AI Email Letter Generator

AI Email Letter Generator — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

• 

  Semantic analytics

  Semantic analytics, also termed semantic relatedness, is the use of ontologies to analyze content in web resources. This field of research combines text analytics and Semantic Web technologies like RDF. Semantic analytics measures the relatedness of different ontological concepts. Some academic research groups that have active project in this area include Kno.e.sis Center at Wright State University among others. == History == An important milestone in the beginning of semantic analytics occurred in 1996, although the historical progression of these algorithms is largely subjective. In his seminal study publication, Philip Resnik established that computers have the capacity to emulate human judgement. Spanning the publications of multiple journals, improvements to the accuracy of general semantic analytic computations all claimed to revolutionize the field. However, the lack of a standard terminology throughout the late 1990s was the cause of much miscommunication. This prompted Budanitsky & Hirst to standardize the subject in 2006 with a summary that also set a framework for modern spelling and grammar analysis. In the early days of semantic analytics, obtaining a large enough reliable knowledge bases was difficult. In 2006, Strube & Ponzetto demonstrated that Wikipedia could be used in semantic analytic calculations. The usage of a large knowledge base like Wikipedia allows for an increase in both the accuracy and applicability of semantic analytics. == Methods == Given the subjective nature of the field, different methods used in semantic analytics depend on the domain of application. No singular methods is considered correct, however one of the most generally effective and applicable method is explicit semantic analysis (ESA). ESA was developed by Evgeniy Gabrilovich and Shaul Markovitch in the late 2000s. It uses machine learning techniques to create a semantic interpreter, which extracts text fragments from articles into a sorted list. The fragments are sorted by how related they are to the surrounding text. Latent semantic analysis (LSA) is another common method that does not use ontologies, only considering the text in the input space. == Applications == Entity linking Ontology building / knowledge base population Search and query tasks Natural language processing Spoken dialog systems (e.g., Amazon Alexa, Google Assistant, Microsoft's Cortana) Artificial intelligence Knowledge management The application of semantic analysis methods generally streamlines organizational processes of any knowledge management system. Academic libraries often use a domain-specific application to create a more efficient organizational system. By classifying scientific publications using semantics and Wikipedia, researchers are helping people find resources faster. Search engines like Semantic Scholar provide organized access to millions of articles.

  Read more →
• 

  Vans challenge

  The Vans challenge is a viral internet challenge that began in March 2019 where people show their Vans shoes landing right-side up after tossing them in the air. The viral sensation reportedly started after a Twitter user shared a video of the occurrence, which was captioned: “Did you know it doesn’t matter how you throw your Vans they will land facing up.” Since then, multiple people on social media posted similar videos of them throwing their Vans in the air and landing right-side up, along with Crocs, UGG boots, and other popular shoes. This theory proved false, as these shoes have not always landed facing up after tossing them.

  Read more →
• 

  Social media newsroom

  A social media newsroom is a company resource, set up to increase the functionality and usability of the traditional online newsroom. Social media newsrooms (SMNs) are intended to encourage dialogue and information sharing. Unlike online newsrooms, content is accessible to more than just journalists, but to all those with whom the company engages such as bloggers, their prospects, customers, business partners and investors. It gives these stakeholders access to news, public relations announcements, images, audio, video and other multimedia files. In addition to posting press releases and corporate news, companies can integrate other social content from sites such as YouTube, Flickr and Slideshow as well as streams from corporate Twitter accounts. Traditional tools for journalists such as corporate fast facts, leadership information, a multimedia library, financial information, awards and other recent media coverage are also included in an SMN. Examples of companies effectively using social media newsrooms include Opel Group, Pressat, First Direct, MyNewsdesk, Scania and Newport Beach.

  Read more →
• 

  European Grid Infrastructure

  EGI (originally an initialism for European Grid Infrastructure) is a federation of computing and storage resource providers that deliver advanced computing and data analytics services for research and innovation. The Federation is governed by its participants represented in the EGI Council and coordinated by the EGI Foundation. As of 2024, the EGI Federation supports 160 scientific communities worldwide and over 95,000 users in their intensive data analysis. The most significant scientific communities supported by EGI in 2022 were Medical and Health Sciences, High Energy Physics, and Engineering and Technology. The EGI Federation provideds services through over 150 data centres, of which 25 are cloud sites, in 43 countries and 64 Research Infrastructures (4 of which are members of the Federation). == Name == Originally, EGI stood for European Grid Infrastructure. This reflected its focus on providing access to high-throughput computing resources across Europe using Grid computing techniques. However, as EGI's service offerings expanded beyond traditional grid computing, particularly with the incorporation of federated cloud services, the original meaning of the acronym became less accurate. To emphasise the broader scope of EGI's services and avoid any confusion associated with the outdated term "grid," it is recommended to refer to EGI simply as EGI. == Structure == === EGI Federation === The EGI Federation delivers a scalable digital research infrastructure (e-infrastructure), empowering tens of thousands of researchers across diverse scientific disciplines. Through the EGI Federation, researchers gain access to advanced computing and data analytics capabilities, including large-scale data analysis, while benefiting from the collaborative efforts of hundreds of service providers from both public and private sectors, consolidating resources from Europe and beyond. Overall, the EGI Federation offers a range of services, encompassing distributed high-throughput computing and cloud computing, storage and data management capabilities, co-development of new solutions, expert support, and comprehensive training opportunities. This ecosystem propels collaboration, scientific progress and innovation. === EGI Foundation === The EGI Foundation is the coordinating body of the EGI Federation. It was established in 2010 with headquarters in Amsterdam, Netherlands. The Foundation coordinates the research and innovation efforts of its members, spanning technical areas critical to data-intensive science, including large-scale data processing and analysis, distributed Artificial Intelligence/Machine Learning, federated Identity and access management and the application of digital twins for research. The day-to-day running of the EGI Foundation is supervised by the Executive Board. The board’s members work closely with the EGI Director on operational, technical and financial issues. The Executive Board’s members are appointed by the EGI Council for a two-year term. === EGI Council === The EGI Council is responsible for defining the strategic direction of the EGI Federation. The Council acts as the senior decision-making and supervisory authority of the EGI Foundation, with a mandate to define the strategic direction of the entire EGI ecosystem. === EGI Services === EGI offers a suite of services to support data-intensive research. These services include compute resources, orchestration tools, storage and data management solutions, training programmes, security and identity services, and applications. Compute resources encompass cloud compute, cloud container compute, high-throughput compute, and software distribution. Orchestration tools include the Workload Manager and infrastructure manager. Storage and data management solutions include online storage, data transfer, and DataHub. Training programmes cover FitSM, ISO 27001, and general training infrastructure. EGI Check-in and Secrets Store are key security and identity services, while applications such as Notebooks and Replay enhance research productivity. In addition to services for Research, EGI also provides services for Federation and Business. Services for Federation are designed to help resource providers and user communities collaborate and share resources. EGI also offers a range of services to support businesses in their digital transformation. Through the EGI Digital Innovation Hub (EGI DIH), companies can access advanced computing resources, networking, funding and training opportunities, collaborate with research institutions, and test solutions before investing. == History == In 2002, the first large-scale experimental facility was successfully demonstrated by the DataGrid project under the lead of CERN with tens of technical architects from the major High Energy Physics institutes in the world. For the first time, distributed computing was applied to data-intensive processing. It aimed at developing a large-scale computational grid to facilitate distributed data-intensive scientific computing across High Energy Physics, Earth Observation, and Biology science applications. On 28 February 2003, the first software release of LCG-MW was published. gLite, the Lightweight Middleware for Grid Computing and LCG, Large Hadron Collider Computing Grid, are the cornerstone of the Worldwide LHC Computing Grid, which expanded over time towards the EGI Federation. 2004 marks the year of the first pilot infrastructure, seeing the participation of CERN and data centres in the United Kingdom, Spain, Germany, the Netherlands, France, Canada, Russia, Bulgaria, the Asia-Pacific region and Switzerland. Over the years, the infrastructure has grown into a federation of 128 data centres and 25 cloud providers serving more than 95,000 users worldwide. In 2004, the first data processing tasks started being formally recorded in a central accounting system. The EGI Accounting Portal provides the accounting data for Compute, Storage and Data services gathered from the data centres of the EGI Federation. A few years later, in 2010, EGI was established as the coordinating body of the EGI Federation to build an integrated pan-European infrastructure to support European research communities primarily. In the same year, EGI launched the flagship project EGI Inspire. That project brought together European organisations to establish a sustainable European Grid Infrastructure for large-scale data analysis. The success of the project was due to the adoption of a distributed computing model to solve big data problems. Moreover, EGI-Inspire harmonised operational policies across its federation of affiliated data centres and cloud service providers worldwide, integrating e-infrastructures from 57 countries. The EGI Federation was the first to apply federation to cloud provisioning, opening a new avenue in large-scale interactive data analysis. In 2015, within EGI Engage, opening a new avenue in large-scale interactive data analysis. The EGI Federated Cloud is an IaaS-type cloud, incorporating academic and private clouds and virtualised resources built using open standards. Its development is driven by the needs of the scientific community, resulting in a novel research e-infrastructure that relies on well-established federated operational services, making EGI a dependable resource for scientific endeavours. In 2015, EGI, EUDAT, GÉANT, LIBER and OpenAIRE published a position paper on a 'European Open Science Cloud for Research'. With the EOSC-hub project in 2016, EGI started contributing in practice to shaping the services for the EOSC. The work continued with a series of projects, like EOSC Enhance, EOSC Life and EOSC Synergy. With EGI-ACE and its contribution to EOSC Future, EGI has continued developing the EOSC Core. In early 2024, EGI started providing services to the EOSC EU Node, and with EOSC Beyond it will provide new EOSC Core capabilities and pilot additional national and thematic nodes. In October 2024, EUDAT, GÉANT, OpenAIRE, PRACE and EGI signed a Memorandum of Understanding establishing the European e-Infrastructures Assembly. This collaboration will bolster the position and promote the services of e-Infrastructures, empowering researchers across Europe to drive innovation and advance scientific discovery.

  Read more →
• 

  Shaded Picture System

  The Shaded Picture System was a 3D raster computer display processor introduced by Evans & Sutherland in October 1973. The Shaded Picture System was the first general-purpose, commercially available raster computer graphics display processor capable of real-time, shaded 3D graphics. It could only display black and white graphics at a resolution of 256 by 256. It was extremely expensive, and very few units were ever sold. == History == The principles of shaded, hidden-line true 3D graphics were pioneered at the University of Utah in 1967. However, this algorithm was slow and would take several minutes to produce an image. In 1970, Gary Watkins developed a FORTRAN simulator of a faster algorithm that would theoretically generate shaded 3D images in real-time, "if implemented in suitable hardware". The simulator itself was still not capable of real-time shaded 3D image rendering. Evans & Sutherland developed a functional prototype of this "suitable hardware", which was later sold as the Shaded Picture System in 1973. About a year earlier in 1972, Evans & Sutherland sold the first and only CT1 to Case Western Reserve University. The CT1, or Continuous Tone 1, was a specialized image generator, not meant as a marketable or mass-produced product. At the time, the CT1, along with G.E./NASA's upgraded Electronic Scene Generator from 1971, would have been the only real-time raster graphics systems sold to customers comparable to the Shaded Picture System, although both the CT1 and Electronic Scene Generator were intentionally produced as one-off products and specialized for the needs of their customers. The Shaded Picture System, in contrast, was intentionally marketed.In early 1975, Evans & Sutherland demonstrated a random-access video frame buffer using relatively low-cost semiconductor memory, which was much more capable than the Shaded Picture System. When interfaced with a (non-shaded) E&S Picture System, the frame buffer had a resolution of 512 by 512 in grayscale and partial color capabilities. By the end of 1975, this frame buffer was commercially available.

  Read more →
• 

  Eduroam

  eduroam (a portmanteau of education and roaming) is an international Wi-Fi internet access roaming service for users in research, higher education and further education. It provides researchers, teachers, and students network access when visiting an institution other than their own. Users are authenticated with credentials from their home institution, regardless of the location of the eduroam access point. Authorization to access the Internet and other resources are handled by the visited institution. Users do not have to pay to use eduroam. In some countries, Internet access via eduroam is also available at other locations than the participating institutions, e.g. in libraries, public buildings, railway stations, city centres and airports. It is also available at many primary and secondary education institutions in Brazil and the US. == History == The eduroam initiative started in 2002 when during the preparations for the creation of TERENA's task force TF-Mobility, Klaas Wierenga of SURFnet shared the idea of combining a RADIUS-based infrastructure with IEEE 802.1X technology to provide roaming network access across research and education networks. Initially, the service was joined by institutions in the Netherlands, Germany, Finland, Portugal, Croatia and the United Kingdom. Later, other NRENs in Europe embraced the idea and started joining the infrastructure, which was then called eduroam. Since 2004, the European Union co-funded further research and development work related to the eduroam service through the GN2 and GN3 projects. From September 2007, the European Union also funded through these projects the continued operation and maintenance of the eduroam service at the European level. The first non-European country to join eduroam was Australia, in December 2004. In Canada, eduroam started as an initiative of the University of British Columbia, which was later taken over by CANARIE as a service of its Canadian Access Federation. In the United States, eduroam was initially a pilot project between the National Science Foundation and the University of Tennessee (UTK). In 2012, Internet2 announced the addition of eduroam to its NET+ service offerings. AnyRoam LLC, a private company, was formed by former UTK staff to serve as an Internet2 active corporate member administering the US top-level servers. In 2021, Internet2 assumed direct management of the eduroam service for US-based organizations. == Technology == The eduroam service uses IEEE 802.1X as the authentication method and a hierarchical system of RADIUS servers. The hierarchy typically consists of RADIUS servers at the participating institutions, national RADIUS servers run by the National Roaming Operators, and regional top-level RADIUS servers for individual world regions. In some cases, institutions contact each other directly via DNS lookups () When a user visits a remote institution, the user's device presents their credentials to the local RADIUS server. That RADIUS server discovers that it is not responsible for the realm of the user's home institution and proxies the access request to another RADIUS server, typically the national RADIUS server. If the visited institution is in a different country than the home institution, the request is in turn proxied to the regional top-level RADIUS server, and then to the national RADIUS server of the user's home country. That national server forwards the credentials to the home institution, where they are verified. The RADIUS response travels back over the proxy-hierarchy to the visited institution and the user is granted access. In eduroam, the user credentials are always presented in the form of an EAP method (). The EAP method is responsible for ensuring that the users credentials are secure, and private. The users credentials can then travel via a number of intermediate servers, not under the control of the home institution of the user. This requirement limits the types of EAP methods that can be used. EAP methods which do not provide for security or privacy of user credentials cannot be used in eduroam. The most commonly used EAP methods in eduroam are EAP-TLS, PEAP, and EAP-TTLS. The methods used generally fall into two broad categories: those that use credentials in the form of some public-key mechanism with certificates and those that use so-called tunnelled authentication with "inner" passwords or other credentials. Most institutions use a tunnelled authentication method that requires a server certificate. These server certificates are used to set up a secure tunnel between the mobile device and the authentication server, through which the user credentials (e.g. name and password) are securely transported. A complication arises if the user's home institution does not use a two-letter country-code top-level domain as part of its realm, but a generic top-level domain such as .edu or .org. By inspection of such realms, it is not possible to determine which national RADIUS server the request should be routed to. Such domains will thus, by default, fail to work in international roaming. The workaround for this problem involves the creation of exceptions in the international RADIUS request routing tables; however, this workaround does not scale as the number of exception entries grows. Several solutions have been proposed to eliminate this workaround in the future, the most promising of which is RADIUS over TLS with Dynamic Discovery, which does not rely on static routing tables inside a RADIUS server configuration to route requests to their proper destination. Instead, the participating institution adds one NAPTR DNS resource record to its own domain's DNS zone, which states by which server eduroam authentication for the domain is handled. == Governance == GÉANT has established a lightweight global governance structure. Recognising the large variety in the organisation and funding of research and education (networking) in different countries and regions, rules imposed on the operations of eduroam are limited to technical and administrative requirements that are necessary to ensure the smooth and secure operations of eduroam worldwide. Moreover, the eduroam operators have the leading role in creating and maintaining the rules of the global eduroam governance. The Global eduroam Governance Committee (GeGC) has the central role in the global eduroam governance structure. While its structure has evolved over time, it presently has three representatives from each of five regions — mirroring those used by the Regional Internet registries — serving a two-year term. In addition, GÉANT may appoint one or more experts as non-voting members of the GeGC. == Geographical deployment == eduroam is available at selected locations in countries with a National Roaming Operator that has signed the eduroam Compliance Statement. Those sixty-seven countries are listed below. In addition, there may be pilot deployments in countries that are in the process of joining eduroam. === Middle East === eduroam is deployed in: === Europe === The NRENs that are members of the consortium of the GN3 project have joined the European eduroam confederation by signing the confederation's policy that requires its members to comply with a set of technical and organisational requirements, which are more specific than those in the global eduroam Compliance Statement. As a consequence, eduroam is deployed in the following countries: In addition, three NRENs that are associate members of the consortium of the GN3 project without voting rights joined the European eduroam confederation; they represent Belarus (UIIP), Moldova (RENAM) and Russia (Joint Supercomputer Center of the Russian Academy of Sciences). Finally, five NRENs not involved in the GN3 project joined the European eduroam confederation on a voluntary basis, enabling the deployment of the service in: The European top-level RADIUS servers are operated by SURFnet and Forskningsnettet. === Asia-Pacific === eduroam is deployed in the following countries and economies: The Asia-Pacific top-level RADIUS servers are operated by AARNet and by the University of Hong Kong. === North America === eduroam is deployed in: === Latin America === eduroam is deployed in: === Africa === eduroam is deployed in: The inter-African RADIUS servers are operated by West-African research and education network WACREN, the UbuntuNet Alliance and TENET.

  Read more →
• 

  List of cryptosystems

  A cryptosystem is a set of cryptographic algorithms that map ciphertexts and plaintexts to each other. == Private-key cryptosystems == Private-key cryptosystems use the same key for encryption and decryption. Caesar cipher Substitution cipher Enigma machine Data Encryption Standard Twofish Serpent Camellia Salsa20 ChaCha20 Blowfish CAST5 Kuznyechik RC4 3DES Skipjack Safer IDEA Advanced Encryption Standard, also known as AES and Rijndael. == Public-key cryptosystems == Public-key cryptosystems use a public key for encryption and a private key for decryption. Diffie–Hellman key exchange RSA encryption Rabin cryptosystem Schnorr signature ElGamal encryption Elliptic-curve cryptography Lattice-based cryptography McEliece cryptosystem Multivariate cryptography Isogeny-based cryptography

  Read more →
• 

  Key (cryptography)

  A key in cryptography is a piece of information, usually a string of numbers or letters that are stored in a file, which, when processed through a cryptographic algorithm, can encode or decode cryptographic data. Based on the used method, the key can be different sizes and varieties, but in all cases, the strength of the encryption relies on the security of the key being maintained. A key's security strength is dependent on its algorithm, the size of the key, the generation of the key, and the process of key exchange. == Scope == The key is what is used to encrypt data from plaintext to ciphertext. There are different methods for utilizing keys and encryption. === Symmetric cryptography === Symmetric cryptography refers to the practice of the same key being used for both encryption and decryption. === Asymmetric cryptography === Asymmetric cryptography has separate keys for encrypting and decrypting. These keys are known as the public and private keys, respectively. == Purpose == Since the key protects the confidentiality and integrity of the system, it is important to be kept secret from unauthorized parties. With public key cryptography, only the private key must be kept secret, but with symmetric cryptography, it is important to maintain the confidentiality of the key. Kerckhoff's principle states that the entire security of the cryptographic system relies on the secrecy of the key. == Key sizes == Key size is the number of bits in the key defined by the algorithm. This size defines the upper bound of the cryptographic algorithm's security. The larger the key size, the longer it will take before the key is compromised by a brute force attack. Since perfect secrecy is not feasible for key algorithms, researches are now more focused on computational security. In the past, keys were required to be a minimum of 40 bits in length, however, as technology advanced, these keys were being broken quicker and quicker. As a response, restrictions on symmetric keys were enhanced to be greater in size. Currently, 2048 bit RSA is commonly used, which is sufficient for current systems. However, current RSA key sizes would all be cracked quickly with a powerful quantum computer. "The keys used in public key cryptography have some mathematical structure. For example, public keys used in the RSA system are the product of two prime numbers. Thus public key systems require longer key lengths than symmetric systems for an equivalent level of security. 3072 bits is the suggested key length for systems based on factoring and integer discrete logarithms which aim to have security equivalent to a 128 bit symmetric cipher." == Key generation == To prevent a key from being guessed, keys need to be generated randomly and contain sufficient entropy. The problem of how to safely generate random keys is difficult and has been addressed in many ways by various cryptographic systems. A key can directly be generated by using the output of a Random Bit Generator (RBG), a system that generates a sequence of unpredictable and unbiased bits. A RBG can be used to directly produce either a symmetric key or the random output for an asymmetric key pair generation. Alternatively, a key can also be indirectly created during a key-agreement transaction, from another key or from a password. Some operating systems include tools for "collecting" entropy from the timing of unpredictable operations such as disk drive head movements. For the production of small amounts of keying material, ordinary dice provide a good source of high-quality randomness. == Establishment scheme == The security of a key is dependent on how a key is exchanged between parties. Establishing a secured communication channel is necessary so that outsiders cannot obtain the key. A key establishment scheme (or key exchange) is used to transfer an encryption key among entities. Key agreement and key transport are the two types of a key exchange scheme that are used to be remotely exchanged between entities . In a key agreement scheme, a secret key, which is used between the sender and the receiver to encrypt and decrypt information, is set up to be sent indirectly. All parties exchange information (the shared secret) that permits each party to derive the secret key material. In a key transport scheme, encrypted keying material that is chosen by the sender is transported to the receiver. Either symmetric key or asymmetric key techniques can be used in both schemes. The Diffie–Hellman key exchange and Rivest-Shamir-Adleman (RSA) are the most two widely used key exchange algorithms. In 1976, Whitfield Diffie and Martin Hellman constructed the Diffie–Hellman algorithm, which was the first public key algorithm. The Diffie–Hellman key exchange protocol allows key exchange over an insecure channel by electronically generating a shared key between two parties. On the other hand, RSA is a form of the asymmetric key system which consists of three steps: key generation, encryption, and decryption. Key confirmation delivers an assurance between the key confirmation recipient and provider that the shared keying materials are correct and established. The National Institute of Standards and Technology recommends key confirmation to be integrated into a key establishment scheme to validate its implementations. == Management == Key management concerns the generation, establishment, storage, usage and replacement of cryptographic keys. A key management system (KMS) typically includes three steps of establishing, storing and using keys. The base of security for the generation, storage, distribution, use and destruction of keys depends on successful key management protocols. == Key vs password == A password is a memorized series of characters including letters, digits, and other special symbols that are used to verify identity. It is often produced by a human user or a password management software to protect personal and sensitive information or generate cryptographic keys. Passwords are often created to be memorized by users and may contain non-random information such as dictionary words. On the other hand, a key can help strengthen password protection by implementing a cryptographic algorithm which is difficult to guess or replace the password altogether. A key is generated based on random or pseudo-random data and can often be unreadable to humans. A password is less safe than a cryptographic key due to its low entropy, randomness, and human-readable properties. However, the password may be the only secret data that is accessible to the cryptographic algorithm for information security in some applications such as securing information in storage devices. Thus, a deterministic algorithm called a key derivation function (KDF) uses a password to generate the secure cryptographic keying material to compensate for the password's weakness. Various methods such as adding a salt or key stretching may be used in the generation.

  Read more →
• 

  Tapingo

  Tapingo was an American mobile commerce application that offers advance ordering for pickup and food delivery services for college campuses. The company was acquired by Grubhub in September 2018 for approximately $150 million. Following the acquisition, Tapingo’s campus-ordering functionality was integrated into the Grubhub app (Grubhub Campus Dining) and the Tapingo service was discontinued during 2019. Tapingo is differentiated from other on-demand delivery/logistics companies, such as Waiter.com, Postmates, or DoorDash, by focusing its efforts on serving the college market. Through Tapingo, users can browse menus, place orders, pay for the meal and schedule the pickup or have it delivered. On certain campuses, students are able to use their university's meal dollars to pay for food. In the spring of 2012, Tapingo first launched its services on five campuses (Santa Clara University, Loyola Marymount University, Biola University, the University of Maine, and California Lutheran University), and has since expanded to more than 200 college campuses across the U.S. and Canada, serving 100 markets. To date, Tapingo has received venture funding from Carmel Ventures, Khosla Ventures, Kinzon Capital, DCM Ventures and Qualcomm Ventures. In fall 2015, Tapingo announced expansion plans through major partnership deals with national brands like Chipotle Mexican Grill and 7-Eleven, regional restaurants such as Taco Bueno, and global foodservice provider Aramark.

  Read more →
• 

  Cipher

  In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is encipherment. To encipher or encode is to convert information into cipher or code. In common parlance, "cipher" is synonymous with "code", as they are both a set of steps that encrypt a message; however, the concepts are distinct in cryptography, especially classical cryptography. Codes generally substitute different length strings of characters in the output, while ciphers generally substitute the same number of characters as are input. A code maps one meaning with another. Words and phrases can be coded as letters or numbers. Codes typically have direct meaning from input to key. Codes primarily function to save time. Ciphers are algorithmic. The given input must follow the cipher's process to be solved. Ciphers are commonly used to encrypt written information. Codes operated by substituting according to a large codebook which linked a random string of characters or numbers to a word or phrase. For example, "UQJHSE" could be the code for "Proceed to the following coordinates.". When using a cipher the original information is known as plaintext, and the encrypted form as ciphertext. The ciphertext message contains all the information of the plaintext message, but is not in a format readable by a human or computer without the proper mechanism to decrypt it. The operation of a cipher usually depends on a piece of auxiliary information, called a key (or, in traditional NSA parlance, a cryptovariable). The encrypting procedure is varied depending on the key, which changes the detailed operation of the algorithm. A key must be selected before using a cipher to encrypt a message, with some exceptions such as ROT13 and Atbash. Most modern ciphers can be categorized in several ways: By whether they work on blocks of symbols usually of a fixed size (block ciphers), or on a continuous stream of symbols (stream ciphers). By whether the same key is used for both encryption and decryption (symmetric key algorithms), or if a different key is used for each (asymmetric key algorithms). If the algorithm is symmetric, the key must be known to the recipient and sender and to no one else. If the algorithm is an asymmetric one, the enciphering key is different from, but closely related to, the deciphering key. If one key cannot be deduced from the other, the asymmetric key algorithm has the public/private key property and one of the keys may be made public without loss of confidentiality. == Etymology == Originating from the Sanskrit word for zero शून्य (śuṇya), via the Arabic word صفر (ṣifr), the word "cipher" spread to Europe as part of the Arabic numeral system during the Middle Ages. The Roman numeral system lacked the concept of zero, and this limited advances in mathematics. In this transition, the word was adopted into Medieval Latin as cifra, and then into Middle French as cifre. This eventually led to the English word cipher (also spelt cypher). One theory for how the term came to refer to encoding is that the concept of zero was confusing to Europeans, and so the term came to refer to a message or communication that was not easily understood. The term cipher was later also used to refer to any Arabic digit, or to calculation using them, so encoding text in the form of Arabic numerals is literally converting the text to "ciphers". == Versus codes == In casual contexts, "code" and "cipher" can typically be used interchangeably; however, the technical usages of the words refer to different concepts. Codes contain meaning; words and phrases are assigned to numbers or symbols, creating a shorter message. An example of this is the commercial telegraph code which was used to shorten long telegraph messages which resulted from entering into commercial contracts using exchanges of telegrams. Another example is given by whole word ciphers, which allow the user to replace an entire word with a symbol or character, much like the way written Japanese utilizes Kanji (meaning Chinese characters in Japanese) characters to supplement the native Japanese characters representing syllables. An example using English language with Kanji could be to replace "The quick brown fox jumps over the lazy dog" by "The quick brown 狐 jumps 上 the lazy 犬". Stenographers sometimes use specific symbols to abbreviate whole words. Ciphers, on the other hand, work at a lower level: the level of individual letters, small groups of letters, or, in modern schemes, individual bits and blocks of bits. Some systems used both codes and ciphers in one system, using superencipherment to increase the security. In some cases the terms codes and ciphers are used synonymously with substitution and transposition, respectively. Historically, cryptography was split into a dichotomy of codes and ciphers, while coding had its own terminology analogous to that of ciphers: "encoding, codetext, decoding" and so on. However, codes have a variety of drawbacks, including susceptibility to cryptanalysis and the difficulty of managing a cumbersome codebook. Because of this, codes have fallen into disuse in modern cryptography, and ciphers are the dominant technique. == Types == There are a variety of different types of encryption. Algorithms used earlier in the history of cryptography are substantially different from modern methods, and modern ciphers can be classified according to how they operate and whether they use one or two keys. === Historical === The Caesar Cipher is one of the earliest known cryptographic systems. Julius Caesar used a cipher that shifts the letters in the alphabet in place by three and wrapping the remaining letters to the front to write to Marcus Tullius Cicero in approximately 50 BC. Historical pen and paper ciphers used in the past are sometimes known as classical ciphers. They include simple substitution ciphers (such as ROT13) and transposition ciphers (such as a Rail Fence Cipher). For example, "GOOD DOG" can be encrypted as "PLLX XLP" where "L" substitutes for "O", "P" for "G", and "X" for "D" in the message. Transposition of the letters "GOOD DOG" can result in "DGOGDOO". These simple ciphers and examples are easy to crack, even without plaintext-ciphertext pairs. In the 1640s, the Parliamentarian commander, Edward Montagu, 2nd Earl of Manchester, developed ciphers to send coded messages to his allies during the English Civil War. The English theologian John Wilkins published a book in 1641 titled "Mercury, or The Secret and Swift Messenger" and described a musical cipher wherein letters of the alphabet were substituted for music notes. This species of melodic cipher was depicted in greater detail by author Abraham Rees in his book Cyclopædia (1778). Simple ciphers were replaced by polyalphabetic substitution ciphers (such as the Vigenère) which changed the substitution alphabet for every letter. For example, "GOOD DOG" can be encrypted as "PLSX TWF" where "L", "S", and "W" substitute for "O". With even a small amount of known or estimated plaintext, simple polyalphabetic substitution ciphers and letter transposition ciphers designed for pen and paper encryption are easy to crack. It is possible to create a secure pen and paper cipher based on a one-time pad, but these have other disadvantages. During the early twentieth century, electro-mechanical machines were invented to do encryption and decryption using transposition, polyalphabetic substitution, and a kind of "additive" substitution. In rotor machines, several rotor disks provided polyalphabetic substitution, while plug boards provided another substitution. Keys were easily changed by changing the rotor disks and the plugboard wires. Although these encryption methods were more complex than previous schemes and required machines to encrypt and decrypt, other machines such as the British Bombe were invented to crack these encryption methods. === Modern === Modern encryption methods can be divided by two criteria: by type of key used, and by type of input data. By type of key used ciphers are divided into: symmetric key algorithms (Private-key cryptography), where one same key is used for encryption and decryption, and asymmetric key algorithms (Public-key cryptography), where two different keys are used for encryption and decryption. In a symmetric key algorithm (e.g., DES and AES), the sender and receiver must have a shared key set up in advance and kept secret from all other parties; the sender uses this key for encryption, and the receiver uses the same key for decryption. The design of AES (Advanced Encryption System) was beneficial because it aimed to overcome the flaws in the design of the DES (Data encryption standard). AES's designer's claim that the common means of modern cipher cryptanalytic attacks are ineffective against AES due to its design structure. Ciphers can be distinguished into two types by the type o

  Read more →
• 

  Social media measurement

  Social media measurement, also called social media controlling, is the management practice of evaluating successful social media communications of brands, companies, or other organizations. Key performance indicators may be measured by extracting information from social media channels, such as blogs, wikis, micro-blogs such as Twitter, social networking sites, or video/photo sharing websites, forums from time to time. It is also used by companies to gauge current trends in the industry. The process first gathers data from different websites and then performs analysis based on different metrics like time spent on the page, click through rate, content share, comments, text analytics to identify positive or negative emotions about the brand. Some other social media metrics include share of voice, owned mentions, and earned mentions. The social media measurement process starts with defining a goal that needs to be achieved and defining the expected outcome of the process. The expected outcome varies per the goal and is usually measured by a variety of metrics. This is followed by defining possible social strategies to be used to achieve the goal. Then the next step is designing strategies to be used and setting up configuration tools that ease the process of collecting the data. In the next step, strategies and tools are deployed in real-time. This step involves conducting Quality Assurance tests of the methods deployed to collect the data. And in the final step, data collected from the system is analyzed and if the need arises, it is refined on the run time to enhance the methodologies used. The last step ensures that the result obtained is more aligned with the goal defined in the first step. == Data Acquisition == Acquiring data from social media is in demand of an exploring the user participation and population with the purpose of retrieving and collecting so many kinds of data(ex: comments, downloads etc.). There are several prevalent techniques to acquire data such as Network traffic analysis, Ad-hoc application and Crawling Network Traffic Analysis - Network traffic analysis is the process of capturing network traffic and observing it closely to determine what is happening in the network. It is primarily done to improve the performance, security and other general management of the network. However concerned about the potential tort of privacy on the Internet, network traffic analysis is always restricted by the government. Furthermore, high-speed links are not adaptable to traffic analysis because of the possible overload problem according to the packet sniffing mechanism Ad-hoc Application - Ad-hoc application is a kind of application that provides services and games to social network users by developing the APIs offered by social network companies (Facebook Developer Platform). The infrastructure of Ad-hoc application allows the user to interact with the interface layer instead of the application servers. The API provides a path for application to access information after the user login. Moreover, the size of the data set collected vary with the popularity of the social media platform i.e. social media platforms having high number of users will have more data than platforms having less user base. Scraping is a process in which the APIs collect online data from social media. The data collected from Scraping is in raw format. However, having access to these types of data is a bit difficult because of its commercial value. Crawling - Crawling is a process in which a web crawler creates indexes of all the words in a web-page, stores them, then follows all the hyperlinks and indexes on that page and again stores them. It is the most popular technique for data acquisition and is also well known for its easy operation based on prevalent Object-Orientated Programming Language (Java or Python etc.). And most important, social network companies (YouTube, Flicker, Facebook, Instagram, etc.) are friendly to crawling techniques by providing public APIs == Applications == === For branding === Monitoring social media allows researchers to find insights into a brand's overall visibility on social media, to measure the impact of campaigns, to identify opportunities for engagement, to assess competitor activity and share of voice, and to detect impending crises. It can also provide valuable information about emerging trends and what consumers and clients think about specific topics, brands or products. This is the work of a cross-section of groups that include market researchers, PR staff, marketing teams, social-engagement, and community staff, agencies and sales teams. Several different providers have developed tools to facilitate the monitoring of a variety of social media channels - from blogging to internet video to internet forums. This allows companies to track what consumers say about their brands and actions. Companies can then react to these conversations and interact with consumers through social media platforms. === In government === Apart from commercial applications, social media monitoring has become a pervasive technique applied by public organizations and governments. Monitoring is a tradition within the public sector, and social-media monitoring provides a real-time approach to detecting and responding to social developments. Governments have come to realize the need for strategies to cope with surprises from the rapid expansion of public issues. Sobkowicz introduced a framework with three blocks of social-media opinion tracking, simulating and forecasting. It includes: real-time detection of emotions, topics and opinions information-flow modelling and agent-based simulation modeling of opinion networks Bekkers introduced the application of social media monitoring in the Netherlands. Public organizations in the Netherlands (such as the Tax Agency and the Education Ministry) have started to use social media monitoring to obtain better insights into the sentiments of target groups. On the one hand, the public sector will be enabled to provide timely and efficient answers to the public by using social media monitoring techniques, but on the other hand, they also have to deal with concerns about ethical issues such as transparency and privacy. == Quantifying social media == Social media management software (SMMS) is an application program or software that facilitates an organization's ability to successfully engage in social media across different communication channels. SMMS is used to monitor inbound and outbound conversations, support customer interaction, audit or document social marketing initiatives and evaluate the usefulness of a social media presence. It can be difficult to measure all social media conversations. Due to privacy settings and other issues, not all social media conversations can be found and reported by monitoring tools. However, whilst social media monitoring cannot give absolute figures, it can be extremely useful for identifying trends and for benchmarking, in addition to the uses mentioned above. These findings can, in turn, influence and shape future business decisions. In order to access social media data (posts, Tweets, and meta-data) and to analyze and monitor social media, many companies use software technologies built for business. These range from in-platform analytics dashboards to dedicated third-party platforms, which offer more advanced capabilities including cross-platform audience intelligence, sentiment analysis, and trend detection at scale. == Location-based == Most social media networks allow users to add a location to their posts (reference all of our feeds). The location can be classified as either 'at-the-location' or 'about-the-location'. "'At-the-location' services can be defined as services where location-based content is created at the geographic location. 'About-the-location' services can be defined as services which are referring to a particular location but the content is not necessarily created in this particular physical place." The added information available from geotagged (link to Geotagging article) posts means that they can be displayed on a map. This means that a location can be used as the start of a social media search rather than a keyword or hashtag. This has major implications for disaster relief, event monitoring, safety and security professionals since a large portion of their job is related to tracking and monitoring specific locations. == Technologies used == Various monitoring platforms use different technologies for social media monitoring and measurement. These technology providers may connect to the API provided by social platforms that are created for 3rd party developers to develop their own applications and services that access data. Facebook's Graph API is one such API that social media monitoring solution products would connect to pull data from. Some social media monitoring and analytics companies use calls to data providers each time an end-user d

  Read more →
• 

  Torus interconnect

  A torus interconnect is a switch-less network topology for connecting processing nodes in a parallel computer system. == Introduction == In geometry, a torus is created by revolving a circle about an axis coplanar to the circle. While this is a general definition in geometry, the topological properties of this type of shape describes the network topology in its essence. === Geometry illustration === In the representations below, the first is a one dimension torus, a simple circle. The second is a two dimension torus, in the shape of a 'doughnut'. The animation illustrates how a two dimension torus is generated from a rectangle by connecting its two pairs of opposite edges. At one dimension, a torus topology is equivalent to a ring interconnect network, in the shape of a circle. At two dimensions, it becomes equivalent to a two dimension mesh, but with extra connection at the edge nodes. === Torus network topology === A torus interconnect is a switch-less topology that can be seen as a mesh interconnect with nodes arranged in a rectilinear array of N = 2, 3, or more dimensions, with processors connected to their nearest neighbors, and corresponding processors on opposite edges of the array connected.[1] In this lattice, each node has 2N connections. This topology is named for the lattice formed in this way, which is topologically homogeneous to an N-dimensional torus. == Visualization == The first 3 dimensions of torus network topology are easier to visualize and are described below: 1D Torus: one dimension, n nodes are connected in closed loop with each node connected to its two nearest neighbors. Communication can take place in two directions, +x and −x. A 1D Torus is the same as ring interconnection. 2D Torus: two dimensions with degree of four, the nodes are imagined laid out in a two-dimensional rectangular lattice of n rows and n columns, with each node connected to its four nearest neighbors, and corresponding nodes on opposite edges connected. Communication can take place in four directions, +x, −x, +y, and −y. The total nodes of a 2D Torus is n2. 3D Torus: three dimensions, the nodes are imagined in a three-dimensional lattice in the shape of a rectangular prism, with each node connected with its six neighbors, with corresponding nodes on opposing faces of the array connected. Each edge consists of n nodes. communication can take place in six directions, +x, −x, +y, −y, +z, −z. Each edge of a 3D Torus consist of n nodes. The total nodes of 3D Torus is n3. ND Torus: N dimensions, each node of an N dimension torus has 2N neighbors, Communication can take place in 2N directions. Each edge consists of n nodes. Total nodes of this torus is nN. The main motivation of having higher dimension of torus is to achieve higher bandwidth, lower latency, and higher scalability. Higher-dimensional arrays are difficult to visualize. The above ruleset shows that each higher dimension adds another pair of nearest neighbor connections to each node. == Performance == A number of supercomputers on the TOP500 list use three-dimensional torus networks, e.g. IBM's Blue Gene/L and Blue Gene/P, and the Cray XT3. IBM's Blue Gene/Q uses a five-dimensional torus network. Fujitsu's K computer and the PRIMEHPC FX10 use a proprietary three-dimensional torus 3D mesh interconnect called Tofu. === 3D Torus performance simulation === Sandeep Palur and Dr. Ioan Raicu from Illinois Institute of Technology conducted experiments to simulate 3D torus performance. Their experiments ran on a computer with 250GB RAM, 48 cores and x86_64 architecture. The simulator they used was ROSS (Rensselaer’s Optimistic Simulation System). They mainly focused on three aspects: Varying network size Varying number of servers Varying message size They concluded that throughput decreases with the increase of servers and network size. Otherwise, throughput increases with the increase of message size. === 6D Torus product performance === Fujitsu Limited developed a 6D torus computer model called "Tofu". In their model, a 6D torus can achieve 100 GB/s off-chip bandwidth, 12 times higher scalability than a 3D torus, and high fault tolerance. The model is used in the K computer and Fugaku. === Cost === While long wrap-around links may be the easiest way to visualize the connection topology, in practice, restrictions on cable lengths often make long wrap-around links impractical. Instead, directly connected nodes—including nodes that the above visualization places on opposite edges of a grid, connected by a long wrap-around link—are physically placed nearly adjacent to each other in a folded torus network. Every link in the folded torus network is very short—almost as short as the nearest-neighbor links in a simple grid interconnect—and therefore low-latency.

  Read more →
• 

  Environmental impact of AI

  The environmental impact of the design, training, deployment and use of artificial intelligence includes the greenhouse gas emissions from generating electricity for data centres and computing hardware, operational and upstream water use, and material impacts from hardware manufacturing, mining and electronic waste. Estimating AI's environmental effects can be difficult because results depend on how impacts are measured, including whether accounting includes only model computation or also data-centre overhead, idle capacity, hardware manufacture, and local electricity supply. As these issues have received greater attention, governments and regulators have increasingly considered data-centre reporting requirements, energy-efficiency standards, and broader transparency measures for AI-related resource use. == Carbon footprint and energy use == AI-related energy use arises at multiple stages, including model training, fine-tuning, inference, storage, networking, and supporting infrastructure such as cooling and power conversion. === Individual level === Published estimates of energy use per AI request vary widely across models, tasks and measurement methods. A benchmark study presented at the 2024 ACM Conference on Fairness, Accountability, and Transparency found substantial differences between task types, with lower energy use for some text tasks and much higher energy use for image generation in the study's test conditions. In that benchmark, simple classification tasks consumed about 0.002–0.007 Wh per prompt on average (about 9% of a smartphone charge for 1,000 prompts), while text generation and text summarisation each used about 0.05 Wh per prompt; image generation averaged 2.91 Wh per prompt, and the least efficient image model in the study used 11.49 Wh per image (roughly equivalent to half a smartphone charge). First-party measurements in production environments have also been published. A 2025 Google study on Gemini assistant serving reported median per-prompt energy, emissions, and water-use estimates under the authors' accounting framework, while noting that different system boundaries can produce substantially different results. The study reported a median text-prompt estimate of about 0.24 Wh, which is roughly as much energy as watching nine seconds of television. The study also stated that software and infrastructure improvements reduced energy use by a factor of 33 and carbon emissions by a factor of 44 for a typical prompt over one year within the authors' framework. Researchers at the University of Michigan measured the energy consumption of various Meta Llama 3.1 models released in 2024 and found that smaller language models (8 billion parameters) use about 114 joules (0.03167 Wh) per response, while larger models (405 billion parameters) require up to 6,700 joules (1.861 Wh) per response. This corresponds to the energy needed to run a microwave oven for roughly one-tenth of a second and eight seconds, respectively. Comparisons between AI systems and human labour for specific tasks have produced mixed results and remain sensitive to assumptions about output quality, workload and system boundaries. A 2024 study in Scientific Reports reported 130 to 2900 times lower estimated carbon emissions for selected AI systems than for human writers and illustrators under its assumptions. A later Scientific Reports paper reported a counterexample for programming tasks under its assumptions, finding 5 to 19 times higher estimated emissions for the evaluated AI system than for human programmers on the benchmark used in that study. === System level === ==== Energy use and efficiency ==== AI electricity intensity depends not only on model architecture but also on hardware and facility efficiency. Data-centre operators commonly report Power usage effectiveness (PUE), which measures the ratio of total facility energy to IT equipment energy; a lower PUE indicates less overhead energy for cooling and other supporting infrastructure. Operators may also publish metrics and case studies on hardware efficiency, cooling systems and power sourcing. In its 2024 environmental report, Google stated that its 2023 total greenhouse gas emissions increased 13% year over year, primarily because of increased data-centre energy consumption and supply-chain emissions, while also reporting lower PUE than industry averages for its own facilities. The International Energy Agency has also reported that data centres remain a relatively small share of global electricity use overall, but that their local effects can be much more pronounced because demand is geographically concentrated. ==== Carbon footprint ==== At system level, AI contributes to rising electricity demand in data centres and related infrastructure. The International Energy Agency estimated that data centres used about 415 TWh of electricity in 2024, or around 1.5% of global electricity consumption, and projected that data-centre electricity use could rise to about 945 TWh by 2030, with AI identified as the main driver of that growth alongside other digital services. The carbon footprint of AI systems depends strongly on electricity sources, hardware efficiency, utilisation rates, and what stages are included in the accounting. Training large models can require substantial electricity, while total lifecycle impacts also depend on deployment scale and the amount of inference performed after training. Early analyses of frontier-model development reported rapid historical growth in training compute for selected systems, although later trends have depended on changes in model design, hardware and efficiency gains. Accounting methods that include upstream or embodied impacts, such as hardware manufacture and facilities construction, can materially affect estimates of AI-related emissions. === Decisions and strategies by individual companies === Large technology companies have reported that the expansion of AI and cloud infrastructure affects their sustainability targets, electricity demand, and resource use. Google, for example, attributed part of its emissions growth in 2023 to increased data-centre energy consumption and supply-chain emissions in its 2024 environmental report. Cloud and AI companies have also announced measures intended to reduce environmental impacts, including investment in more efficient hardware, low-carbon electricity procurement, alternative cooling systems, and water stewardship programmes. The extent, comparability, and third-party verification of such disclosures vary between firms and jurisdictions. == Water usage == Data centres can use water directly for cooling and indirectly through the water used in electricity generation, depending on the local energy mix. Public reporting on data-centre water use has often been inconsistent, making comparisons between operators and regions difficult. To standardise operational reporting, The Green Grid proposed the metric water usage effectiveness (WUE), defined as annual site water use divided by IT equipment energy use. WUE does not by itself measure local water stress, source sustainability, or all upstream water impacts. Studies of AI water use also distinguish between water withdrawal and water consumption. Research on AI-specific water use has argued that the water footprint of AI systems can be difficult to observe and may vary substantially by location, cooling design, and electricity source. A 2025 Communications of the ACM article summarised methods for estimating AI water footprints and emphasised the distinction between water withdrawal and water consumption. Li and colleagues estimated that global AI water withdrawal could reach 4.2–6.6 billion cubic metres in 2027 under the scenarios examined in their article. Using GPT-3, released by OpenAI in 2020, as an example, they estimated that training the model in Microsoft's U.S. data centres could consume about 700,000 litres of onsite water and about 5.4 million litres in total when offsite electricity-related water use was included; they also estimated that 10–50 medium-length GPT-3 responses could consume about 500 mL of water, depending on when and where the model was deployed. Published prompt-level estimates have also varied by system and accounting framework: the 2025 Google study on Gemini assistant serving reported a median text-prompt estimate of about 0.26 mL under its framework. Location can materially affect the significance of data-centre water use. Research on U.S. data centres found that one-fifth of servers' direct water footprint came from moderately to highly water-stressed watersheds, while nearly half of servers were fully or partially powered by plants located in water-stressed regions. A 2025 Reuters report, citing data from Verisk Maplecroft and NatureFinance, said that an average mid-sized data centre uses about 1.4 million litres of water per day for cooling and that Phoenix would experience a 32% increase in annual water stress if currently pl

  Read more →
• 

  Cipher device

  A cipher device was a term used by the US military in the first half of the 20th century to describe a manually operated cipher equipment that converted the plaintext into ciphertext or vice versa. A similar term, cipher machine, was used to describe the cipher equipment that required external power for operation. Cipher box or crypto box is a physical cryptographic device used to encrypt and decrypt messages between plaintext (unencrypted) and ciphertext (encrypted or secret) forms. The ciphertext is suitable for transmission over a channel, such as radio, that might be observed by an adversary the communicating parties wish to conceal the plaintext from.

  Read more →
• 

  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.

  Read more →