A virtual influencer, sometimes described as a virtual persona or virtual model, is a computer-generated fictional character that can be used for a variety of marketing-related purposes, but most frequently for social media marketing, in lieu of online human "influencers". Most virtual influencers are designed using computer graphics and motion capture technology to resemble real people in realistic situations. Common derivatives of virtual influencers include VTubers, which broadly refer to online entertainers and YouTubers who represent themselves using virtual avatars instead of their physical selves. == History == Virtual influencers are fundamentally synonymous with virtual idols, which originate from Japan's anime and Japanese idol culture that dates back to the 1980s. The first virtual idol created was Lynn Minmay, a fictional singer and main character of the anime television series Super Dimension Fortress Macross (1982) and the animated film adaptation Macross: Do You Remember Love? (1984). Minmay's success led to the production of more Japanese virtual idols, such as EVE from the Japanese cyberpunk anime Megazone 23 (1985), and Sharon Apple in Macross Plus (1994). Virtual idols were not always well received – in 1995, Japanese talent agency Horipro created Kyoko Date, which was inspired by the Macross franchise and dating sim games such as Tokimeki Memorial (1994). Date failed to gain commercial success despite drawing headlines for her debut as a CGI idol, largely due to technical limitations leading to issues such as unnatural movements, an issue also known as the uncanny valley. Since their inception, many virtual idols created have achieved continual success, with notable names including the Vocaloid singer Hatsune Miku, and the VTuber Kizuna AI. Technological advancements have also enabled production teams to use artificial intelligence and advanced techniques to customize the personalities and behavior of virtual idols. Due to modern-day advancements in technology, many virtual idols have held real-life tours and events. Notable ones include Hatsune Miku's titular tour Miku Expo and Hololive's concerts with many of their idols from their English, Japanese and Indonesian branches. Some notable events including virtual singers and influencers have included: Hatsune Miku opening for Lady Gaga in 2014 and Hoshimachi Suisei's concerts at the famous Budokan venue in Japan and her addition to the Forbes Japan list of '30 Under 30' individuals who are changing the world in their respective fields. == Benefits and criticism == From a branding perspective, virtual influencers are perceived to be much less likely to be mired in scandals. In China, celebrities caught in bad publicity such as singer Wang Leehom and entertainer Kris Wu have heightened the appeal of virtual influencers, since their existence relies entirely on computer-generated imagery and they are therefore unlikely to cause any damage to a brand's image by association. Some studies have also suggested that Generation Z consumers have a unique appetite for virtual idols and influencers, since they grew up in the age of the internet. Studies also show that human-like appearance of virtual influencers show higher message credibility than anime-like virtual influencers. Scholars and commentators have also questioned the ethics and cultural impact of virtual influencers, arguing that computer-generated personas can entrench unrealistic beauty standards while diffusing accountability for labor, identity, and consent. Business and marketing analysts have also warned that disclosure and governance remain inconsistent, recommending clearer guardrails and transparency when brands deploy synthetic spokespeople. In 2025, reporting highlighted concerns that AI-driven "virtual humans" could displace human creators and sales workers, intensifying debates over the future of creative labor and authenticity online. == Notable examples == === Virtual bands === Eternity - A South Korean virtual idol group formed by Pulse9. Gorillaz - A virtual band formed in 1998. K/DA - A virtual K-pop girl group created as part of the League of Legends video game franchise. MAVE: - A South Korean virtual girl group formed in 2023 by Metaverse Entertainment. Pentakill - A virtual heavy metal band created as part of the League of Legends video game franchise. Plave (band) - A South Korean virtual boy band formed by VLast. Squid Sisters and Off the Hook - Two virtual pop idol duos as part of the Splatoon series. Studio Killers - A Finnish-Danish-British virtual band formed in 2011. === Vocaloids === Hatsune Miku (modeled after Saki Fujita) Kagamine Rin/Len (modeled after Asami Shimoda) Megurine Luka (modeled after Yū Asakawa) Meiko (modeled after Meiko Haigō) Kaito (modeled after Naoto Fūga) === VTubers === Kano Kizuna AI Neuro-sama VShojo Ironmouse Projekt Melody Nijisanji Hololive Akai Haato Gawr Gura Hoshimachi Suisei Natsuiro Matsuri === Other examples === Ami Yamato Crazy Frog FN Meka IA Kuki AI Kyoko Date Kyra Miquela Naevis Shudu Gram
Lexical Markup Framework
Language resource management – Lexical markup framework (LMF; ISO 24613), produced by ISO/TC 37, is the ISO standard for natural language processing (NLP) and machine-readable dictionary (MRD) lexicons. The scope is standardization of principles and methods relating to language resources in the contexts of multilingual communication. == Objectives == The goals of LMF are to provide a common model for the creation and use of lexical resources, to manage the exchange of data between and among these resources, and to enable the merging of large number of individual electronic resources to form extensive global electronic resources. Types of individual instantiations of LMF can include monolingual, bilingual or multilingual lexical resources. The same specifications are to be used for both small and large lexicons, for both simple and complex lexicons, for both written and spoken lexical representations. The descriptions range from morphology, syntax, computational semantics to computer-assisted translation. The covered languages are not restricted to European languages but cover all natural languages. The range of targeted NLP applications is not restricted. LMF is able to represent most lexicons, including WordNet, EDR and PAROLE lexicons. == History == In the past, lexicon standardization has been studied and developed by a series of projects like GENELEX, EDR, EAGLES, MULTEXT, PAROLE, SIMPLE and ISLE. Then, the ISO/TC 37 National delegations decided to address standards dedicated to NLP and lexicon representation. The work on LMF started in Summer 2003 by a new work item proposal issued by the US delegation. In Fall 2003, the French delegation issued a technical proposition for a data model dedicated to NLP lexicons. In early 2004, the ISO/TC 37 committee decided to form a common ISO project with Nicoletta Calzolari (CNR-ILC Italy) as convenor and Gil Francopoulo (Tagmatica France) and Monte George (ANSI, United States) as editors. The first step in developing LMF was to design an overall framework based on the general features of existing lexicons and to develop a consistent terminology to describe the components of those lexicons. The next step was the actual design of a comprehensive model that best represented all of the lexicons in detail. A large panel of 60 experts contributed a wide range of requirements for LMF that covered many types of NLP lexicons. The editors of LMF worked closely with the panel of experts to identify the best solutions and reach a consensus on the design of LMF. Special attention was paid to the morphology in order to provide powerful mechanisms for handling problems in several languages that were known as difficult to handle. 13 versions have been written, dispatched (to the National nominated experts), commented and discussed during various ISO technical meetings. After five years of work, including numerous face-to-face meetings and e-mail exchanges, the editors arrived at a coherent UML model. In conclusion, LMF should be considered a synthesis of the state of the art in NLP lexicon field. == Current stage == The ISO number is 24613. The LMF specification has been published officially as an International Standard on 17 November 2008. == As one of the members of the ISO/TC 37 family of standards == The ISO/TC 37 standards are currently elaborated as high level specifications and deal with word segmentation (ISO 24614), annotations (ISO 24611 a.k.a. MAF, ISO 24612 a.k.a. LAF, ISO 24615 a.k.a. SynAF, and ISO 24617-1 a.k.a. SemAF/Time), feature structures (ISO 24610), multimedia containers (ISO 24616 a.k.a. MLIF), and lexicons (ISO 24613). These standards are based on low level specifications dedicated to constants, namely data categories (revision of ISO 12620), language codes (ISO 639), scripts codes (ISO 15924), country codes (ISO 3166) and Unicode (ISO 10646). The two level organization forms a coherent family of standards with the following common and simple rules: the high level specification provides structural elements that are adorned by the standardized constants; the low level specifications provide standardized constants as metadata. == Key standards == The linguistics constants like /feminine/ or /transitive/ are not defined within LMF but are recorded in the Data Category Registry (DCR) that is maintained as a global resource by ISO/TC 37 in compliance with ISO/IEC 11179-3:2003. And these constants are used to adorn the high level structural elements. The LMF specification complies with the modeling principles of Unified Modeling Language (UML) as defined by Object Management Group (OMG). The structure is specified by means of UML class diagrams. The examples are presented by means of UML instance (or object) diagrams. An XML DTD is given in an annex of the LMF document. == Model structure == LMF is composed of the following components: The core package that is the structural skeleton which describes the basic hierarchy of information in a lexical entry. Extensions of the core package which are expressed in a framework that describes the reuse of the core components in conjunction with the additional components required for a specific lexical resource. The extensions are specifically dedicated to morphology, MRD, NLP syntax, NLP semantics, NLP multilingual notations, NLP morphological patterns, multiword expression patterns, and constraint expression patterns. == Example == In the following example, the lexical entry is associated with a lemma clergyman and two inflected forms clergyman and clergymen. The language coding is set for the whole lexical resource. The language value is set for the whole lexicon as shown in the following UML instance diagram. The elements Lexical Resource, Global Information, Lexicon, Lexical Entry, Lemma, and Word Form define the structure of the lexicon. They are specified within the LMF document. On the contrary, languageCoding, language, partOfSpeech, commonNoun, writtenForm, grammaticalNumber, singular, plural are data categories that are taken from the Data Category Registry. These marks adorn the structure. The values ISO 639-3, clergyman, clergymen are plain character strings. The value eng is taken from the list of languages as defined by ISO 639-3. With some additional information like dtdVersion and feat, the same data can be expressed by the following XML fragment: This example is rather simple, while LMF can represent much more complex linguistic descriptions the XML tagging is correspondingly complex. == Selected publications about LMF == The first publication about the LMF specification as it has been ratified by ISO (this paper became (in 2015) the 9th most cited paper within the Language Resources and Evaluation conferences from LREC papers): Language Resources and Evaluation LREC-2006/Genoa: Gil Francopoulo, Monte George, Nicoletta Calzolari, Monica Monachini, Nuria Bel, Mandy Pet, Claudia Soria: Lexical Markup Framework (LMF) About semantic representation: Gesellschaft für linguistische Datenverarbeitung GLDV-2007/Tübingen: Gil Francopoulo, Nuria Bel, Monte George Nicoletta Calzolari, Monica Monachini, Mandy Pet, Claudia Soria: Lexical Markup Framework ISO standard for semantic information in NLP lexicons About African languages: Traitement Automatique des langues naturelles, Marseille, 2014: Mouhamadou Khoule, Mouhamad Ndiankho Thiam, El Hadj Mamadou Nguer: Toward the establishment of a LMF-based Wolof language lexicon (Vers la mise en place d'un lexique basé sur LMF pour la langue wolof) [in French] About Asian languages: Lexicography, Journal of ASIALEX, Springer 2014: Lexical Markup Framework: Gil Francopoulo, Chu-Ren Huang: An ISO Standard for Electronic Lexicons and its Implications for Asian Languages DOI 10.1007/s40607-014-0006-z About European languages: COLING 2010: Verena Henrich, Erhard Hinrichs: Standardizing Wordnets in the ISO Standard LMF: Wordnet-LMF for GermaNet EACL 2012: Judith Eckle-Kohler, Iryna Gurevych: Subcat-LMF: Fleshing out a standardized format for subcategorization frame interoperability EACL 2012: Iryna Gurevych, Judith Eckle-Kohler, Silvana Hartmann, Michael Matuschek, Christian M Meyer, Christian Wirth: UBY - A Large-Scale Unified Lexical-Semantic Resource Based on LMF. About Semitic languages: Journal of Natural Language Engineering, Cambridge University Press (to appear in Spring 2015): Aida Khemakhem, Bilel Gargouri, Abdelmajid Ben Hamadou, Gil Francopoulo: ISO Standard Modeling of a large Arabic Dictionary. Proceedings of the seventh Global Wordnet Conference 2014: Nadia B M Karmani, Hsan Soussou, Adel M Alimi: Building a standardized Wordnet in the ISO LMF for aeb language. Proceedings of the workshop: HLT & NLP within Arabic world, LREC 2008: Noureddine Loukil, Kais Haddar, Abdelmajid Ben Hamadou: Towards a syntactic lexicon of Arabic Verbs. Traitement Automatique des Langues Naturelles, Toulouse (in French) 2007: Khemakhem A, Gargouri B, Abdelwahed A, Francopoulo G: Modélisation des paradigmes de fl
Data governance
Data governance is a term used on both a macro and a micro level. The former is a political concept and forms part of international relations and Internet governance; the latter is a data management concept and forms part of corporate/organizational data governance. Data governance involves delegating authority over data and exercising that authority through decision-making processes. It plays a role in enhancing the value of data assets. == Macro level == Data governance at the macro level involves regulating cross-border data flows among countries, which is more precisely termed international data governance. This field was first formed in the early 2000s, and consists of "norms, principles and rules governing various types of data." There have been several international groups established by research organizations that aim to grant access to their data. These groups that enable an exchange of data are, as a result, exposed to domestic and international legal interpretations that ultimately decide how data is used. However, as of 2023, there are no international laws or agreements specifically focused on data protection. == Data governance (Data Management) == Data governance is the set of principles, policies, and processes that guide the effective and responsible use of data within an organization. It creates a framework for decision making, accountability, and oversight across the data lifecycle, from creation and storage to sharing and disposal. Data governance is closely linked with data management, which provides the practical methods to carry out governance objectives. These methods include data quality assurance, metadata management, master data management, security controls, and compliance monitoring. Together, governance and management aim to maximize the value of data as a strategic asset, reduce risks from misuse or inaccuracy, and ensure compliance with regulatory, ethical, and business requirements. The importance of this discipline has grown with the rise of big data, cloud computing, and artificial intelligence, where consistent standards and stewardship are essential for privacy protection, interoperability, and informed decision making. == Data governance drivers == While data governance initiatives can be driven by a desire to improve data quality, they are often driven by C-level leaders responding to external regulations. In a recent report conducted by the CIO WaterCooler community, 54% stated the key driver was efficiencies in processes; 39% - regulatory requirements; and only 7% customer service. Examples of these regulations include Sarbanes–Oxley Act, Basel I, Basel II, HIPAA, GDPR, cGMP, and a number of data privacy regulations. To achieve compliance with these regulations, business processes and controls require formal management processes to govern the data subject to these regulations. Successful programs identify drivers that are meaningful to both supervisory and executive leadership. Common themes among the external regulations center on the need to manage risk. The risks can be financial misstatement, inadvertent release of sensitive data, or poor data quality for key decisions. Methods to manage these risks vary from industry to industry. Examples of commonly referenced best practices and guidelines include COBIT, ISO/IEC 38500, and others. The proliferation of regulations and standards creates challenges for data governance professionals, particularly when multiple regulations overlap the data being managed. Organizations often launch data governance initiatives to address these challenges. == Data governance initiatives (Dimensions) == Data governance initiatives improve the quality of data by assigning a team responsible for data's accuracy, completeness, consistency, timeliness, validity, and uniqueness. This team usually consists of executive leadership, project management, line-of-business managers, and data stewards. The team usually employs a methodology for tracking and improving enterprise data, such as Six Sigma, and tools for data mapping, profiling, cleansing, and monitoring data. Data governance initiatives may be aimed at achieving a number of objectives including offering better visibility to internal and external customers (such as supply chain management), compliance with regulatory law, improving operations after rapid company growth or corporate mergers, or to aid the efficiency of enterprise knowledge workers by reducing confusion and error and increasing their scope of knowledge. Many data governance initiatives are also inspired by past attempts to fix information quality at the departmental level, which can lead to incongruent and redundant data quality processes. Most large companies have many applications and databases that can not easily share information. Therefore, knowledge workers within large organizations may not have access to the data they need to best do their jobs. When they do have access to the data, the data quality may be poor. By setting up a data governance practice or corporate data authority (individual or area responsible for determining how to proceed, in the best interest of the business, when a data issue arises), these problems can be mitigated. == Implementation == Implementation of a data governance initiative may vary in scope as well as origin. Sometimes, an executive mandate will arise to initiate an enterprise-wide effort. Sometimes the mandate will be to create a pilot project or projects, limited in scope and objectives, aimed at either resolving existing issues or demonstrating value. Sometimes, an initiative originates from lower down in the organization's hierarchy and will be deployed in a limited scope to demonstrate value to potential sponsors higher up in the organization. The initial scope of an implementation can vary greatly as well, from review of a one-off IT system to a cross-organization initiative. == Data governance tools == Leaders of successful data governance programs declared at the Data Governance Conference in Orlando, FL, in December 2006, that data governance is about 80 to 95 percent communication. That stated, it is a given that many of the objectives of a data governance program must be accomplished with appropriate tools. Many vendors are now positioning their products as data governance tools. Due to the different focus areas of various data governance initiatives, a given tool may or may not be appropriate. Additionally, many tools that are not marketed as governance tools address governance needs and demands.
Media contacts database
In public relations (PR) and marketing, a media contacts database is a resource which catalogs the names, contact information, and other details about people who work in various media professions. These include journalists, reporters, editors, publishers, contributors, freelance journalists, opinion writers, social media personalities/ influencers, TV show anchors, radio show hosts, DJs, and others. A media contacts database usually contains the following information: Full name of the media contact, The publication or channel they work for Designations (past and present) Topics they cover, or their beat Contact information found in public domains Online presence like blogs and other social networking sites Education Information == Overview == A media contacts database is a public relations tool that is maintained and used by PR professionals to pitch stories on a particular topic, product, or company to a specific group of journalists. These journalists would then write or speak about the particular topic in a relevant issue or episode of their shows. A media contacts database allows a PR professional to gain easy access to hundreds of journalists within a short span of time. Media contacts database are created and sold by many media research companies that offer such PR software for professionals.
Data thinking
Data Thinking is a framework that integrates data science with the design process. It combines computational thinking, statistical thinking, and domain-specific knowledge to guide the development of data-driven solutions in product development. The framework is used to explore, design, develop, and validate solutions, with a focus on user experience and data analytics, including data collection and interpretation The framework aims to apply data literacy and inform decision-making through data-driven insights. == Major components == According to "Computational thinking in the era of data science": Data thinking involves understanding that solutions require both data-driven and domain-knowledge-driven rules. Data thinking evaluates whether data accurately represents real-life scenarios and improves data collection where necessary. The framework highlights the importance of preserving domain-specific meaning during data analysis. Data thinking incorporates statistical and logical analysis to identify patterns and irregularities. Data thinking involves testing solutions in real-life contexts and iteratively improving models based on new data. The process requires evaluating problems from multiple abstraction levels and understanding the potential for biases in generalizations. == Major phases == === Strategic context and risk analysis === Analyzing the broader digital strategy and assessing risks and opportunities is a common step before beginning a project. Techniques like coolhunting, trend analysis, and scenario planning can be used to assist with this. === Ideation and exploration === In this phase, focus areas are identified, and use cases are developed by integrating organizational goals, user needs, and data requirements. Design thinking methods, such as personas and customer journey mapping, are applied. === Prototyping === A proof of concept is created to test feasibility and refine solutions through iterative evaluation to optimize for effective performance. === Implementation and monitoring === Solutions are tested and monitored for performance and continual improvement. == Implementing Data Thinking == The following resources explain more about data thinking and its applications: "Data Thinking: Framework for data-based solutions" by StackFuel "What is Data Thinking? A modern approach to designing a data strategy" by Mantel Group "Data Science Thinking" by SpringerLink These sources provide detailed insights into the methodology, phases, and benefits of adopting Data Thinking in organizational processes.
Instance selection
Instance selection (or dataset reduction, or dataset condensation) is an important data pre-processing step that can be applied in many machine learning (or data mining) tasks. Approaches for instance selection can be applied for reducing the original dataset to a manageable volume, leading to a reduction of the computational resources that are necessary for performing the learning process. Algorithms of instance selection can also be applied for removing noisy instances, before applying learning algorithms. This step can improve the accuracy in classification problems. Algorithm for instance selection should identify a subset of the total available data to achieve the original purpose of the data mining (or machine learning) application as if the whole data had been used. Considering this, the optimal outcome of IS would be the minimum data subset that can accomplish the same task with no performance loss, in comparison with the performance achieved when the task is performed using the whole available data. Therefore, every instance selection strategy should deal with a trade-off between the reduction rate of the dataset and the classification quality. == Instance selection algorithms == The literature provides several different algorithms for instance selection. They can be distinguished from each other according to several different criteria. Considering this, instance selection algorithms can be grouped in two main classes, according to what instances they select: algorithms that preserve the instances at the boundaries of classes and algorithms that preserve the internal instances of the classes. Within the category of algorithms that select instances at the boundaries it is possible to cite DROP3, ICF and LSBo. On the other hand, within the category of algorithms that select internal instances, it is possible to mention ENN and LSSm. In general, algorithm such as ENN and LSSm are used for removing harmful (noisy) instances from the dataset. They do not reduce the data as the algorithms that select border instances, but they remove instances at the boundaries that have a negative impact on the data mining task. They can be used by other instance selection algorithms, as a filtering step. For example, the ENN algorithm is used by DROP3 as the first step, and the LSSm algorithm is used by LSBo. There is also another group of algorithms that adopt different selection criteria. For example, the algorithms LDIS, CDIS and XLDIS select the densest instances in a given arbitrary neighborhood. The selected instances can include both, border and internal instances. The LDIS and CDIS algorithms are very simple and select subsets that are very representative of the original dataset. Besides that, since they search by the representative instances in each class separately, they are faster (in terms of time complexity and effective running time) than other algorithms, such as DROP3 and ICF. Besides that, there is a third category of algorithms that, instead of selecting actual instances of the dataset, select prototypes (that can be synthetic instances). In this category it is possible to include PSSA, PSDSP and PSSP. The three algorithms adopt the notion of spatial partition (a hyperrectangle) for identifying similar instances and extract prototypes for each set of similar instances. In general, these approaches can also be modified for selecting actual instances of the datasets. The algorithm ISDSP adopts a similar approach for selecting actual instances (instead of prototypes).
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.