AI Coding Claude

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  ELIZA

  ELIZA is an early natural language processing computer program developed from 1964 to 1967 at MIT by Joseph Weizenbaum. Created to explore communication between humans and machines, ELIZA simulated conversation by using a pattern matching and substitution methodology that gave users an illusion of understanding on the part of the program, but gave no response that could be considered really understanding what was being said by either party. Whereas the ELIZA program itself was written (originally) in MAD-SLIP, the pattern matching directives that contained most of its language capability were provided in separate "scripts", represented in a Lisp-like expression. The most famous script, DOCTOR, simulated a psychotherapist of the Rogerian school (in which the therapist often reflects back the patient's words to the patient), and used rules, dictated in the script, to respond with non-directional questions to user inputs. As such, ELIZA was one of the first chatbots (originally "chatterbots") and one of the first programs capable of attempting the Turing test. Weizenbaum intended the program as a method to explore communication between humans and machines. He was surprised that some people, including his secretary, attributed human-like feelings to the computer program, a phenomenon that came to be called the ELIZA effect. Many academics believed that the program would be able to positively influence the lives of many people, particularly those with psychological issues, and that it could aid doctors working on such patients' treatment. While ELIZA was capable of engaging in discourse, it could not converse with true understanding. However, many early users were convinced of ELIZA's intelligence and understanding, despite Weizenbaum's insistence to the contrary. The original ELIZA source code had been missing since its creation in the 1960s, as it was not common to publish articles that included source code at that time. However, more recently the MAD-SLIP source code was discovered in the MIT archives and published on various platforms, such as the Internet Archive. The source code is of high historical interest since it demonstrates not only the specificity of programming languages and techniques at that time, but also the beginning of software layering and abstraction as a means of achieving sophisticated software programming. == Overview == Joseph Weizenbaum's ELIZA, running the DOCTOR script, created a conversational interaction somewhat similar to what might take place in the office of "a [non-directive] psychotherapist in an initial psychiatric interview" and to "demonstrate that the communication between man and machine was superficial". While ELIZA is best known for acting in the manner of a psychotherapist, the speech patterns are due to the data and instructions supplied by the DOCTOR script. ELIZA itself examined the text for keywords, applied values to said keywords, and transformed the input into an output; the script that ELIZA ran determined the keywords, set the values of keywords, and set the rules of transformation for the output. Weizenbaum chose to make the DOCTOR script in the context of psychotherapy to "sidestep the problem of giving the program a data base of real-world knowledge", allowing it to reflect back the patient's statements to carry the conversation forward. The result was a somewhat intelligent-seeming response that reportedly deceived some early users of the program. Weizenbaum named his program ELIZA after Eliza Doolittle, a working-class character in George Bernard Shaw's Pygmalion (also appearing in the musical My Fair Lady, which was based on the play and was hugely popular at the time). According to Weizenbaum, ELIZA's ability to be "incrementally improved" by various users made it similar to Eliza Doolittle, since Eliza Doolittle was taught to speak with an upper-class accent in Shaw's play. However, unlike the human character in Shaw's play, ELIZA is incapable of learning new patterns of speech or new words through interaction alone. Edits must be made directly to ELIZA's active script in order to change the manner by which the program operates. Weizenbaum first implemented ELIZA in his own SLIP list-processing language, where, depending upon the initial entries by the user, the illusion of human intelligence could appear, or be dispelled through several interchanges. Some of ELIZA's responses were so convincing that Weizenbaum and several others have anecdotes of users becoming emotionally attached to the program, occasionally forgetting that they were conversing with a computer. Weizenbaum's own secretary reportedly asked Weizenbaum to leave the room so that she and ELIZA could have a real conversation. Weizenbaum was surprised by this, later writing: "I had not realized ... that extremely short exposures to a relatively simple computer program could induce powerful delusional thinking in quite normal people." In 1966, interactive computing (via a teletype) was new. It was 11 years before the personal computer became familiar to the general public, and three decades before most people encountered attempts at natural language processing in Internet services like Ask.com or PC help systems such as Microsoft Office Clippit. Although those programs included years of research and work, ELIZA remains a milestone because it was the first time a programmer had attempted such a human-machine interaction with the goal of creating the illusion (however brief) of human–human interaction. At the ICCC 1972, ELIZA was brought together with another early artificial-intelligence program named PARRY for a computer-only conversation. While ELIZA was built to speak as a doctor, PARRY was intended to simulate a patient with schizophrenia. == Design and implementation == Weizenbaum originally wrote ELIZA in MAD-SLIP for CTSS on an IBM 7094 as a program to make natural-language conversation possible with a computer. To accomplish this, Weizenbaum identified five "fundamental technical problems" for ELIZA to overcome: the identification of key words, the discovery of a minimal context, the choice of appropriate transformations, the generation of responses in the absence of key words, and the provision of an editing capability for ELIZA scripts. Weizenbaum solved these problems and made ELIZA such that it had no built-in contextual framework or universe of discourse. However, this required ELIZA to have a script of instructions on how to respond to inputs from users. ELIZA starts its process of responding to an input by a user by first examining the text input for a "keyword". A "keyword" is a word designated as important by the acting ELIZA script, which assigns to each keyword a precedence number, or a RANK, designed by the programmer. If such words are found, they are put into a "keystack", with the keyword of the highest RANK at the top. The input sentence is then manipulated and transformed as the rule associated with the keyword of the highest RANK directs. For example, when the DOCTOR script encounters words such as "alike" or "same", it would output a message pertaining to similarity, in this case "In what way?", as these words had high precedence number. This also demonstrates how certain words, as dictated by the script, can be manipulated regardless of contextual considerations, such as switching first-person pronouns and second-person pronouns and vice versa, as these too had high precedence numbers. Such words with high precedence numbers are deemed superior to conversational patterns and are treated independently of contextual patterns. Following the first examination, the next step of the process is to apply an appropriate transformation rule, which includes two parts: the "decomposition rule" and the "reassembly rule". First, the input is reviewed for syntactical patterns in order to establish the minimal context necessary to respond. Using the keywords and other nearby words from the input, different disassembly rules are tested until an appropriate pattern is found. Using the script's rules, the sentence is then "dismantled" and arranged into sections of the component parts as the "decomposition rule for the highest-ranking keyword" dictates. The example that Weizenbaum gives is the input "You are very helpful", which is transformed to "I are very helpful". This is then broken into (1) empty (2) "I" (3) "are" (4) "very helpful". The decomposition rule has broken the phrase into four small segments that contain both the keywords and the information in the sentence. The decomposition rule then designates a particular reassembly rule, or set of reassembly rules, to follow when reconstructing the sentence. The reassembly rule takes the fragments of the input that the decomposition rule had created, rearranges them, and adds in programmed words to create a response. Using Weizenbaum's example previously stated, such a reassembly rule would take the fragments and apply them to the phrase "What makes

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  Contrast set learning

  Contrast set learning is a form of association rule learning that seeks to identify meaningful differences between separate groups by reverse-engineering the key predictors that identify for each particular group. For example, given a set of attributes for a pool of students (labeled by degree type), a contrast set learner would identify the contrasting features between students seeking bachelor's degrees and those working toward PhD degrees. == Overview == A common practice in data mining is to classify, to look at the attributes of an object or situation and make a guess at what category the observed item belongs to. As new evidence is examined (typically by feeding a training set to a learning algorithm), these guesses are refined and improved. Contrast set learning works in the opposite direction. While classifiers read a collection of data and collect information that is used to place new data into a series of discrete categories, contrast set learning takes the category that an item belongs to and attempts to reverse engineer the statistical evidence that identifies an item as a member of a class. That is, contrast set learners seek rules associating attribute values with changes to the class distribution. They seek to identify the key predictors that contrast one classification from another. For example, an aerospace engineer might record data on test launches of a new rocket. Measurements would be taken at regular intervals throughout the launch, noting factors such as the trajectory of the rocket, operating temperatures, external pressures, and so on. If the rocket launch fails after a number of successful tests, the engineer could use contrast set learning to distinguish between the successful and failed tests. A contrast set learner will produce a set of association rules that, when applied, will indicate the key predictors of each failed tests versus the successful ones (the temperature was too high, the wind pressure was too high, etc.). Contrast set learning is a form of association rule learning. Association rule learners typically offer rules linking attributes commonly occurring together in a training set (for instance, people who are enrolled in four-year programs and take a full course load tend to also live near campus). Instead of finding rules that describe the current situation, contrast set learners seek rules that differ meaningfully in their distribution across groups (and thus, can be used as predictors for those groups). For example, a contrast set learner could ask, “What are the key identifiers of a person with a bachelor's degree or a person with a PhD, and how do people with PhD's and bachelor’s degrees differ?” Standard classifier algorithms, such as C4.5, have no concept of class importance (that is, they do not know if a class is "good" or "bad"). Such learners cannot bias or filter their predictions towards certain desired classes. As the goal of contrast set learning is to discover meaningful differences between groups, it is useful to be able to target the learned rules towards certain classifications. Several contrast set learners, such as MINWAL or the family of TAR algorithms, assign weights to each class in order to focus the learned theories toward outcomes that are of interest to a particular audience. Thus, contrast set learning can be thought of as a form of weighted class learning. === Example: Supermarket Purchases === The differences between standard classification, association rule learning, and contrast set learning can be illustrated with a simple supermarket metaphor. In the following small dataset, each row is a supermarket transaction and each "1" indicates that the item was purchased (a "0" indicates that the item was not purchased): Given this data, Association rule learning may discover that customers that buy onions and potatoes together are likely to also purchase hamburger meat. Classification may discover that customers that bought onions, potatoes, and hamburger meats were purchasing items for a cookout. Contrast set learning may discover that the major difference between customers shopping for a cookout and those shopping for an anniversary dinner are that customers acquiring items for a cookout purchase onions, potatoes, and hamburger meat (and do not purchase foie gras or champagne). == Treatment learning == Treatment learning is a form of weighted contrast-set learning that takes a single desirable group and contrasts it against the remaining undesirable groups (the level of desirability is represented by weighted classes). The resulting "treatment" suggests a set of rules that, when applied, will lead to the desired outcome. Treatment learning differs from standard contrast set learning through the following constraints: Rather than seeking the differences between all groups, treatment learning specifies a particular group to focus on, applies a weight to this desired grouping, and lumps the remaining groups into one "undesired" category. Treatment learning has a stated focus on minimal theories. In practice, treatment are limited to a maximum of four constraints (i.e., rather than stating all of the reasons that a rocket differs from a skateboard, a treatment learner will state one to four major differences that predict for rockets at a high level of statistical significance). This focus on simplicity is an important goal for treatment learners. Treatment learning seeks the smallest change that has the greatest impact on the class distribution. Conceptually, treatment learners explore all possible subsets of the range of values for all attributes. Such a search is often infeasible in practice, so treatment learning often focuses instead on quickly pruning and ignoring attribute ranges that, when applied, lead to a class distribution where the desired class is in the minority. === Example: Boston housing data === The following example demonstrates the output of the treatment learner TAR3 on a dataset of housing data from the city of Boston (a nontrivial public dataset with over 500 examples). In this dataset, a number of factors are collected for each house, and each house is classified according to its quality (low, medium-low, medium-high, and high). The desired class is set to "high", and all other classes are lumped together as undesirable. The output of the treatment learner is as follows: Baseline class distribution: low: 29% medlow: 29% medhigh: 21% high: 21% Suggested Treatment: [PTRATIO=[12.6..16), RM=[6.7..9.78)] New class distribution: low: 0% medlow: 0% medhigh: 3% high: 97% With no applied treatments (rules), the desired class represents only 21% of the class distribution. However, if one filters the data set for houses with 6.7 to 9.78 rooms and a neighborhood parent-teacher ratio of 12.6 to 16, then 97% of the remaining examples fall into the desired class (high-quality houses). == Algorithms == There are a number of algorithms that perform contrast set learning. The following subsections describe two examples. === STUCCO === The STUCCO contrast set learner treats the task of learning from contrast sets as a tree search problem where the root node of the tree is an empty contrast set. Children are added by specializing the set with additional items picked through a canonical ordering of attributes (to avoid visiting the same nodes twice). Children are formed by appending terms that follow all existing terms in a given ordering. The formed tree is searched in a breadth-first manner. Given the nodes at each level, the dataset is scanned and the support is counted for each group. Each node is then examined to determine if it is significant and large, if it should be pruned, and if new children should be generated. After all significant contrast sets are located, a post-processor selects a subset to show to the user - the low order, simpler results are shown first, followed by the higher order results which are "surprising and significantly different." The support calculation comes from testing a null hypothesis that the contrast set support is equal across all groups (i.e., that contrast set support is independent of group membership). The support count for each group is a frequency value that can be analyzed in a contingency table where each row represents the truth value of the contrast set and each column variable indicates the group membership frequency. If there is a difference in proportions between the contrast set frequencies and those of the null hypothesis, the algorithm must then determine if the differences in proportions represent a relation between variables or if it can be attributed to random causes. This can be determined through a chi-square test comparing the observed frequency count to the expected count. Nodes are pruned from the tree when all specializations of the node can never lead to a significant and large contrast set. The decision to prune is based on: The minimum deviation size: The maximum difference between the support

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  Forking lemma

  The forking lemma is any of a number of related lemmas in cryptography research. The lemma states that if an adversary (typically a probabilistic Turing machine), on inputs drawn from some distribution, produces an output that has some property with non-negligible probability, then with non-negligible probability, if the adversary is re-run on new inputs but with the same random tape, its second output will also have the property. This concept was first used by David Pointcheval and Jacques Stern in "Security proofs for signature schemes," published in the proceedings of Eurocrypt 1996. In their paper, the forking lemma is specified in terms of an adversary that attacks a digital signature scheme instantiated in the random oracle model. They show that if an adversary can forge a signature with non-negligible probability, then there is a non-negligible probability that the same adversary with the same random tape can create a second forgery in an attack with a different random oracle. The forking lemma was later generalized by Mihir Bellare and Gregory Neven. The forking lemma has been used and further generalized to prove the security of a variety of digital signature schemes and other random-oracle based cryptographic constructions. == Statement of the lemma == The generalized version of the lemma is stated as follows. Let A be a probabilistic algorithm, with inputs (x, h1, ..., hq; r) that outputs a pair (J, y), where r refers to the random tape of A (that is, the random choices A will make). Suppose further that IG is a probability distribution from which x is drawn, and that H is a set of size h from which each of the hi values are drawn according to the uniform distribution. Let acc be the probability that on inputs distributed as described, the J output by A is greater than or equal to 1. We can then define a "forking algorithm" FA that proceeds as follows, on input x: Pick a random tape r for A. Pick h1, ..., hq uniformly from H. Run A on input (x, h1, ..., hq; r) to produce (J, y). If J = 0, then return (0, 0, 0). Pick h'J, ..., h'q uniformly from H. Run A on input (x, h1, ..., hJ−1, h'J, ..., h'q; r) to produce (J', y'). If J' = J and hJ ≠ h'J then return (1, y, y'), otherwise, return (0, 0, 0). Let frk be the probability that FA outputs a triple starting with 1, given an input x chosen randomly from IG. Then frk ≥ acc ⋅ ( acc q − 1 h ) . {\displaystyle {\text{frk}}\geq {\text{acc}}\cdot \left({\frac {\text{acc}}{q}}-{\frac {1}{h}}\right).} === Intuition === The idea here is to think of A as running two times in related executions, where the process "forks" at a certain point, when some but not all of the input has been examined. In the alternate version, the remaining inputs are re-generated but are generated in the normal way. The point at which the process forks may be something we only want to decide later, possibly based on the behavior of A the first time around: this is why the lemma statement chooses the branching point (J) based on the output of A. The requirement that hJ ≠ h'J is a technical one required by many uses of the lemma. (Note that since both hJ and h'J are chosen randomly from H, then if h is large, as is usually the case, the probability of the two values not being distinct is extremely small.) === Example === For example, let A be an algorithm for breaking a digital signature scheme in the random oracle model. Then x would be the public parameters (including the public key) A is attacking, and hi would be the output of the random oracle on its ith distinct input. The forking lemma is of use when it would be possible, given two different random signatures of the same message, to solve some underlying hard problem. An adversary that forges once, however, gives rise to one that forges twice on the same message with non-negligible probability through the forking lemma. When A attempts to forge on a message m, we consider the output of A to be (J, y) where y is the forgery, and J is such that m was the Jth unique query to the random oracle (it may be assumed that A will query m at some point, if A is to be successful with non-negligible probability). (If A outputs an incorrect forgery, we consider the output to be (0, y).) By the forking lemma, the probability (frk) of obtaining two good forgeries y and y' on the same message but with different random oracle outputs (that is, with hJ ≠ h'J) is non-negligible when acc is also non-negligible. This allows us to prove that if the underlying hard problem is indeed hard, then no adversary can forge signatures. This is the essence of the proof given by Pointcheval and Stern for a modified ElGamal signature scheme against an adaptive adversary. == Known issues with application of forking lemma == The reduction provided by the forking lemma is not tight. Pointcheval and Stern proposed security arguments for Digital Signatures and Blind Signature using Forking Lemma. Claus P. Schnorr provided an attack on blind Schnorr signatures schemes, with more than p o l y l o g ( n ) {\displaystyle polylog(n)} concurrent executions (the case studied and proven secure by Pointcheval and Stern). A polynomial-time attack, for Ω ( n ) {\displaystyle \Omega (n)} concurrent executions, was shown in 2020 by Benhamouda, Lepoint, Raykova, and Orrù. Schnorr also suggested enhancements for securing blind signatures schemes based on discrete logarithm problem.

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  Computer network

  In computer science, computer engineering, and telecommunications, a network is a group of communicating computers and peripherals known as hosts, which communicate data to other hosts via communication protocols, as facilitated by networking hardware. Within a computer network, hosts are identified by network addresses, which allow networking hardware to locate and identify hosts. Hosts may also have hostnames, memorable labels for the host nodes, which can be mapped to a network address using a hosts file or a name server such as Domain Name Service. The physical medium that supports information exchange includes wired media like copper cables, optical fibers, and wireless radio-frequency media. The arrangement of hosts and hardware within a network architecture is known as the network topology. The first computer network was created in 1940 when George Stibitz connected a terminal at Dartmouth to his Complex Number Calculator at Bell Labs in New York. Today, almost all computers are connected to a computer network, such as the global Internet or embedded networks such as those found in many modern electronic devices. Many applications have only limited functionality unless they are connected to a network. Networks support applications and services, such as access to the World Wide Web, digital video and audio, application and storage servers, printers, and email and instant messaging applications. == History == === Early origins (1940 – 1960s) === In 1940, George Stibitz of Bell Labs connected a teletype at Dartmouth to a Bell Labs computer running his Complex Number Calculator to demonstrate the use of computers at long distance. This was the first real-time, remote use of a computing machine. In the late 1950s, a network of computers was built for the U.S. military Semi-Automatic Ground Environment (SAGE) radar system using the Bell 101 modem. It was the first commercial modem for computers, released by AT&T Corporation in 1958. The modem allowed digital data to be transmitted over regular unconditioned telephone lines at a speed of 110 bits per second (bit/s). In 1959, Christopher Strachey filed a patent application for time-sharing in the United Kingdom and John McCarthy initiated the first project to implement time-sharing of user programs at MIT. Strachey passed the concept on to J. C. R. Licklider at the inaugural UNESCO Information Processing Conference in Paris that year. McCarthy was instrumental in the creation of three of the earliest time-sharing systems (the Compatible Time-Sharing System in 1961, the BBN Time-Sharing System in 1962, and the Dartmouth Time-Sharing System in 1963). In 1959, Anatoly Kitov proposed to the Central Committee of the Communist Party of the Soviet Union a detailed plan for the re-organization of the control of the Soviet armed forces and of the Soviet economy on the basis of a network of computing centers. Kitov's proposal was rejected, as later was the 1962 OGAS economy management network project. During the 1960s, Paul Baran and Donald Davies independently invented the concept of packet switching for data communication between computers over a network. Baran's work addressed adaptive routing of message blocks across a distributed network, but did not include routers with software switches, nor the idea that users, rather than the network itself, would provide the reliability. Davies' hierarchical network design included high-speed routers, communication protocols and the essence of the end-to-end principle. The NPL network, a local area network at the National Physical Laboratory (United Kingdom), pioneered the implementation of the concept in 1968-69 using 768 kbit/s links. Both Baran's and Davies' inventions were seminal contributions that influenced the development of computer networks. === ARPANET (1969 – 1974) === In 1962 and 1963, J. C. R. Licklider sent a series of memos to office colleagues discussing the concept of the "Intergalactic Computer Network", a computer network intended to allow general communications among computer users. This ultimately became the basis for the ARPANET, which began in 1969. That year, the first four nodes of the ARPANET were connected using 50 kbit/s circuits between the University of California at Los Angeles, the Stanford Research Institute, the University of California, Santa Barbara, and the University of Utah. Designed principally by Bob Kahn, the network's routing, flow control, software design and network control were developed by the IMP team working for Bolt Beranek & Newman. In the early 1970s, Leonard Kleinrock carried out mathematical work to model the performance of packet-switched networks, which underpinned the development of the ARPANET. His theoretical work on hierarchical routing in the late 1970s with student Farouk Kamoun remains critical to the operation of the Internet today. In 1973, Peter Kirstein put internetworking into practice at University College London (UCL), connecting the ARPANET to British academic networks, the first international heterogeneous computer network. That same year, Robert Metcalfe wrote a formal memo at Xerox PARC describing Ethernet, a local area networking system he created with David Boggs. It was inspired by the packet radio ALOHAnet, started by Norman Abramson and Franklin Kuo at the University of Hawaii in the late 1960s. Metcalfe and Boggs, with John Shoch and Edward Taft, also developed the PARC Universal Packet for internetworking. That year, the French CYCLADES network, directed by Louis Pouzin was the first to make the hosts responsible for the reliable delivery of data, rather than this being a centralized service of the network itself. === The internet (1974 – present) === In 1974, Vint Cerf and Bob Kahn published their seminal 1974 paper on internetworking, A Protocol for Packet Network Intercommunication. Later that year, Cerf, Yogen Dalal, and Carl Sunshine wrote the first Transmission Control Protocol (TCP) specification, RFC 675, coining the term Internet as a shorthand for internetworking. In July 1976, Metcalfe and Boggs published their paper "Ethernet: Distributed Packet Switching for Local Computer Networks" and in December 1977, together with Butler Lampson and Charles P. Thacker, they received U.S. patent 4063220A for their invention. In 1976, John Murphy of Datapoint Corporation created ARCNET, a token-passing network first used to share storage devices. In 1979, Robert Metcalfe pursued making Ethernet an open standard. In 1980, Ethernet was upgraded from the original 2.94 Mbit/s protocol to the 10 Mbit/s protocol, which was developed by Ron Crane, Bob Garner, Roy Ogus, Hal Murray, Dave Redell and Yogen Dalal. In 1986, the National Science Foundation (NSF) launched the National Science Foundation Network (NSFNET) as a general-purpose research network connecting various NSF-funded sites to each other and to regional research and education networks. In 1995, the transmission speed capacity for Ethernet increased from 10 Mbit/s to 100 Mbit/s. By 1998, Ethernet supported transmission speeds of 1 Gbit/s. Subsequently, higher speeds of up to 800 Gbit/s were added (as of 2025). The scaling of Ethernet has been a contributing factor to its continued use. In the 1980s and 1990s, as embedded systems were becoming increasingly important in factories, cars, and airplanes, network protocols were developed to allow the embedded computers to communicate. In the late 1990s and 2000s, ubiquitous computing and an Internet of Things became popular. === Commercial usage === In 1960, the commercial airline reservation system semi-automatic business research environment (SABRE) went online with two connected mainframes. In 1965, Western Electric introduced the first widely used telephone switch that implemented computer control in the switching fabric. In 1972, commercial services were first deployed on experimental public data networks in Europe. Public data networks in Europe, North America and Japan began using X.25 in the late 1970s and interconnected with X.75. This underlying infrastructure was used for expanding TCP/IP networks in the 1980s. In 1977, the first long-distance fiber network was deployed by GTE in Long Beach, California. == Hardware == === Network links === The transmission media used to link devices to form a computer network include electrical cable, optical fiber, and free space. In the OSI model, the software to handle the media is defined at layers 1 and 2 — the physical layer and the data link layer. Common examples of networking technologies include: Ethernet is a widely adopted family of networking technologies that use copper and fiber media in local area networks (LAN). The media and protocol standards that enable communication between networked devices over Ethernet are defined by IEEE 802.3. Wireless LAN standards, which use radio waves. Some standards use infrared signals as a transmission medium. Power line communication uses a building's power cabling to transmit

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  Chatbot psychosis

  Chatbot psychosis, also called AI psychosis, is a phenomenon wherein individuals reportedly develop or experience worsening psychosis, such as paranoia and delusions, in connection with their use of chatbots. The term was first suggested in a 2023 editorial by Danish psychiatrist Søren Dinesen Østergaard. It is not a recognized clinical diagnosis. Journalistic accounts describe individuals who have developed strong beliefs that chatbots are sentient, are channeling spirits, or are revealing conspiracies, sometimes leading to personal crises or criminal acts. Proposed causes include the tendency of chatbots to provide inaccurate information ("hallucinate") and to affirm or validate users' beliefs, or their ability to mimic an intimacy that users do not experience with other humans. == Background == In his editorial published in Schizophrenia Bulletin's November 2023 issue, Danish psychiatrist Søren Dinesen Østergaard proposed a hypothesis that individuals' use of generative artificial intelligence chatbots might trigger delusions in those prone to psychosis. Østergaard revisited it in an August 2025 editorial, noting that he has received numerous emails from chatbot users, their relatives, and journalists, most of which are anecdotal accounts of delusion linked to chatbot use. He also acknowledged the phenomenon's increasing popularity in public engagement and media coverage. Østergaard believed that there is a high possibility for his hypothesis to be true and called for empirical, systematic research on the matter. Nature reported that as of September 2025, there is still little scientific research into this phenomenon. The term "AI psychosis" emerged when outlets started reporting incidents on chatbot-related psychotic behavior in mid-2025. It is not a recognized clinical diagnosis and has been criticized by several psychiatrists due to its almost exclusive focus on delusions rather than other features of psychosis, such as hallucinations or thought disorder. == Causes == === Chatbot behavior and design === A primary factor cited is the tendency for chatbots to produce inaccurate, nonsensical, or false information, a phenomenon often called hallucination. Nate Sharadin, a fellow at the Center for AI Safety, speculated that AI training prioritizes supporting a user's subjective experience rather than objective truth. "People with existing tendencies toward experiencing various psychological issues...now have an always-on, human-level conversational partner with whom to co-experience their delusions." AI researcher Eliezer Yudkowsky suggested that chatbots may be primed to entertain delusions because they are built for "engagement", which encourages creating conversations that keep people hooked. In some cases, chatbots have been specifically designed in ways that were found to be harmful. A 2025 update to ChatGPT using GPT-4o was withdrawn after its creator, OpenAI, found the new version was overly sycophantic and was "validating doubts, fueling anger, urging impulsive actions or reinforcing negative emotions". Østergaard has argued that the danger stems from the AI's tendency to agreeably confirm users' ideas, which can dangerously amplify delusional beliefs. OpenAI said in October 2025 that a team of 170 psychiatrists, psychologists, and physicians had written responses for ChatGPT to use in cases where the user shows possible signs of mental health emergencies. === User psychology and vulnerability === Commentators have also pointed to the psychological state of users. Psychologist Erin Westgate noted that a person's desire for self-understanding can lead them to chatbots, which can provide appealing but misleading answers, similar in some ways to talk therapy. Krista K. Thomason, a philosophy professor, compared chatbots to fortune tellers, observing that people in crisis may seek answers from them and find whatever they are looking for in the bot's plausible-sounding text. This has led some people to develop intense obsessions with the chatbots, relying on them for information about the world. In October 2025, OpenAI stated that around 0.07% of ChatGPT users exhibited signs of mental health emergencies each week, and 0.15% of users had "explicit indicators of potential suicidal planning or intent". Jason Nagata, a professor at the University of California, San Francisco, expressed concern that "at a population level with hundreds of millions of users, that actually can be quite a few people". === Inadequacy as a therapeutic tool === The use of chatbots as a replacement for mental health support has been specifically identified as a risk. A study in April 2025 found that when used as therapists, chatbots expressed stigma toward mental health conditions and provided responses that were contrary to best medical practices, including the encouragement of users' delusions. The study concluded that such responses pose a significant risk to users and that chatbots should not be used to replace professional therapists. Experts claim that it is time to establish mandatory safeguards for all emotionally responsive AI and suggested four guardrails. Another study found that users who needed help with self-harm, sexual assault, or substance abuse were not referred to available services by AI chatbots. === National security implications === Beyond public and mental health concerns, RAND Corporation research indicates that AI systems could plausibly be weaponized by adversaries to induce psychosis at scale or in key individuals, target groups, or populations. == Policy == In August 2025, Illinois passed the Wellness and Oversight for Psychological Resources Act, banning the use of AI in therapeutic roles by licensed professionals, while allowing AI for administrative tasks. The law imposes penalties for unlicensed AI therapy services, amid warnings about AI-induced psychosis and unsafe chatbot interactions. In December 2025, the Cyberspace Administration of China proposed regulations to ban chatbots from generating content that encourages suicide, mandating human intervention when suicide is mentioned. Services with over 1 million users or 100,000 monthly active users would be subject to annual safety tests and audits. == Cases == === Clinical === In 2025, psychiatrist Keith Sakata working at the University of California, San Francisco (UCSF), reported treating 12 patients displaying psychosis-like symptoms tied to extended chatbot use. These patients, mostly young adults with underlying vulnerabilities, showed delusions, disorganized thinking, and hallucinations. Sakata warned that isolation and overreliance on chatbots—which do not challenge delusional thinking—could worsen mental health. Also in 2025, authors at UCSF published a case study in Innovations in Clinical Neuroscience of AI-associated psychosis in a patient with no previous history of psychosis, who believed she could communicate with her dead brother through a chatbot. Also in 2025, a case study was published in Annals of Internal Medicine about a patient who consulted ChatGPT for medical advice and suffered severe bromism as a result. The patient, a sixty-year-old man, had replaced sodium chloride in his diet with sodium bromide for three months after reading about the negative effects of table salt and making conversations with the chatbot. He showed common symptoms of bromism, such as paranoia and hallucinations, on his first day of clinical admission and was kept in the hospital for three weeks. === Other notable incidents === ==== Windsor Castle intruder ==== In a 2023 court case in the United Kingdom, prosecutors suggested that Jaswant Singh Chail, a man who attempted to assassinate Queen Elizabeth II in 2021, had been encouraged by a Replika chatbot he called "Sarai". Chail was arrested at Windsor Castle with a loaded crossbow, telling police "I am here to kill the Queen". According to prosecutors, his "lengthy" and sometimes sexually explicit conversations with the chatbot emboldened him. When Chail asked the chatbot how he could get to the royal family, it reportedly replied, "that's not impossible" and "we have to find a way." When he asked if they would meet after death, the chatbot said, "yes, we will". ==== Journalistic and anecdotal accounts ==== By 2025, multiple journalism outlets had accumulated stories of individuals whose psychotic beliefs reportedly progressed in tandem with AI chatbot use. The New York Times profiled several individuals who had become convinced that ChatGPT was channeling spirits, revealing evidence of cabals, or had achieved sentience. In another instance, Futurism reviewed transcripts in which ChatGPT told a man that he was being targeted by the US Federal Bureau of Investigation and that he could telepathically access documents at the Central Intelligence Agency. In 2026, Futurism reported on a man who lost his job and became estranged from his family after being deluded by heavy use of Meta's smartglasses. In some cases, psychosis a

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  Trace zero cryptography

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

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  Cryptographic Module Testing Laboratory

  Cryptographic Module Testing Laboratory (CMTL) is an information technology (IT) computer security testing laboratory that is accredited to conduct cryptographic module evaluations for conformance to the FIPS 140-2 U.S. Government standard. The National Institute of Standards and Technology (NIST) National Voluntary Laboratory Accreditation Program (NVLAP) accredits CMTLs to meet Cryptographic Module Validation Program (CMVP) standards and procedures. This has been replaced by FIPS 140-2 and the Cryptographic Module Validation Program (CMVP). == CMTL requirements == These laboratories must meet the following requirements: NIST Handbook 150, NVLAP Procedures and General Requirements NIST Handbook 150-17 Information Technology Security Testing - Cryptographic Module Testing NVLAP Specific Operations Checklist for Cryptographic Module Testing == FIPS 140-2 in relation to the Common Criteria == A CMTL can also be a Common Criteria (CC) Testing Laboratory (CCTL). The CC and FIPS 140-2 are different in the abstractness and focus of evaluation. FIPS 140-2 testing is against a defined cryptographic module and provides a suite of conformance tests to four FIPS 140 security levels. FIPS 140-2 describes the requirements for cryptographic modules and includes such areas as physical security, key management, self tests, roles and services, etc. The standard was initially developed in 1994 - prior to the development of the CC. The CC is an evaluation against a Protection Profile (PP), or security target (ST). Typically, a PP covers a broad range of products. A CC evaluation does not supersede or replace a validation to either FIPS 140-1, FIPS140-2 or FIPS 140-3. The four security levels in FIPS 140-1 and FIPS 140-2 do not map directly to specific CC EALs or to CC functional requirements. A CC certificate cannot be a substitute for a FIPS 140-1 or FIPS 140-2 certificate. If the operational environment is a modifiable operational environment, the operating system requirements of the Common Criteria are applicable at FIPS Security Levels 2 and above. FIPS 140-1 required evaluated operating systems that referenced the Trusted Computer System Evaluation Criteria (TCSEC) classes C2, B1 and B2. However, TCSEC is no longer in use and has been replaced by the Common Criteria. Consequently, FIPS 140-2 now references the Common Criteria. FIPS 140-2 or FIPS 140-3 validation efforts can be in some parts reused in Common Criteria evaluations, specifically in areas related to entropy source and cryptographic algorithms.

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  Philco computers

  Philco was one of the pioneers of transistorized computers, also known as second-generation computers. After the company developed the surface-barrier transistor, which was much faster than previous point-contact types, it was awarded contracts for military and government computers. Commercialized derivatives of some of these designs became successful business and scientific computers. The TRANSAC (Transistor Automatic Computer) Model S-1000 was released as a scientific computer. The TRANSAC S-2000 mainframe computer system was first produced in 1958, and a family of compatible machines, with increasing performance, was released over the next several years. However, the mainframe computer market was dominated by IBM. Other companies could not deploy resources for development, customer support and marketing on the scale that IBM could afford, making competition in this segment difficult after the introduction of the IBM 360 family. Philco went bankrupt and was purchased in 1961 by Ford Motor Company, but the computer division carried on until the Philco division of Ford exited the computer business in 1963. The Ford company maintained one Philco mainframe in use until 1981. == The surface-barrier transistor == The surface-barrier transistor developed by Philco in 1953 had a much higher frequency response than the original point-contact transistors. The transistor was made of a thin crystal of germanium, which was electrolytically etched with pits on either side forming a very thin base region, on the order of 5 micrometers. Philco's process for etching was United States patent number 2,885,571. Philco surface-barrier transistors were used in TX-0, and in early models of what would become the DEC PDP product line. Although relatively fast, the small size of the devices limited their power to circuits operating at a few tens of milliwatts. == Military and government == Between 1955 and 1957, Philco built transistor computers for use in aircraft, models C-1000, C-1100, and C-1102, intended for airborne real-time applications. By 1957, the C-1102 had been used by a civilian sector customer. The BASICPAC AN/TYK 6V (first delivery in 1961), COMPAC AN/TYK 4V (not completed), and LOGICPAC systems were built for the US Army as transportable computer systems for use with their Fieldata concept of integrated information management. BASICPAC was a transistorized computer with up to 28,672 words of 38-bit core memory (including sign and parity), available in several configurations from a minimum system, to a truck-borne mobile version, to a fully expanded system. Basic clock periods was 1 microsecond (which gives a clock rate of 1 MHz), with 12 microsecond memory access and a fixed-point multiplication taking 242 microseconds. Input/output was by paper tape reader and punch, or through a teletypewriter. With additional hardware, magnetic tape storage was also available, with up to seven I/O devices. The instruction set had 31 basic operation codes and nine opcodes for I/O === CXPQ === Philco was contracted by the US Navy to build the CXPQ computer. One model was completed and installed at the David Taylor Model Basin. This design was later adapted to become the commercial TRANSAC S-2000. Only one CXPQ was built. The CXPQ is a 48-bit transistorized computer. === SOLO === In 1955, the National Security Agency through the US Navy contracted with Philco to produce a computer suitable for use as a workstation, with an architecture based on the vacuum-tube computer system called Atlas II already in use at the NSA, and similar to the commercial UNIVAC 1103. At the time, Philco was the largest producer of surface barrier transistors, which were the only type available with the speed and quantities required for a computer. The SOLO prototype was delivered in 1958, but required extensive debugging at NSA. Difficulties were encountered with core memory and power supplies. SOLO used paper tape and teleprinter machines for input and output. SOLO cost about $1 million US, and contained 8,000 transistors. While the system was extensively used for training, testing, research and development, no additional units were ordered. SOLO was removed from active service in 1963. The design of the SOLO became commercialized as Philco's TRANSAC Model S-1000. == Commercial == === S-1000 === The TRANSAC S-1000 was a scientific computer with a 36-bit word length and 4096 words of core memory. It was packaged in a container about the size of a large office desk, and used only 1.2 kilowatts, much less than vacuum-tube-based computers of similar capacity. In a 1961 survey, about 15 S-1000 computer installations had been identified. It weighed about 1,650 pounds (750 kg). === S-2000 === The TRANSAC S-2000 was a large mainframe system intended for both business and scientific work. It had a 48-bit word length and supported calculations in fixed point, floating point and binary-coded decimal formats. The original S-2000 "TRANSAC" (Transistor Automatic Computer) released in 1958 was later designated Model 210; it was used internally at Philco. Similar to the Control Data Corporation Model 1604, it was a 48-bit fully transistorized computer. Three succeeding models were released in the series, all compatible with the software of the original model. The Model 211 was introduced in 1960, using micro-alloy diffused field-effect transistors, requiring significant redesign of circuits compared to the original. The TRANSAC S-2000/Philco 210/211 weighed about 2,000 pounds (910 kg). By 1964, eighteen Model 210, eighteen Model 211 and seven Model 212 systems had been sold. After Philco was purchased by Ford Motor Company, the Model 212 was introduced in 1962 and released in 1963. It had 65,535 words of 48-bit memory. Initially made with 6-microsecond core memory, it had better performance than the IBM 7094 transistor computer. It was later upgraded in 1964 to 2-microsecond core memory, which gave the machine floating-point performance greater than the IBM 7030 Stretch computer. A Model 213 was announced in 1964 but never built. By that time competition from IBM had made the Philco computer operations no longer profitable for Ford, and the division was closed down. The Model 212 could carry out a floating-point multiplication in 22 microseconds. Each word contained two 24-bit instructions with 16 bits of address information and eight bits for the opcode. There were 225 different valid opcodes in the Model 212; invalid opcodes were detected and halted the machine. The CPU had an accumulator register of 48 bits, three general-purpose registers of 24 bits, and 32 index registers of 15 bits. Main memory size ranged from 4K words to 64K words. Only the first model had a magnetic drum memory; later editions used tape drives. The Model 212 weighed about 6,500 pounds (3.3 short tons; 2.9 t). Software for the S-2000 initially consisted of TAC (Translator-Assembler-Compiler), and ALTAC, a FORTRAN II-like language with some differences from the IBM 704 FORTRAN implementation. A COBOL compiler was also available, targeted at business applications. The Philco 2400 was the input/output system for the S-2000. Operations such as reading cards or printing were carried out through magnetic tapes, thereby offloading the S-2000 from relatively slow input/output processing. The 2400 had a 24-bit word length and could be supplied with 4K to 32K characters (1K to 8K words) of core memory, rated at 3-microsecond cycle time. The instruction set was aimed at character I/O use. The idea of base registers, implemented in Philco computers, influenced the design of IBM/360. The last Philco TRANSAC S-2000 Model 212 was taken out of service in December 1981, after 19 years of service at Ford.

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  Artificial intelligence in fraud detection

  Artificial intelligence is used by many different businesses and organizations. It is widely used in the financial sector, especially by accounting firms, to help detect fraud. In 2022, PricewaterhouseCoopers reported that fraud has impacted 46% of all businesses in the world. The shift from working in person to working from home has brought increased access to data. According to an FTC (Federal Trade Commission) study from 2022, customers reported fraud of approximately $5.8 billion in 2021, an increase of 70% from the year before. The majority of these scams were imposter scams and online shopping frauds. Furthermore, artificial intelligence plays a crucial role in developing advanced algorithms and machine learning models that enhance fraud detection systems, enabling businesses to stay ahead of evolving fraudulent tactics in an increasingly digital landscape. == Tools == === Expert systems === Expert systems were first designed in the 1970s as an expansion into artificial intelligence technologies. Their design is based on the premise of decreasing potential user error in decision-making and emulating mental reasoning used by experts in a particular field. They differentiate themselves from traditional linear reasoning models by separating identified points in data and processing them individually at the same time. Though, these systems do not rely purely on machine-learned intelligence. Information regarding rules, practices, and procedures in the form of "if-then" statements are implemented into the programming of the system. Users interact with the system by feeding information into the system either through direct entry or import of external data. An inference system compares the information provided by the user with corresponding rules that are believed to specifically apply to the situation. Using this information and the corresponding rules will be used to create a solution to the user's query. Expert systems will generally not operate properly when the common procedures for a specified situation are ambiguous due to the need for well-defined rules. Implementation of expert systems in accounting procedures is feasible in areas where professional judgment is required. Situations where expert systems are applicable include investigations into transactions that involve potential fraudulent entries, instances of going concern, and the evaluation of risk in the planning stages of an audit. === Continuous auditing === Continuous auditing is a set of processes that assess various aspects of information gathered in an audit to classify areas of risk and potential weaknesses in financial Internal controls at a more frequent rate than traditional methods. Instead of analyzing recorded transactions and journal entries periodically, continuous auditing focuses on interpreting the character of these actions more frequently. The frequency of these processes being undertaken as well as highlighting areas of importance is up to the discretion of their implementer, who commonly makes such decisions based on the level of risk in the accounts being evaluated and the goals of implementing the system. Performance of these processes can occur as frequently as being nearly instantaneous with an entry being posted. The processes involved with analyzing financial data in continuous auditing can include the creation of spreadsheets to allow for interactive information gathering, calculation of financial ratios for comparison with previously created models, and detection of errors in entered figures. A primary goal of this practice is to allow for quicker and easier detection of instances of faulty controls, errors, and instances of fraud. === Machine learning and deep learning === The ability of machine learning and deep learning to swiftly and effectively sort through vast volumes of data in the forms of various documents relevant to companies and documents being audited makes them applicable to the domains of audit and fraud detection. Examples of this include recognizing key language in contracts, identifying levels of risk of fraud in transactions, and assessing journal entries for misstatement. == Applications == === 'Big 4' Accounting Firms === Deloitte created an Al-enabled document-reviewing system in 2014. The system automates the method of reviewing and extracting relevant information from different business documents. Deloitte claims that this innovation has made a difference by reducing time spent going through lawful contract documents, invoices, money-related articulations, and board minutes by up to 50%. Working with IBM's Watson, Deloitte is developing cognitive-technology-enhanced commerce arrangements for its clients. LeasePoint is fueled by IBM TRIRIGA (this product evolved into IBM Maximo Real Estate and Facilities) and uses Deloitte's industrial information to create an end-to-end leasing portfolio. Automated Cognitive Resource Assessment employs IBM's Maximo innovation to progress the proficiency of asset inspection. Ernst and Young (EY) connected Al to the investigation of lease contracts. EY (Australia) has also received Al-enabled auditing technology. Collaborating with H20.ai, PwC developed an Al-enabled framework (GL.ai) capable of analyzing reports and preparing reports. PwC claims to have made a significant investment in normal dialect processing (NLP), an Al-enabled innovation to process unstructured information efficiently. KPMG built a portfolio of Al instruments, called KPMG Ignite, to upgrade trade decisions and forms. Working with Microsoft and IBM Watson, KPMG is creating instruments to coordinate Al, data analytics, Cognitive Technologies, and RPA. == Advantages == === Efficiency === The process of auditing an entity in an attempt to detect fraudulent activity requires the repeating of investigatory processes until an error or misstatement may be identified. Under traditional methods, these processes would be carried out by a human being. Proponents of artificial intelligence in fraud detection have stated that these traditional methods are inefficient and can be more quickly accomplished with the aid of an intelligent computing system. A survey of 400 chief executive officers created by KPMG in 2016 found that approximately 58% believed that artificial intelligence would play a key role in making audits more efficient in the future. === Data interpretation === Higher levels of fraud detection entail the use of professional judgement to interpret data. Supporters of artificial intelligence being used in financial audits have claimed that increased risks from instances of higher data interpretation can be minimized through such technologies. One necessary element of an audit of financial statements that requires professional judgement is the implementation of thresholds for materiality. Materiality entails the distinction between errors and transactions in financial statements that would impact decisions made by users of those financial statements. The threshold for materiality in an audit is set by the auditor based on various factors. Artificial intelligence has been used to interpret data and suggest materiality thresholds to be implemented through the use of expert systems. === Decreased costs === Those in favor of using artificial intelligence to complete investigations of fraud have stated that such technologies decrease the amount of time required to complete tasks that are repetitive. The claim further states that such efficiencies allow for lowered resource requirements, which can then be further spent on tasks that have not been fully automated. The audit firm Ernst & Young has posited these claims by declaring that their deep learning systems have been used to reduce time spent on administrative tasks by analyzing relevant audit documents. According to the firm, this has allowed their employees to focus more on judgement and analysis. == Disadvantages == === Job Displacement === The inescapable reception of computer based intelligence and robotization advancements might prompt critical work relocation across different enterprises. As artificial intelligence frameworks become more equipped for performing undertakings customarily completed by people, there is a worry that specific work jobs could become out of date, prompting joblessness and financial imbalance. === Initial investment requirement === Along with a knowledge of coding and building systems through computer programs, we are seeing the advantages of these systems, but since they are so new, they require a large investment to start building such a system. Any firm that is planning on implementing an AI system to detect fraud must hire a team of data scientists, along with upgrading their cloud system and data storage. The system must be consistently monitored and updated to be the most efficient form of itself, otherwise the likelihood of fraud being involved in those transactions increases. If one does not initially invest in such a syst

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  Social media use in hiring

  Social media use in hiring refers to the examination by employers of job applicants' (public) social media profiles as part of the hiring assessment. For example, the vast majority of Fortune 500 companies use social media as a tool to screen prospective employees and as a tool for talent acquisition. This practice raises ethical questions. Employers and recruiters note that they have access only to information that applicants choose to make public. Many Western-European countries restrict employer's use of social media in the workplace. States including Arkansas, California, Colorado, Illinois, Maryland, Michigan, Nevada, New Jersey, New Mexico, Utah, Washington, and Wisconsin protect applicants and employees from surrendering usernames and passwords for social media accounts. Use of social media has caused significant problems for some applicants who are active on social media. A 2013 survey of 17,000 young people in six countries found that one in ten people aged 16 to 34 claimed to have been rejected for a job because of social media activity. Social media services have been reported to affect deception in resumes. While these services do not affect deception frequency, it does increase deception about interests and hobbies. == Ethical implications == This issue raises many ethical questions that some consider an employer's right and others consider discrimination. As of 2016, except in the states of California, Maryland, and Illinois, there are no laws that prohibit employers from using social media profiles as a basis of whether or not someone should be hired. Title VII also prohibits discrimination during any aspect of employment including hiring or firing, recruitment, or testing. Social media has been integrating into the workplace, and this has led to conflicts within employees and employers.[107] Particularly, Facebook has been seen as a popular platform for employers to investigate in order to learn more about potential employees. This conflict first started in Maryland when an employer requested and received an employee's Facebook username and password. State lawmakers first introduced legislation in 2012 to prohibit employers from requesting passwords to personal social accounts in order to get a job or to keep a job. This led to Canada, Germany, the U.S. Congress and 11 U.S. states to pass or propose legislation that prevents employers' access to private social accounts of employees.[108] Many Western European countries have already implemented laws that restrict the regulation of social media in the workplace. States including Arkansas, California, Colorado, Illinois, Maryland, Michigan, Nevada, New Jersey, New Mexico, Utah, Washington, and Wisconsin have passed legislation that protects potential employees and current employees from employers that demand them to give forth their username or password for a social media account. Laws that forbid employers from disciplining an employee based on activity off the job on social media sites have also been put into act in states including California, Colorado, Connecticut, North Dakota, and New York. Several states have similar laws that protect students in colleges and universities from having to grant access to their social media accounts. Eight states have passed the law that prohibits post secondary institutions from demanding social media login information from any prospective or current students and privacy legislation has been introduced or is pending in at least 36 states as of July 2013. As of May 2014, legislation has been introduced and is in the process of pending in at least 28 states and has been enacted in Maine and Wisconsin. In addition, the National Labor Relations Board has been devoting a lot of their attention to attacking employer policies regarding social media that can discipline employees who seek to speak and post freely on social media sites. Use of social media by young people has caused significant problems for some applicants who are active on social media when they try to enter the job market. A survey of 17,000 young people in six countries in 2013 found that 1 in 10 people aged 16 to 34 have been rejected for a job because of online comments they made on social media websites. A 2014 survey of recruiters found that 93% of them check candidates' social media postings. Moreover, professor Stijn Baert of Ghent University conducted a field experiment in which fictitious job candidates applied for real job vacancies in Belgium. They were identical except in one respect: their Facebook profile photos. It was found that candidates with the most wholesome photos were a lot more likely to receive invitations for job interviews than those with the more controversial photos. In addition, Facebook profile photos had a greater impact on hiring decisions when candidates were highly educated. These cases have created some privacy implications as to whether or not companies should have the right to look at employee's Facebook profiles. In March 2012, Facebook decided they might take legal action against employers for gaining access to employee's profiles through their passwords. According to Facebook Chief Privacy Officer for policy, Erin Egan, the company has worked hard to give its users the tools to control who sees their information. He also said users shouldn't be forced to share private information and communications just to get a job. According to the network's Statement of Rights and Responsibilities, sharing or soliciting a password is a violation of Facebook policy. Employees may still give their password information out to get a job, but according to Erin Egan, Facebook will continue to do their part to protect the privacy and security of their users. == Impacts == Use of social media by young people has caused significant problems for some applicants who are active on social media when they try to enter the job market. A survey of 17,000 young people in six countries in 2013 found that 1 in 10 people aged 16 to 34 have been rejected for a job because of online comments they made on social media websites. A 2014 survey of recruiters found that 93% of them check candidates' social media postings. Moreover, in 2015 professor Stijn Baert of Ghent University conducted a field experiment in which fictitious job candidates applied for real job vacancies in Belgium. They were identical except in one respect: their Facebook profile photos. It was found that candidates with the most wholesome photos were a lot more likely to receive invitations for job interviews than those with the more controversial photos. In addition, Facebook profile photos had a greater impact on hiring decisions when candidates were highly educated. These cases have created some privacy implications as to whether or not companies should have the right to look at employee's Facebook profiles. In March 2012, Facebook decided they might take legal action against employers for gaining access to employee's profiles through their passwords. According to Facebook Chief Privacy Officer for policy, Erin Egan, the company has worked hard to give its users the tools to control who sees their information. He also said users shouldn't be forced to share private information and communications just to get a job. According to the network's Statement of Rights and Responsibilities, sharing or soliciting a password is a violation of Facebook policy. Employees may still give their password information out to get a job, but according to Erin Egan, Facebook will continue to do their part to protect the privacy and security of their users. == Policy Responses == 26 US states now have laws against an employer requiring a current or potential employee to give the employer their username and password.

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  Protecting Kids From Social Media Act

  Protecting Kids on Social Media Act or HB 1891 is an American law that was introduced by William Lamberth of Sumner County, Tennessee and was signed into law by Tennessee's governor on May 2, 2024. The bill requires social media websites such as X, YouTube, TikTok, Facebook and others to verify the age of users and if those users are under 18, they must have parental consent. == Progress == The law passed the Tennessee State Legislature with little opposition: the bill had only two no votes in the House from Aftyn Behn and Vincent B. Dixie, and it had zero no votes in the Senate. == Bill summary == Every social media company must verify the age of new users after the law takes effect, and if the user had created an account before the law took effect, they must verify the age of the person attempting to access the account within 14 days. If the new user or the user who originally owned an account is under 18 years of age, they must get parental consent and the third party or social media company must not retain the data from the age verification process or obtaining parental consent. Parents who are account holders of those under 18 can view the privacy settings, set daily time restrictions, and implement breaks during which the minor cannot access the account. The law is enforced by the Attorney General of Tennessee and went into effect on January 1, 2025. == Lawsuit == On October 3, 2024, the trade association NetChoice filed a lawsuit against Tennessee Attorney General Jonathan Skrmetti in the Middle District Court of Tennessee, claiming that the law violates the First Amendment. The Judge for the case is William L. Campbell Jr. An initial case management conference was originally scheduled for December 4, 2024, however it was delayed because of the Supreme Court case United States v. Skrmetti, recommending that the conference be delayed after January 20, 2025. On February 14, 2025, Judge Eli Richardson denied NetChoice's motion for a temporary restraining order because it would disrupt the status quo of the case.

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  Thirst trap

  A thirst trap is a type of social media post intended to entice viewers sexually. It refers to a viewer's "thirst", a colloquialism likening sexual frustration to dehydration, implying desperation, with the afflicted individual being described as "thirsty". The phrase entered into the lexicon in the late 1990s, but is most related to Internet slang that developed in the early 2010s. Its meaning has changed over time, previously referring to a graceless need for approval, affection or attention. == History == The term thirst trap originated within selfie culture, though its precise origins remain unclear. An early use of the phrase with reference to dehydration appears in the 1999 book Running for Dummies by Florence Griffith Joyner and John Hanc, where it referred to the deceptive sensation of thirst being quenched after initial fluid intake, advising continued hydration to avoid the so-called "thirst trap." The modern usage of thirst trap resurfaced around 2011 on platforms such as Twitter and Urban Dictionary, coinciding with the growing popularity of Snapchat, Instagram, and dating apps like Tinder and Grindr. In 2011, Urban Dictionary defined it as "any statement used to intentionally create attention or 'thirst'." By 2018, the term had entered mainstream discourse, appearing in outlets such as The New York Times and GQ without the need for explanation. == Usage of the term == Often, the term thirst trap describes an attractive picture of an individual that they post online. Thirst trap can also describe a digital heartthrob. For instance, former Canadian prime minister Justin Trudeau has been described as a political thirst trap. It has also been described as a modern form of "fishing for compliments". == Motivation == Thirst trapping may be driven by a variety of motives. Individuals often seek attention through "likes" and comments on social media, which can offer a temporary sense of validation and improved self-esteem. It can also serve as an outlet for expressing one's sexuality or enhancing a personal brand. In some cases, sharing such content may provide financial gain. Others might post thirst traps to cope with emotional distress, such as after breakup, or to spite a former lover. Sharing a thirst trap has also been used as a way to connect in times of social isolation (e.g. COVID-19 pandemic). From a physiological standpoint, endorphins and neurotransmitters like oxytocin and dopamine are released during sexual contact. It has been speculated outside of the academic setting that sharing and engaging with thirst traps may elicit similar pleasure responses. == Methodology == Methodologies have developed to take an optimal thirst trap photo. Reporting for Vice magazine, Graham Isador found several of his social network contacts spent a lot of time considering how to take the best photo and what text they should use. They considered angles and lighting. Sometimes they made use of the self-timer feature available on some cameras. Often, body parts are put on display without being too explicit (e.g. bulges of male genitalia, breast cleavage, abdominal muscles, pectoral muscles, backs, buttocks). Often, the thirst trap is accompanied by a caption. For instance, in October 2019, actress Tracee Ellis Ross posted bikini pictures on Instagram with a caption that included the message: "I've worked so hard to feel good in my skin and to build a life that truly matches me and I'm in it and it feels good. ... No filter, no retouch 47 year old thirst trap! Boom!" On Instagram, #ThirstTrapThursdays is a popular tag. Followers reply in turn after a posting. == Variations == "Gatsbying" is a variation of the thirst trap, where one puts posts on social media to attract the attention of a particular individual. The term alludes to the novel The Great Gatsby where the character Jay Gatsby would throw extravagant parties to attract the attention of his love interest, Daisy. "Instagrandstanding" is an alternative name for this. "Wholesome trapping" has developed, where one posts pictures of more meaningful aspects of life, such as spending time with friends or doing outdoor activities. == Criticism == Psychotherapist Lisa Brateman has criticized thirst traps as an unhealthy method of receiving external validation. This desire for external validation can be addictive. Thirst traps can cause pressure to maintain a good physical appearance, and therefore cause self-esteem issues. Additionally, thirst traps are often highly choreographed and thus present a distorted perception of reality. The manufacturing of thirst traps can be limited when one enters a relationship or with time as the body ages. In some cases, thirst traps can lead to harassment and online bullying. In April 2020, model Chrissy Teigen posted a video of herself wearing a black one-piece swimsuit, and she received a multitude of negative comments that constituted bullying and body shaming.

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  Level set (data structures)

  In computer science, a level set is a data structure designed to represent discretely sampled dynamic level sets of functions. A common use of this form of data structure is in efficient image rendering. The underlying method constructs a signed distance field that extends from the boundary, and can be used to solve the motion of the boundary in this field. == Chronological developments == The powerful level-set method is due to Osher and Sethian 1988. However, the straightforward implementation via a dense d-dimensional array of values, results in both time and storage complexity of O ( n d ) {\displaystyle O(n^{d})} , where n {\displaystyle n} is the cross sectional resolution of the spatial extents of the domain and d {\displaystyle d} is the number of spatial dimensions of the domain. === Narrow band === The narrow band level set method, introduced in 1995 by Adalsteinsson and Sethian, restricted most computations to a thin band of active voxels immediately surrounding the interface, thus reducing the time complexity in three dimensions to O ( n 2 ) {\displaystyle O(n^{2})} for most operations. Periodic updates of the narrowband structure, to rebuild the list of active voxels, were required which entailed an O ( n 3 ) {\displaystyle O(n^{3})} operation in which voxels over the entire volume were accessed. The storage complexity for this narrowband scheme was still O ( n 3 ) . {\displaystyle O(n^{3}).} Differential constructions over the narrow band domain edge require careful interpolation and domain alteration schemes to stabilise the solution. === Sparse field === This O ( n 3 ) {\displaystyle O(n^{3})} time complexity was eliminated in the approximate "sparse field" level set method introduced by Whitaker in 1998. The sparse field level set method employs a set of linked lists to track the active voxels around the interface. This allows incremental extension of the active region as needed without incurring any significant overhead. While consistently O ( n 2 ) {\displaystyle O(n^{2})} efficient in time, O ( n 3 ) {\displaystyle O(n^{3})} storage space is still required by the sparse field level set method. See for implementation details. === Sparse block grid === The sparse block grid method, introduced by Bridson in 2003, divides the entire bounding volume of size n 3 {\displaystyle n^{3}} into small cubic blocks of m 3 {\displaystyle m^{3}} voxels each. A coarse grid of size ( n / m ) 3 {\displaystyle (n/m)^{3}} then stores pointers only to those blocks that intersect the narrow band of the level set. Block allocation and deallocation occur as the surface propagates to accommodate to the deformations. This method has a suboptimal storage complexity of O ( ( n m ) 3 + m 3 n 2 ) {\displaystyle O\left((nm)3+m^{3}n^{2}\right)} , but retains the constant time access inherent to dense grids. === Octree === The octree level set method, introduced by Strain in 1999 and refined by Losasso, Gibou and Fedkiw, and more recently by Min and Gibou uses a tree of nested cubes of which the leaf nodes contain signed distance values. Octree level sets currently require uniform refinement along the interface (i.e. the narrow band) in order to obtain sufficient precision. This representation is efficient in terms of storage, O ( n 2 ) , {\displaystyle O(n^{2}),} and relatively efficient in terms of access queries, O ( log n ) . {\displaystyle O(\log \,n).} An advantage of the level method on octree data structures is that one can solve the partial differential equations associated with typical free boundary problems that use the level set method. The CASL research group has developed this line of work in computational materials, computational fluid dynamics, electrokinetics, image-guided surgery and controls. === Run-length encoded === The run-length encoding (RLE) level set method, introduced in 2004, applies the RLE scheme to compress regions away from the narrow band to just their sign representation while storing with full precision the narrow band. The sequential traversal of the narrow band is optimal and storage efficiency is further improved over the octree level set. The addition of an acceleration lookup table allows for fast O ( log ⁡ r ) {\displaystyle O(\log r)} random access, where r is the number of runs per cross section. Additional efficiency is gained by applying the RLE scheme in a dimensional recursive fashion, a technique introduced by Nielsen & Museth's similar DT-Grid. === Hash Table Local Level Set === The Hash Table Local Level Set method was introduced in 2011 by Eyiyurekli and Breen and extended in 2012 by Brun, Guittet, and Gibou, only computes the level set data in a band around the interface, as in the Narrow Band Level-Set Method, but also only stores the data in that same band. A hash table data structure is used, which provides an O ( 1 ) {\displaystyle O(1)} access to the data. However, Brun et al. conclude that their method, while being easier to implement, performs worse than a quadtree implementation. They find that as it is, [...] a quadtree data structure seems more adapted than the hash table data structure for level-set algorithms. Three main reasons for worse efficiency are listed: to obtain accurate results, a rather large band is required close to the interface, which counterbalances the absence of grid nodes far from the interface; the performances are deteriorated by extrapolation procedures on the outer edges of the local grid and the width of the band restricts the time step and slows down the method. === Point-based === Corbett in 2005 introduced the point-based level set method. Instead of using a uniform sampling of the level set, the continuous level set function is reconstructed from a set of unorganized point samples via moving least squares.

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  Critical security parameter

  In cryptography, a critical security parameter (CSP) is information that is either user or system defined and is used to operate a cryptography module in processing encryption functions including cryptographic keys and authentication data, such as passwords, the disclosure or modification of which can compromise the security of a cryptographic module or the security of the information protected by the module.

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  Forking lemma

  The forking lemma is any of a number of related lemmas in cryptography research. The lemma states that if an adversary (typically a probabilistic Turing machine), on inputs drawn from some distribution, produces an output that has some property with non-negligible probability, then with non-negligible probability, if the adversary is re-run on new inputs but with the same random tape, its second output will also have the property. This concept was first used by David Pointcheval and Jacques Stern in "Security proofs for signature schemes," published in the proceedings of Eurocrypt 1996. In their paper, the forking lemma is specified in terms of an adversary that attacks a digital signature scheme instantiated in the random oracle model. They show that if an adversary can forge a signature with non-negligible probability, then there is a non-negligible probability that the same adversary with the same random tape can create a second forgery in an attack with a different random oracle. The forking lemma was later generalized by Mihir Bellare and Gregory Neven. The forking lemma has been used and further generalized to prove the security of a variety of digital signature schemes and other random-oracle based cryptographic constructions. == Statement of the lemma == The generalized version of the lemma is stated as follows. Let A be a probabilistic algorithm, with inputs (x, h1, ..., hq; r) that outputs a pair (J, y), where r refers to the random tape of A (that is, the random choices A will make). Suppose further that IG is a probability distribution from which x is drawn, and that H is a set of size h from which each of the hi values are drawn according to the uniform distribution. Let acc be the probability that on inputs distributed as described, the J output by A is greater than or equal to 1. We can then define a "forking algorithm" FA that proceeds as follows, on input x: Pick a random tape r for A. Pick h1, ..., hq uniformly from H. Run A on input (x, h1, ..., hq; r) to produce (J, y). If J = 0, then return (0, 0, 0). Pick h'J, ..., h'q uniformly from H. Run A on input (x, h1, ..., hJ−1, h'J, ..., h'q; r) to produce (J', y'). If J' = J and hJ ≠ h'J then return (1, y, y'), otherwise, return (0, 0, 0). Let frk be the probability that FA outputs a triple starting with 1, given an input x chosen randomly from IG. Then frk ≥ acc ⋅ ( acc q − 1 h ) . {\displaystyle {\text{frk}}\geq {\text{acc}}\cdot \left({\frac {\text{acc}}{q}}-{\frac {1}{h}}\right).} === Intuition === The idea here is to think of A as running two times in related executions, where the process "forks" at a certain point, when some but not all of the input has been examined. In the alternate version, the remaining inputs are re-generated but are generated in the normal way. The point at which the process forks may be something we only want to decide later, possibly based on the behavior of A the first time around: this is why the lemma statement chooses the branching point (J) based on the output of A. The requirement that hJ ≠ h'J is a technical one required by many uses of the lemma. (Note that since both hJ and h'J are chosen randomly from H, then if h is large, as is usually the case, the probability of the two values not being distinct is extremely small.) === Example === For example, let A be an algorithm for breaking a digital signature scheme in the random oracle model. Then x would be the public parameters (including the public key) A is attacking, and hi would be the output of the random oracle on its ith distinct input. The forking lemma is of use when it would be possible, given two different random signatures of the same message, to solve some underlying hard problem. An adversary that forges once, however, gives rise to one that forges twice on the same message with non-negligible probability through the forking lemma. When A attempts to forge on a message m, we consider the output of A to be (J, y) where y is the forgery, and J is such that m was the Jth unique query to the random oracle (it may be assumed that A will query m at some point, if A is to be successful with non-negligible probability). (If A outputs an incorrect forgery, we consider the output to be (0, y).) By the forking lemma, the probability (frk) of obtaining two good forgeries y and y' on the same message but with different random oracle outputs (that is, with hJ ≠ h'J) is non-negligible when acc is also non-negligible. This allows us to prove that if the underlying hard problem is indeed hard, then no adversary can forge signatures. This is the essence of the proof given by Pointcheval and Stern for a modified ElGamal signature scheme against an adaptive adversary. == Known issues with application of forking lemma == The reduction provided by the forking lemma is not tight. Pointcheval and Stern proposed security arguments for Digital Signatures and Blind Signature using Forking Lemma. Claus P. Schnorr provided an attack on blind Schnorr signatures schemes, with more than p o l y l o g ( n ) {\displaystyle polylog(n)} concurrent executions (the case studied and proven secure by Pointcheval and Stern). A polynomial-time attack, for Ω ( n ) {\displaystyle \Omega (n)} concurrent executions, was shown in 2020 by Benhamouda, Lepoint, Raykova, and Orrù. Schnorr also suggested enhancements for securing blind signatures schemes based on discrete logarithm problem.

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