms and principles that underlie them. Social computing can be defined as follows: "Social Computing" refers to systems that support the gathering, representation, processing, use, and dissemination of information that is distributed across social collectivities such as teams, communities, organizations, and markets. Moreover, the information is not "anonymous" but is significantly precise because it is linked to people, who are in turn linked to other people. More recent definitions, however, have foregone the restrictions regarding anonymity of information, acknowledging the continued spread and increasing pervasiveness of social computing. As an example, Hemmatazad, N. (2014) defined social computing as "the use of computational devices to facilitate or augment the social interactions of their users, or to evaluate those interactions in an effort to obtain new information." Social computing has to do with supporting "computations" that are carried out by groups of people, an idea that has been popularized in James Surowiecki's book, The Wisdom of Crowds. Examples of social computing in this sense include collaborative filtering, online auctions, reputation systems, computational social choice, tagging, and verification games. The social information processing page focuses on this sense of social computing. == History == === Technology infrastructure === Users were able to interact more with websites after the development of Web 2.0. This was an advancement from Web 1.0. Comode G. and Krishnamurthy B. (2008) note that "content creators were few in Web 1.0 with the vast majority of users simply acting as consumers of content." Web 2.0 provided functionalities that allowed for low-cost web-hosting services and introduced features with browser windows that used basic information structure and expanded it to as many devices as possible using HTTP, or Hypertext Transfer Protocol. Sometimes referred to as "Enterprise 2.0", a term derived from Web 2.0, social software for enterprise generally refers to the use of social computing in corporate intranets and in other medium- and large-scale business environments. It consisted of a class of tools that allowed for networking and social changes to businesses at the time. It was a layering of the business tools on Web 2.0 and brought forth several applications and collaborative software with specific uses. FinanceElectronic negotiation, which first came up in 1969 and was adapted over time to suit financial markets networking needs, represents an important and desirable coordination mechanism for electronic markets. Negotiation between agents (software agents as well as humans) allows cooperative and competitive sharing of information to determine a proper price. Recent research and practice has also shown that electronic negotiation is beneficial for the coordination of complex interactions among organizations. Electronic negotiation has recently emerged as a very dynamic, interdisciplinary research area covering aspects from disciplines such as Economics, Information Systems, Computer Science, Communication Theory, Sociology and Psychology.Social computing has become more widely known because of its relationship to a number of recent trends. These include the growing popularity of social software and Web 3.0, increased academic interest in social network analysis, the rise of open source as a viable method of production, and a growing conviction that all of this can have a profound impact on daily life. A February 13, 2006 paper by market research company Forrester Research suggested that: === Developments === PLATO was one of the earliest examples of social computing in a live production environment with initially hundreds and soon thousands of users. The PLATO computer system was developed by the University of Illinois at Urbana Champaign in 1960s. In the 70s, the system supported social software applications for multi-us
Social media marketing
Social media marketing is the use of social media platforms and websites to promote a product or service. Although the terms e-marketing and digital marketing are still dominant in academia, social media marketing is becoming more popular for practitioners and researchers. Social media platforms such as Facebook, LinkedIn, Instagram, and Twitter, among others, have built-in data analytics tools that companies can use to track the progress, success, and engagement of social media marketing campaigns. Companies address a range of stakeholders through social media marketing, including current and potential customers, current and potential employees, journalists, bloggers, and the general public. On a strategic level, social media marketing includes the management of a marketing campaign, governance, setting the scope (e.g. more active or passive use) and the establishment of a firm's desired social media "culture" and "tone". Firms that use social media marketing can allow customers and Internet users to post user-generated content (e.g., online comments, product reviews, etc.), also known as "earned media", rather than use marketer-prepared advertising copy. == Purposes and tactics == Social media may be employed in marketing as a communications tool that makes companies accessible to those who are interested in their product and visible to those who are not familiar with their products. It is used by companies to create buzz, learn from customers, and target them. Of the top 10 factors that correlate with a strong Google organic search, seven are social media-dependent. This means that if brands with little to no social media presence tend to show up less on Google searches. While platforms such as Twitter, Facebook and—in the past—Google+ have a larger number of monthly users, the visual media-sharing-based mobile platforms garner a higher interaction rate in comparison, and have registered the fastest growth, and have changed the ways in which consumers engage with brand content. Instagram has an interaction rate of 1.46% with an average of 130 million users monthly as opposed to Twitter, which has a .03% interaction rate with an average of 210 million monthly users. Unlike traditional media that are often cost-prohibitive to many companies, a social media strategy does not require significant financial investment. To this end, companies make use of platforms such as Facebook, Twitter, YouTube, TikTok and Instagram to reach audiences much wider than through traditional print, television, or radio advertisements alone at a fraction of the cost, as most social networking sites can be used at little or no cost (however, some websites charge companies for premium services). This has changed the ways that companies approach and interact with customers, as a substantial percentage of consumer interactions are now being carried out over online platforms with much higher visibility. Customers can post reviews of products and services, rate customer service, and ask questions or voice concerns directly to companies through social media platforms. According to Measuring Success, over 80% of consumers use the web to research products and services. Thus social media marketing is also used by businesses in order to build relationships of trust with consumers. To this aim, companies may hire personnel to specifically handle these social media interactions, who usually report under the title of online community managers. Handling these interactions in a satisfactory manner can result in an increase of consumer trust. To both this aim and to fix the public's perception of a company, three steps are taken in order to address consumer concerns: Identifying the extent of the social chatter Engaging the influencers to help Developing a proportional response == Strategies == === Passive approach === Social media can be a useful source of market information and a way to hear customers' perspectives. Blogs, content communities, and forums are platforms where individuals share their reviews and recommendations of brands, products, and services. Businesses are able to tap into and analyze customer voices and feedback generated in social media for marketing purposes. In this sense, social media is a relatively inexpensive source of market intelligence which can be used by marketers and managers to track and respond to consumer-identified problems and detect market opportunities. === Active approach === Social media can be used as a public relations tool, a direct marketing tool, and a communication channel to target very specific audiences, with social media influencers and social media personalities as effective customer engagement tools. This tactic is widely known as influencer marketing, which gives brands the opportunity to reach their target audience via a group of selected influencers advertising their product or service. Brands were projected to spend up to $15 billion on influencer marketing by 2022, per Business Insider Intelligence estimates, based on Mediakix data. The use of customer influencers, such as popular bloggers, can be an efficient and cost-effective method to launch new products or services. == Engagement == Engagement with the social web means that customers and stakeholders are active participants rather than passive spectators. An example of these are consumer advocacy groups and groups that criticize companies (e.g., lobby groups or advocacy organizations). The use of Social media in a business or political context allows people to express and share opinions about a company's products, services or business practices, or a government's actions. On social media, each participant becomes part of the marketing department (or a challenge to the marketing effort) as other customers read their comments or reviews. The effectiveness of social media marketing campaigns is dependent on the promotion of online engagement. With the advent of social media marketing, it has become increasingly important to gain customer interest in products and services, which can eventually be translated into buying behavior, or voting and donating behavior in a political context. New online marketing concepts of engagement and loyalty have emerged which aim to build customer participation and brand reputation. Engagement in social media for the purpose of a social media strategy is divided into two parts. The first is proactive, regular posting of new online content, which can be seen through digital photos, digital videos, text, and conversations. It is also represented through sharing of content and information from others via weblinks. The second part is reactive conversations, with social media users responding to those who reach out to others' social media profiles through comments or messages. == Campaigns == === Local businesses === Small businesses use social networking sites as a promotional technique. Businesses can follow individuals' social media usage in their local area and advertise specials and deals, which can be exclusive and in the form of "get a free drink with a copy of this tweet". This type of message encourages other locals to follow the business on their official websites in order to obtain the promotional deal. The business's brand visibility is enhanced in the process. Social networking sites are also used by small businesses to develop their own market research on new products and services. By encouraging their customers to give feedback on new product ideas, businesses can gain insights on whether or not a product may be accepted by their target market enough to merit full production. In addition, customers will feel the company has engaged them in the process of co-creation—the process in which the business uses customer feedback to create or modify a product or service to fill a need of the target market. Such feedback can be presented in various forms, such as surveys, contests, and polls. Social networking sites such as LinkedIn, also provide opportunities for small businesses to find candidates to fill staff positions. Review sites such as Yelp help small businesses build their reputation beyond brand visibility. Positive customer peer reviews help influence new prospects to purchase goods and services more than company advertising. == Benefits == Social Media Marketing allows companies to promote themselves to large, diverse audiences that could not be reached through traditional marketing such as phone and email-based advertising. Marketing on most social media platforms also comes at little to no cost, making it accessible to virtually any size business. Social Media Marketing accommodates personalized and direct marketing that targets specific demographics and markets. Companies can engage with customers directly, allowing them to obtain feedback and resolve issues almost immediately. Another advantage of social media marketing is that it's an ideal environment for a company to conduct market research. It can be used
Service Assurance Agent
IP SLA (Internet Protocol Service Level Agreement) is an active computer network measurement technology that was initially developed by Cisco Systems. IP SLA was previously known as Service Assurance Agent (SAA) or Response Time Reporter (RTR). IP SLA is used to track network performance like latency, ping response, and jitter, it also helps to provide service quality. == Functions == Routers and switches enabled with IP SLA perform periodic network tests or measurements such as Hypertext Transfer Protocol (HTTP) GET File Transfer Protocol (FTP) downloads Domain Name System (DNS) lookups User Datagram Protocol (UDP) echo, for VoIP jitter and mean opinion score (MOS) Data-Link Switching (DLSw) (Systems Network Architecture (SNA) tunneling protocol) Dynamic Host Configuration Protocol (DHCP) lease requests Transmission Control Protocol (TCP) connect Internet Control Message Protocol (ICMP) echo (remote ping) The exact number and types of available measurements depends on the IOS version. IP SLA is very widely used in service provider networks to generate time-based performance data. It is also used together with Simple Network Management Protocol (SNMP) and NetFlow, which generate volume-based data. == Usage considerations == For IP SLA tests, devices with IP SLA support are required. IP SLA is supported on Cisco routers and switches since IOS version 12.1. Other vendors like Juniper Networks or Enterasys Networks support IP SLA on some of their devices. IP SLA tests and data collection can be configured either via a console (command-line interface) or via SNMP. When using SNMP, both read and write community strings are needed. The IP SLA voice quality feature was added starting with IOS version 12.3(4)T. All versions after this, including 12.4 mainline, contain the MOS and ICPIF voice quality calculation for the UDP jitter measurement.
Security and Privacy in Computer Systems
Security and Privacy in Computer Systems is a paper by Willis Ware that was first presented to the public at the 1967 Spring Joint Computer Conference. == Significance == Ware's presentation was the first public conference session about information security and privacy in respect of computer systems, especially networked or remotely-accessed ones. The IEEE Annals of the History of Computing said that Ware's 1967 Spring Joint Computer Conference session, together with 1970's Ware report, marked the start of the field of computer security.
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.