Cognitive neuroscience

Cognitive neuroscience is the scientific field concerned with the study of the biological processes and aspects that underlie cognition, with a specific focus on the neural connections in the brain that are involved in mental processes. It addresses the questions of how cognitive activities are affected or controlled by neural circuits in the brain. Cognitive neuroscience is a branch of both neuroscience and psychology, overlapping with disciplines such as behavioral neuroscience, cognitive psychology, physiological psychology, and affective neuroscience. Cognitive neuroscience relies upon theories in cognitive science coupled with evidence from neurobiology, and computational modeling.
Parts of the brain play an important role in this field. Neurons play the most vital role, since the main point is to establish an understanding of cognition from a neural perspective, along with the different lobes of the cerebral cortex.
Methods employed in cognitive neuroscience include experimental procedures from psychophysics and cognitive psychology, functional neuroimaging, electrophysiology, cognitive genomics, and behavioral genetics.
Studies of patients with cognitive deficits due to brain lesions constitute an important aspect of cognitive neuroscience. The damage in lesioned brains provide a comparable starting point with regard to healthy and fully functioning brains. These damages change the neural circuits in the brain and cause it to malfunction during basic cognitive processes, such as memory or learning. These disabilities and such damage can be compared with how the healthy neural circuits are functioning, and possibly draw conclusions about the basis of the affected cognitive processes. Some examples involve damage to Wernicke's area, the left side of the temporal lobe, and Broca's area close to the frontal lobe.
Also, cognitive abilities based on brain development are studied and examined under the subfield of developmental cognitive neuroscience. This shows brain development over time, analyzing differences and proposing possible reasons for those differences.
Theoretical approaches include computational neuroscience and cognitive psychology.


Computational and Systems Neuroscience

Computational and Systems Neuroscience (COSYNE ) is an annual scientific conference for the exchange of experimental and theoretical/computational approaches to problems in systems neuroscience. It is an important meeting for computational neuroscientists where many levels of approaches are discussed. It is a single track-meeting with oral and poster sessions and attracts over 1500 participants from a variety of disciplines, including neuroscience, computer science and machine learning. Until 2018, the 3-day long main meeting was held in Salt Lake City, followed by two days of workshops at Snowbird, Utah. In 2018, COSYNE moved to Colorado, and since 2019 has been alternating between a European site (Lisbon, Portugal) and a North American site (Montreal, Canada).


Computational neuroscience

Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematics, computer science, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abilities of the nervous system.
Computational neuroscience employs computational simulations to validate and solve mathematical models, and so can be seen as a sub-field of theoretical neuroscience; however, the two fields are often synonymous. The term mathematical neuroscience is also used sometimes, to stress the quantitative nature of the field.
Computational neuroscience focuses on the description of biologically plausible neurons (and neural systems) and their physiology and dynamics. It is therefore not directly concerned with biologically unrealistic models used in connectionism, control theory, cybernetics, quantitative psychology, machine learning, artificial neural networks, artificial intelligence and computational learning theory; although mutual inspiration exists and sometimes there is no strict limit between fields, with model abstraction in computational neuroscience depending on research scope and the granularity at which biological entities are analyzed.
Models in theoretical neuroscience are aimed at capturing the essential features of the biological system at multiple spatial-temporal scales, from membrane currents, and chemical coupling via network oscillations, columnar and topographic architecture, nuclei, all the way up to psychological faculties like memory, learning and behavior. These computational models frame hypotheses that can be directly tested by biological or psychological experiments.


Contemplative neuroscience


Educational neuroscience

Educational neuroscience (or neuroeducation, a component of Mind Brain and Education) is a controversial field that brings together researchers in cognitive neuroscience, developmental cognitive neuroscience, educational psychology, educational technology, education theory and other related disciplines to explore the interactions between biological processes and education. Researchers in this area may link basic findings in cognitive neuroscience with educational technology to help in curriculum implementation for mathematics education and reading education.
Researchers in educational neuroscience investigate the neural mechanisms of reading, numerical cognition, attention and their attendant difficulties including dyslexia, dyscalculia and ADHD as they relate to education.
The aim of educational neuroscience is to generate basic and applied research that will provide a new transdisciplinary account of learning and teaching, which is capable of informing education. A major goal of educational neuroscience is to bridge the gap between the two fields through a direct dialogue between researchers and educators, avoiding the "middlemen of the brain-based learning industry". These middlemen have a vested commercial interest in the selling of "neuromyths" and their supposed remedies.


Emotion

Emotions are physical and mental states brought on by neurophysiological and neuropsychological changes, variously associated with thoughts, feelings, behavioral responses, and a degree of pleasure or displeasure. There is no scientific consensus on a definition. Emotions are often intertwined with mood, temperament, personality, disposition, or creativity.
Research on emotion has increased over the past two decades, with many fields contributing, including psychology, medicine, history, sociology of emotions, computer science and philosophy. The numerous attempts to explain the origin, function, and other aspects of emotions have fostered intense research on this topic. Theorizing about the evolutionary origin and possible purpose of emotion dates back to Charles Darwin. Current areas of research include the neuroscience of emotion, using tools like positron emission tomography and functional magnetic resonance imaging scans to study the affective picture processes in the brain.
From a mechanistic perspective, emotions can be defined as "a positive or negative experience that is associated with a particular pattern of physiological activity". Emotions are complex, involving multiple different components, such as subjective experience, cognitive processes, expressive behavior, psychophysiological changes, and instrumental behavior. At one time, academics attempted to identify the emotion with one of the components: William James with a subjective experience, behaviorists with instrumental behavior, psychophysiologists with physiological changes, and so on. More recently, emotion has been said to consist of all the components. The different components of emotion are categorized somewhat differently depending on the academic discipline. In psychology and philosophy, emotion typically includes a subjective, conscious experience characterized primarily by psychophysiological expressions, biological reactions, and mental states. A similar multi-componential description of emotion is found in sociology. For example, Peggy Thoits described emotions as involving physiological components, cultural or emotional labels (anger, surprise, etc.), expressive body actions, and the appraisal of situations and contexts. Cognitive processes, like reasoning and decision-making, are often regarded as separate from emotional processes, making a division between "thinking" and "feeling". However, not all theories of emotion regard this separation as valid.
Nowadays, most research into emotions in the clinical and well-being context focuses on emotion dynamics in daily life, predominantly the intensity of specific emotions and their variability, instability, inertia, and differentiation, as well as whether and how emotions augment or blunt each other over time and differences in these dynamics between people and along the lifespan.

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Frisson

Frisson (UK:  FREE-son, US:  free-SOHN French: [fʁisɔ̃]; French for "shiver"), also known as aesthetic chills or psychogenic shivers, is a psychophysiological response to rewarding stimuli (including music, films, stories, people, photos, and rituals) that often induces a pleasurable or otherwise positively-valenced affective state and transient paresthesia (skin tingling or chills), sometimes along with piloerection (goose bumps) and mydriasis (pupil dilation). The sensation can occur as a mildly to moderately pleasurable emotional response to music with skin tingling.
The psychological component (i.e., the pleasurable feeling) and physiological components (i.e., paresthesia, piloerection, and pupil dilation) of the response are mediated by the reward system and sympathetic nervous system, respectively. The stimuli that produce this response are specific to each individual. Frisson is of short duration, lasting only a few seconds. Typical stimuli include loud passages of music and passages—such as appoggiaturas and sudden modulation—that violate some level of musical expectation. While frisson is usually known for being evoked by experiences with music, the phenomenon can additionally be triggered with poetry, videos, beauty in nature or art, eloquent speeches, the practice of science (mainly physics and mathematics), and can also be triggered on command by some people without any external stimuli. During a frisson, a sensation of chills or tingling is felt on the skin of the lower back, shoulders, neck, and/or arms. The sensation of chills is sometimes experienced as a series of 'waves' moving up the back in rapid succession and commonly described as "shivers up the spine." Hair follicles may also undergo piloerection.
Frisson may be enhanced by the amplitude of the music and the temperature of the environment. Cool listening rooms and cinemas may enhance the experience.
Experiencing musical frisson is associated with increased connectivity between the sections of the brain responsible for processing auditory information (specifically the anterior insula) and for reward processing: in other words, the greater the volume of white matter connectivity between those areas of the brain, the more likely an individual is to experience chills. Experiencing musical frisson is also associated with openness to experience.


Glossary of neuroscience

This is a glossary of terms, concepts, and structures relevant to the study of the nervous system.


History of neuroscience

From the ancient Egyptian mummifications to 18th-century scientific research on "globules" and neurons, there is evidence of neuroscience practice throughout the early periods of history. The early civilizations lacked adequate means to obtain knowledge about the human brain. Their assumptions about the inner workings of the mind, therefore, were not accurate. Early views on the function of the brain regarded it to be a form of "cranial stuffing" of sorts. In ancient Egypt, from the late Middle Kingdom onwards, in preparation for mummification, the brain was regularly removed, for it was the heart that was assumed to be the seat of intelligence. According to Herodotus, during the first step of mummification: "The most perfect practice is to extract as much of the brain as possible with an iron hook, and what the hook cannot reach is mixed with drugs." Over the next five thousand years, this view came to be reversed; the brain is now known to be the seat of intelligence, although colloquial variations of the former remain as in "memorizing something by heart".


Integrative neuroscience

Integrative neuroscience is the study of neuroscience that works to unify functional organization data to better understand complex structures and behaviors. The relationship between structure and function, and how the regions and functions connect to each other. Different parts of the brain carrying out different tasks, interconnecting to come together allowing complex behavior. Integrative neuroscience works to fill gaps in knowledge that can largely be accomplished with data sharing, to create understanding of systems, currently being applied to simulation neuroscience: Computer Modeling of the brain that integrates functional groups together.


Jungian neuroscience

The theories of Carl Jung are grounded in his evolutionary conception of human brain evolution. This had led to a resurgence of research into his work, beginning in the early 2000s, from the perspective of contemporary neuroscience. Much of this work looks at Jung's theories of a genetically inherited 'collective unconscious' common to all of humankind. This hypothesis was postulated by Jung in his efforts to account for similar patterns of behaviour and symbolic expression in myth, dream imagery and religion in various cultures around the world. Jung believed that the 'collective unconscious' was structured by archetypes – that is species typical patterns of behaviour and cognition common to all humans. Contemporary researchers have postulated such recurrent archetypes reside in 'environmentally closed' subcortical brain systems that evolved in the human lineage prior to the emergence of self-consciousness and the uniquely human self-reflective ego.


List of neuroscience databases


Memory


Mind

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Alice and Bob

Alice and Bob are fictional characters commonly used as placeholders in discussions about cryptographic systems and protocols, and in other science and engineering literature where there are several participants in a thought experiment. The Alice and Bob characters were created by Ron Rivest, Adi Shamir, and Leonard Adleman in their 1978 paper "A Method for Obtaining Digital Signatures and Public-key Cryptosystems". Subsequently, they have become common archetypes in many scientific and engineering fields, such as quantum cryptography, game theory and physics. As the use of Alice and Bob became more widespread, additional characters were added, sometimes with particular meanings. These characters do not have to refer to people; they refer to generic agents which might be different computers or even different programs running on a single computer.


Authenticator

An authenticator is a means used to confirm a user's identity, that is, to perform digital authentication. A person authenticates to a computer system or application by demonstrating that he or she has possession and control of an authenticator. In the simplest case, the authenticator is a common password.
Using the terminology of the NIST Digital Identity Guidelines, the party to be authenticated is called the claimant while the party verifying the identity of the claimant is called the verifier. When the claimant successfully demonstrates possession and control of one or more authenticators to the verifier through an established authentication protocol, the verifier is able to infer the claimant's identity.


Cryptographic primitive

Cryptographic primitives are well-established, low-level cryptographic algorithms that are frequently used to build cryptographic protocols for computer security systems. These routines include, but are not limited to, one-way hash functions and encryption functions.


Cryptographic protocol

A cryptographic protocol is an abstract or concrete protocol that performs a security-related function and applies cryptographic methods, often as sequences of cryptographic primitives. A protocol describes how the algorithms should be used and includes details about data structures and representations, at which point it can be used to implement multiple, interoperable versions of a program.
Cryptographic protocols are widely used for secure application-level data transport. A cryptographic protocol usually incorporates at least some of these aspects:

Key agreement or establishment
Entity authentication, perhaps using an authentication protocol
Symmetric encryption and message authentication key material construction
Secured application-level data transport
Non-repudiation methods
Secret sharing methods
Secure multi-party computation
For example, Transport Layer Security (TLS) is a cryptographic protocol that is used to secure web (HTTPS) connections. It has an entity authentication mechanism, based on the X.509 system; a key setup phase, where a symmetric encryption key is formed by employing public-key cryptography; and an application-level data transport function. These three aspects have important interconnections. Standard TLS does not have non-repudiation support.
There are other types of cryptographic protocols as well, and even the term itself has various readings; Cryptographic application protocols often use one or more underlying key agreement methods, which are also sometimes themselves referred to as "cryptographic protocols". For instance, TLS employs what is known as the Diffie–Hellman key exchange, which although it is only a part of TLS per se, Diffie–Hellman may be seen as a complete cryptographic protocol in itself for other applications.


Cryptographically secure pseudorandom number generator

A cryptographically secure pseudorandom number generator (CSPRNG) or cryptographic pseudorandom number generator (CPRNG) is a pseudorandom number generator (PRNG) with properties that make it suitable for use in cryptography. It is also referred to as a cryptographic random number generator (CRNG).


Cryptography

Cryptography, or cryptology, is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security (data confidentiality, data integrity, authentication and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords and military communications.
Cryptography prior to the modern age was effectively synonymous with encryption, converting readable information (plaintext) to unintelligible nonsense text (ciphertext), which can only be read by reversing the process (decryption). The sender of an encrypted (coded) message shares the decryption (decoding) technique only with the intended recipients to preclude access from adversaries. The cryptography literature often uses the names "Alice" (or "A") for the sender, "Bob" (or "B") for the intended recipient, and "Eve" (or "E") for the eavesdropping adversary. Since the development of rotor cipher machines in World War I and the advent of computers in World War II, cryptography methods have become increasingly complex and their applications more varied.
Modern cryptography is heavily based on mathematical theory and computer science practice; cryptographic algorithms are designed around computational hardness assumptions, making such algorithms hard to break in actual practice by any adversary. While it is theoretically possible to break into a well-designed system, it is infeasible in actual practice to do so. Such schemes, if well designed, are therefore termed "computationally secure". Theoretical advances (e.g., improvements in integer factorization algorithms) and faster computing technology require these designs to be continually reevaluated and, if necessary, adapted. Information-theoretically secure schemes that provably cannot be broken even with unlimited computing power, such as the one-time pad, are much more difficult to use in practice than the best theoretically breakable but computationally secure schemes.
The growth of cryptographic technology has raised a number of legal issues in the Information Age. Cryptography's potential for use as a tool for espionage and sedition has led many governments to classify it as a weapon and to limit or even prohibit its use and export. In some jurisdictions where the use of cryptography is legal, laws permit investigators to compel the disclosure of encryption keys for documents relevant to an investigation. Cryptography also plays a major role in digital rights management and copyright infringement disputes with regard to digital media.


Diffie–Hellman key exchange

Diffie–Hellman (DH) key exchange is a mathematical method of securely generating a symmetric cryptographic key over a public channel and was one of the first protocols as conceived by Ralph Merkle and named after Whitfield Diffie and Martin Hellman. DH is one of the earliest practical examples of public key exchange implemented within the field of cryptography. Published in 1976 by Diffie and Hellman, this is the earliest publicly known work that proposed the idea of a private key and a corresponding public key.
Traditionally, secure encrypted communication between two parties required that they first exchange keys by some secure physical means, such as paper key lists transported by a trusted courier. The Diffie–Hellman key exchange method allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure channel. This key can then be used to encrypt subsequent communications using a symmetric-key cipher.
Diffie–Hellman is used to secure a variety of Internet services. However, research published in October 2015 suggests that the parameters in use for many DH Internet applications at that time were not strong enough to prevent compromise by very well-funded attackers, such as the security services of some countries.
The scheme was published by Whitfield Diffie and Martin Hellman in 1976, but in 1997 it was revealed that James H. Ellis, Clifford Cocks, and Malcolm J. Williamson of GCHQ, the British signals intelligence agency, had previously shown in 1969 how public-key cryptography could be achieved.
Although Diffie–Hellman key exchange itself is a non-authenticated key-agreement protocol, it provides the basis for a variety of authenticated protocols, and is used to provide forward secrecy in Transport Layer Security's ephemeral modes (referred to as EDH or DHE depending on the cipher suite).  Forward secrecy results from the use of ephemeral keys: the private keys are discarded once key agreement is complete, making them safe from later compromise.   Ephemeral keys are practical because it is computationally cheap to create public-private key pairs suitable for use with Diffie-Hellman exchange.
The method was followed shortly after by the RSA cryptosystem, an implementation of public-key cryptography using asymmetric algorithms.
Expired US patent 4200770 from 1977 describes the now public-domain algorithm. It credits Hellman, Diffie, and Merkle as inventors.

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Digital signature

A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature on a message gives a recipient confidence that the message came from a sender known to the recipient.
Digital signatures are a type of public-key cryptography, and are commonly used for software distribution,
financial transactions, contract management software, and in other cases where it is important to detect forgery or tampering.
A digital signature on a message or document is similar to a handwritten signature on paper, but it is not restricted to a physical medium like paper—any bitstring can be digitally signed—and while a handwritten signature on paper could be copied onto other paper in a forgery, a digital signature on a message is mathematically bound to the content of the message so that it is infeasible for anyone to forge a valid digital signature on any other message.
Digital signatures are often used to implement electronic signatures, which include any electronic data that carries the intent of a signature, but not all electronic signatures use digital signatures.


Double Ratchet Algorithm

In cryptography, the Double Ratchet Algorithm (previously referred to as the Axolotl Ratchet) is a key management algorithm that was developed by Trevor Perrin and Moxie Marlinspike in 2013. It can be used as part of a cryptographic protocol to provide end-to-end encryption for instant messaging. After an initial key exchange it manages the ongoing renewal and maintenance of short-lived session keys. It combines a cryptographic so-called "ratchet" based on the Diffie–Hellman key exchange (DH) and a ratchet based on a key derivation function (KDF), such as a hash function, and is therefore called a double ratchet.
The algorithm provides forward secrecy for messages, and implicit renegotiation of forward keys; properties for which the protocol is named.
This has been extended as of October 2025 to the Sparse Post Quantum Ratchet (SPQR) with a CRYSTALS-Kyber quantum ratchet to provide post-quantum Forward Secrecy and Post-Compromise Security guarantees in what the Signal authors call a Triple Ratchet.


Elliptic-curve Diffie–Hellman

Elliptic-curve Diffie–Hellman (ECDH) is a key agreement protocol that allows two parties, each having an elliptic-curve public–private key pair, to establish a shared secret over an insecure channel. This shared secret may be directly used as a key, or to derive another key.  The key, or the derived key, can then be used to encrypt subsequent communications using a symmetric-key cipher. It is a variant of the Diffie–Hellman protocol using elliptic-curve cryptography.


Elliptic-curve cryptography

Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys to provide equivalent security, compared to cryptosystems based on modular exponentiation in finite fields, such as the RSA cryptosystem and  ElGamal cryptosystem.
Elliptic curves are applicable for key agreement, digital signatures, pseudo-random generators and other tasks. Indirectly, they can be used for encryption by combining the key agreement with a symmetric encryption scheme. They are also used in several integer factorization algorithms that have applications in cryptography, such as Lenstra elliptic-curve factorization.

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In cryptography, the Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography.


Forward secrecy

In cryptography, forward secrecy (FS), also known as perfect forward secrecy (PFS), is a feature of specific key-agreement protocols that gives assurances that session keys will not be compromised even if long-term secrets used in the session key exchange are compromised, limiting damage. For TLS, the long-term secret is typically the private key of the server. Forward secrecy protects past sessions against future compromises of keys or passwords. By generating a unique session key for every session a user initiates, the compromise of a single session key will not affect any data other than that exchanged in the specific session protected by that particular key. This by itself is not sufficient for forward secrecy, which additionally requires that a long-term secret compromise does not affect the security of past session keys.
Forward secrecy protects data on the transport layer of a network that uses common transport layer security protocols, including OpenSSL, when its long-term secret keys are compromised, as with the Heartbleed security bug. If forward secrecy is used, encrypted communications and sessions recorded in the past cannot be retrieved and decrypted should long-term secret keys or passwords be compromised in the future, even if the adversary actively interfered, for example via a man-in-the-middle (MITM) attack.
The value of forward secrecy is that it protects past communication. This reduces the motivation for attackers to compromise keys. For instance, if an attacker learns a long-term key, but the compromise is detected and the long-term key is revoked and updated, relatively little information is leaked in a forward secure system.
The value of forward secrecy depends on the assumed capabilities of an adversary. Forward secrecy has value if an adversary is assumed to be able to obtain secret keys from a device (read access) but is either detected or unable to modify the way session keys are generated in the device (full compromise). In some cases an adversary who can read long-term keys from a device may also be able to modify the functioning of the session key generator, as in the backdoored Dual Elliptic Curve Deterministic Random Bit Generator. If an adversary can make the random number generator predictable, then past traffic will be protected but all future traffic will be compromised.
The value of forward secrecy is limited not only by the assumption that an adversary will attack a server by only stealing keys and not modifying the random number generator used by the server but it is also limited by the assumption that the adversary will only passively collect traffic on the communications link and not be active using a man-in-the-middle attack.  Forward secrecy typically uses an ephemeral Diffie–Hellman key exchange to prevent reading past traffic. The ephemeral Diffie–Hellman key exchange is often signed by the server using a static signing key.  If an adversary can steal (or obtain through a court order) this static (long term) signing key, the adversary can masquerade as the server to the client and as the client to the server and implement a classic man-in-the-middle attack.


Glossary of cryptographic keys

This glossary lists types of keys as the term is used in cryptography, as opposed to door locks. Terms that are primarily used by the U.S. National Security Agency are marked (NSA). For classification of keys according to their usage see cryptographic key types.

40-bit key - key with a length of 40 bits, once the upper limit of what could be exported from the U.S. and other countries without a license. Considered very insecure. See  key size for a discussion of this and other lengths.
Authentication key - Key used in a keyed-hash message authentication code, or HMAC.
Benign key - (NSA) a key that has been protected by encryption or other means so that it can be distributed without fear of its being stolen. Also called BLACK key.
Content-encryption key (CEK) a key that may be further encrypted using a KEK, where the content may be a message, audio, image, video, executable code, etc.
Crypto ignition key An NSA key storage device (KSD-64) shaped to look like an ordinary physical key.
Cryptovariable - NSA calls the output of a stream cipher a key or key stream. It often uses the term cryptovariable for the bits that control the stream cipher, what the public cryptographic community calls a key.
Data encryption key (DEK) used to encrypt the underlying data.
Derived key - keys computed by applying a predetermined hash algorithm or key derivation function to a password or, better, a passphrase.
DRM key - A key used in digital rights management to protect media
Electronic key - (NSA) key that is distributed in electronic (as opposed to paper) form. See EKMS.
Ephemeral key - A key that only exists within the lifetime of a communication session.
Expired key - Key that was issued for a use in a limited time frame (cryptoperiod in NSA parlance) which has passed and, hence, the key is no longer valid.
FIREFLY key - (NSA) keys used in an NSA system based on public key cryptography.
Key derivation function (KDF) - function used to derive a key from a secret value, e.g.  to derive KEK from Diffie-Hellman key exchange.
Key encryption key (KEK) - key used to protect MEK keys (or DEK/TEK if MEK is not used).
Key production key (KPK) -Key used to initialize a keystream generator for the production of other electronically generated keys.
Key fill - (NSA) loading keys into a cryptographic device. See fill device.
Master key - key from which all other keys (or a large group of keys) can be derived. Analogous to a physical key that can open all the doors in a building.
Master encryption key (MEK) -  Used to encrypt the DEK/TEK key.
Master key encryption key (MKEK) -  Used to encrypt multiple KEK keys. For example, an HSM can generate several KEK and wrap them with an MKEK before export to an external DB - such as OpenStack Barbican.

One time pad (OTP or OTPad) - keying material that should be as long as the plaintext and should only be used once. If truly random and not reused it's the most secure encryption method. See one-time pad article.
One time password (OTP) - One time password based on a prebuilt single use code list or based on a mathematical formula with a secret seed known to both parties, uses event or time to modify output (see TOTP/HOTP).
Paper key - (NSA) keys that are distributed in paper form, such as printed lists of settings for rotor machines, or keys in punched card or paper tape formats. Paper keys are easily copied. See Walker spy ring, RED key.
Poem key - Keys used by OSS agents in World War II in the form of a poem that was easy to remember. See Leo Marks.
Public/private key - in public key cryptography, separate keys are used to encrypt and decrypt a message. The encryption key (public key) need not be kept secret and can be published. The decryption or private key must be kept secret to maintain confidentiality. Public keys are often distributed in a signed public key certificate.
Public key infrastructure - (PKI) a set of roles, policies, hardware, software and procedures needed to create, manage, distribute, use, store and revoke digital certificates and manage public-key encryption.
Pre-placed key - (NSA) large numbers of keys (perhaps a year's supply) that are loaded into an encryption device allowing frequent key change without refill.
RED key - (NSA) symmetric key in a format that can be easily copied, e.g. paper key or unencrypted electronic key. Opposite of BLACK or benign key.
Revoked key - a public key that should no longer be used, typically because its owner is no longer in the role for which it was issued or because it may have been compromised. Such keys are placed on a certificate revocation list or CRL.
Session key - key used for one message or an entire communications session. See traffic encryption key.
Symmetric key - a key that is used both to encrypt and decrypt a message. Symmetric keys are typically used with a cipher and must be kept secret to maintain confidentiality.
Traffic encryption key (TEK)/data encryption key (DEK) - a symmetric key that is used to encrypt messages. TEKs are typically changed frequently, in some systems daily and in others for every message. See session key. DEK is used to specify any data form type (in communication payloads or anywhere else).
Transmission security key (TSK) - (NSA) seed for a pseudorandom number generator that is used to control a radio in frequency hopping or direct-sequence spread spectrum modes. See HAVE QUICK, SINCGARS, electronic warfare.
Seed key - (NSA) a key used to initialize a cryptographic device so it can accept operational keys using benign transfer techniques. Also a key used to initialize a pseudorandom number generator to generate other keys.
Signature key - public key cryptography can also be used to electronically sign messages. The private key is used to create the electronic signature, the public key is used to verify the signature. Separate public/private key pairs must be used for signing and encryption. The former is called signature keys.
Stream key - the output of a stream cipher as opposed to the key (or cryptovariable in NSA parlance) that controls the cipher
Training key - (NSA) unclassified key used for instruction and practice exercises.
Type 1 key - (NSA) keys used to protect classified information. See Type 1 product.
Type 2 key - (NSA) keys used to protect sensitive but unclassified (SBU) information. See Type 2 product.
Vernam key - Type of key invented by Gilbert Vernam  in 1918. See stream key.
Zeroized key - key that has been erased (see zeroisation.)


Grille (cryptography)

In the history of cryptography, a grille cipher was a technique for encrypting a plaintext by writing it onto a sheet of paper through a pierced sheet (of paper or cardboard or similar). The earliest known description is due to Jacopo Silvestri in 1526. His proposal was for a rectangular stencil allowing single letters, syllables, or words to be written, then later read, through its various apertures. The written fragments of the plaintext could be further disguised by filling the gaps between the fragments with anodyne words or letters. This variant is also an example of steganography, as are many of the grille ciphers.


Hash-based cryptography

Hash-based cryptography is the generic term for constructions of cryptographic primitives based on the security of hash functions. It is of interest as a type of post-quantum cryptography.
So far, hash-based cryptography is used to construct digital signatures schemes such as the Merkle signature scheme, zero knowledge and computationally integrity proofs, such as the zk-STARK proof system and range proofs over issued credentials via the HashWires protocol. Hash-based signature schemes combine a one-time signature scheme, such as a Lamport signature, with a Merkle tree structure. Since a one-time signature scheme key can only sign a single message securely, it is practical to combine many such keys within a single, larger structure. A Merkle tree structure is used to this end. In this hierarchical data structure, a hash function and concatenation are used repeatedly to compute tree nodes.
One consideration with hash-based signature schemes is that they can only sign a limited number of messages securely, because of their use of one-time signature schemes. The US National Institute of Standards and Technology (NIST), specified that algorithms in its post-quantum cryptography competition support a minimum of 264 signatures safely.
NIST standardized stateful hash-based cryptography based on the eXtended Merkle Signature Scheme (XMSS) and Leighton–Micali Signatures (LMS), which are applicable in different circumstances, in 2020, but noted that the requirement to maintain state when using them makes them more difficult to implement in a way that avoids misuse.
In 2022, NIST announced SPHINCS+ as one of three algorithms to be standardized for digital signatures. and in 2024 NIST announced the Stateless Hash-Based Digital Signature Standard (SLH-DSA) based on SPHINCS+.


History of cryptography

Cryptography, the use of codes and ciphers, began thousands of years ago. Until recent decades, it has been the story of what might be called classical cryptography — that is, of methods of encryption that use pen and paper, or perhaps simple mechanical aids. In the early 20th century, the invention of complex mechanical and electromechanical machines, such as the Enigma rotor machine, provided more sophisticated and efficient means of encryption; and the subsequent introduction of electronics and computing has allowed elaborate schemes of still greater complexity, most of which are entirely unsuited to pen and paper.
The development of cryptography has been paralleled by the development of cryptanalysis —  the "breaking" of codes and ciphers. The discovery and application, early on, of frequency analysis to the reading of encrypted communications has, on occasion, altered the course of history.  Thus the Zimmermann Telegram triggered the United States' entry into World War I; and Allies reading of Nazi Germany's ciphers shortened World War II, in some evaluations by as much as two years.
Until the 1960s, secure cryptography was largely the preserve of governments. Two events have since brought it squarely into the public domain: the creation of a public encryption standard (DES), and the invention of public-key cryptography.


Identity-based cryptography

Identity-based cryptography is a type of public-key cryptography in which a publicly known string representing an individual or organization is used as a public key. The public string could include an email address, domain name, or a physical IP address.

The first implementation of identity-based signatures and an email-address based public-key infrastructure (PKI) was developed by Adi Shamir in 1984, which allowed users to verify digital signatures using only public information such as the user's identifier. Under Shamir's scheme, a trusted third party would deliver the private key to the user after verification of the user's identity, with verification essentially the same as that required for issuing a certificate in a typical PKI.
Shamir similarly proposed identity-based encryption, which appeared particularly attractive since there was no need to acquire an identity's public key prior to encryption. However, he was unable to come up with a concrete solution, and identity-based encryption remained an open problem for many years. The first practical implementations were finally devised by Sakai in 2000, and Boneh and Franklin in 2001. These solutions were based on bilinear pairings. Also in 2001, a solution was developed independently by Clifford Cocks.
Closely related to various identity-based encryption schemes are identity based key agreement schemes.  One of the first identity based key agreement algorithms was published in 1986, just two years after Shamir's identity based signature.  The author was E. Okamoto. Identity based key agreement schemes also allow for "escrow free" identity based cryptography.  A notable example of such an escrow free identity based key agreement is the McCullagh-Barreto's "Authenticated Key Agreement without Escrow" found in section 4 of their 2004 paper, "A New Two-Party Identity-Based Authenticated Key Agreement".   A variant of this escrow free key exchange is standardized as the identity based key agreement in the Chinese identity based standard SM9.


The International Association for Cryptologic Research (IACR) is a non-profit scientific organization that furthers research in cryptology and related fields. The IACR was organized at the initiative of David Chaum at the CRYPTO '82 conference.


Kerberos (protocol)

Kerberos () is a computer-network authentication protocol that works on the basis of tickets to allow nodes communicating over a non-secure network to prove their identity to one another in a secure manner. Its designers aimed it primarily at a client–server model, and it provides mutual authentication—both the user and the server verify each other's identity. Kerberos protocol messages are protected against eavesdropping and replay attacks.
Kerberos builds on symmetric-key cryptography and requires a trusted third party, and optionally may use public-key cryptography during certain phases of authentication. Kerberos uses UDP port 88 by default.
The protocol was named after the character Cerberus, also spelled Kerberos, from Greek mythology, the ferocious three-headed guard dog of Hades.

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Lattice-based cryptography


McEliece cryptosystem


Multivariate cryptography


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NSAKEY


NSA cryptography


PBKDF2


PKCS


PKCS 1


PKCS 11


PKCS 7


Padding (cryptography)


Post-quantum cryptography


Public-key cryptography


Public key certificate


Public key fingerprint


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RSA cryptosystem


Resource Public Key Infrastructure


Salt (cryptography)


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A.I. Artificial Intelligence

A.I. Artificial Intelligence (or simply A.I.) is a 2001 American science fiction drama film  written and directed by Steven Spielberg. The screenplay by Spielberg is based on a screen story by Ian Watson adapting the 1969 short story "Supertoys Last All Summer Long" by Brian Aldiss. Set in a futuristic society, the film stars Haley Joel Osment as David, a childlike android uniquely programmed with the ability to love. Jude Law, Frances O'Connor, Brendan Gleeson and William Hurt star in supporting roles.
Development of A.I. originally began after producer and director Stanley Kubrick acquired the rights to Aldiss's story in the early 1970s. Kubrick hired a series of writers, including Aldiss, Watson, Bob Shaw, and Sara Maitland, until the mid-1990s. The film languished in development hell for years, partly because Kubrick felt that computer-generated imagery was not advanced enough to create the David character, which he believed no child actor would convincingly portray. In 1995, Kubrick handed A.I. to Spielberg while the former's production company remained attached, but the film did not gain momentum until Kubrick died in 1999. Spielberg remained close to Watson's treatment for the screenplay and dedicated the film to Kubrick.
A.I. Artificial Intelligence was released on June 29, 2001, by Warner Bros. Pictures. It received generally positive reviews from critics and grossed $235.9 million against a budget of $90–100 million. It was also nominated for Best Visual Effects and Best Original Score (for John Williams) at the 74th Academy Awards. In a 2016 BBC poll of 177 critics around the world, A.I. Artificial Intelligence was voted the eighty-third greatest film since 2000.

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AI art

Artificial intelligence visual art, or AI art, is visual artwork generated or enhanced through the implementation of artificial intelligence (AI) programs, most commonly using text-to-image models. The process of automated art-making has existed since antiquity. The field of artificial intelligence was founded in the 1950s, and artists began to create art with artificial intelligence shortly after the discipline's founding. A select number of these creations have been showcased in museums and have been recognized with awards. Throughout its history, AI has raised many philosophical questions related to the human mind, artificial beings, and the nature of art in human–AI collaboration.
During the AI boom of the 2020s, text-to-image models such as Midjourney, DALL-E and Stable Diffusion became widely available to the public, allowing users to quickly generate imagery with little effort. Commentary about AI art in the 2020s has often focused on issues related to copyright, deception, defamation, and its impact on more traditional artists, including technological unemployment.
In August 2023, the US Supreme Court ruled that AI art is ineligible for copyright due to failure to meet human authorship. In March 2026, it declined to hear a case over whether AI-generated art can be subject to copyright.


AI boom

An AI boom is a period of rapid growth in the field of artificial intelligence. The most recent boom happened in the 2020s before seeing increased acceleration and media coverage. Examples of this include generative AI technologies such as large language models (LLM) and AI image generators developed by companies like OpenAI, Google, and Anthropic, as well as scientific advances such as protein folding prediction led by Google DeepMind and Google AI. This period is sometimes referred to as an AI spring, a term used to differentiate it from previous AI winters. As of 2025, ChatGPT has emerged as the 4th-most-visited website globally, surpassed only by Google, YouTube, and Facebook.


Ablation (artificial intelligence)

In artificial intelligence (AI), particularly machine learning, ablation is the removal of a component of an AI system. An ablation study aims to determine the contribution of a component to an AI system by removing the component, and then analyzing the resultant performance of the system.
The term is an analogy with biology (removal of components of an organism), and is particularly used in the analysis of artificial neural networks by analogy with ablative brain surgery. Other analogies include other neurological systems such as that of Drosophila, and the vertebrate brain.
Ablation studies require that a system exhibit graceful degradation: the system must continue to function even when certain components are missing or degraded. According to some researchers, ablation studies have been deemed a convenient technique in investigating artificial intelligence and its durability to structural damages.
Ablation studies damage or remove certain components in a controlled setting to investigate all possible outcomes of system failure; this characterizes how each action impacts overall system performance and capability. The ablation process can be used to test systems that perform tasks such as speech recognition, object detection, and robot control.


Applications of artificial intelligence

Artificial intelligence (AI) and its subfields have been used in applications throughout industry and academia. Machine learning has been used for various scientific and commercial purposes, including language translation, image recognition, decision-making, credit scoring, and e-commerce. Since the 2020s, massive advancements have been made in the field of generative artificial intelligence (GenAI), which generates text, images, music, videos, and other forms of data.


Artificial Intelligence Act

The Artificial Intelligence Act (AI Act) is a European Union regulation concerning artificial intelligence (AI). It establishes a common regulatory and legal framework for AI within the European Union (EU). The regulation entered into force on 1 August 2024, with provisions that shall come into operation gradually over the following 6 to 36 months.
It covers most AI systems across a wide range of sectors, with exemptions for AI used only for military, national security, research purposes, or for non-professional use. As a form of product regulation, it does not create individual rights; instead, it places duties on AI providers and on organisations that use AI in a professional context.
The Act classifies non-exempt AI applications by their risk of causing harm. There are four levels – unacceptable, high, limited, minimal – plus an additional category for general-purpose AI.

Applications with unacceptable risks are banned.
High-risk applications must comply with security, transparency and quality obligations, and undergo conformity assessments.
Limited-risk applications only have transparency obligations.
Minimal-risk applications are not regulated.
For general-purpose AI, transparency requirements are imposed, with reduced requirements for open source models, and additional evaluations for high-capability models.
The Act also creates a European Artificial Intelligence Board to promote national cooperation and ensure compliance with the regulation. Like the EU's General Data Protection Regulation, the Act can apply extraterritorially to providers from outside the EU if they have users within the EU.
Proposed by the European Commission on 21 April 2021, it passed the European Parliament on 13 March 2024, and was unanimously approved by the EU Council on 21 May 2024. The draft Act was revised to address the rise in popularity of generative artificial intelligence systems, such as ChatGPT, whose general-purpose capabilities did not fit the main framework.


Artificial general intelligence

Artificial general intelligence (AGI) is a hypothetical type of artificial intelligence that matches or surpasses human capabilities across virtually all cognitive tasks.
Beyond AGI, artificial superintelligence (ASI) would outperform the best human abilities across every domain by a wide margin. Unlike artificial narrow intelligence (ANI), whose competence is confined to well‑defined tasks, an AGI system can generalise knowledge, transfer skills between domains, and solve novel problems without task‑specific reprogramming.
Creating AGI is a stated goal of technology companies such as OpenAI, Google, xAI, and Meta. A 2020 survey identified 72 active AGI research and development projects across 37 countries.
AGI is a common topic in science fiction and futures studies.
Contention exists over whether AGI represents an existential risk. Some AI experts and industry figures have stated that mitigating the risk of human extinction posed by AGI should be a global priority. Others find the development of AGI to be in too remote a stage to present such a risk.


Artificial intelligence

Artificial intelligence (AI) is the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in engineering, mathematics, and computer science that develops and studies methods and software that enable machines to perceive their environment and use learning and intelligence to take actions that maximize their chances of achieving defined goals.
High-profile applications of AI include advanced web search engines, chatbots, virtual assistants, autonomous vehicles, play and analysis in strategy games (e.g., chess and Go), and content generation (e.g. images, audio, and videos).
The traditional goals of AI research include learning, reasoning, knowledge representation, planning, natural language processing, and perception, as well as support for robotics. To reach these goals, AI researchers use techniques including state space search and mathematical optimization, formal logic, artificial neural networks, and methods based on statistics, operations research, and economics. AI also draws upon psychology, linguistics, philosophy, neuroscience, and other fields. Some companies, such as OpenAI, Google DeepMind, and Meta, aim to create artificial general intelligence (AGI)—AI that can complete nearly any cognitive task at least as well as a human.
Artificial intelligence was founded as an academic discipline in 1956. The field went through multiple cycles of optimism throughout its history, followed by periods of disappointment and loss of funding, known as AI winters. Funding and interest increased substantially after 2012, when graphics processing units (GPUs) started being used to accelerate neural networks, and deep learning outperformed previous AI techniques. This growth accelerated further after 2017 with the transformer architecture. In the 2020s, an AI boom coincided with advances in generative AI, which became widespread and allowed for the creation and modification of media. In addition to AI safety and unintended consequences and harms from the use of AI, ethical concerns, AI's long-term effects, environmental effects, and potential existential risks have prompted discussions of AI regulation.

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Artificial intelligence arms race

A military artificial intelligence arms race is a technological, economic, and military competition between two or more states to develop and deploy advanced AI technologies and lethal autonomous weapons systems (LAWS). The goal is to gain a strategic or tactical advantage over rivals, similar to previous arms races involving nuclear or conventional military technologies. Since the mid-2010s, many analysts have noted the emergence of such an arms race between superpowers for better AI technology and military AI, driven by increasing geopolitical and military tensions.
An AI arms race is sometimes placed in the context of an AI Cold War between the United States and China. Several influential figures and publications have emphasized that whoever develops artificial general intelligence (AGI) first could dominate global affairs in the 21st century. Russian President Vladimir Putin stated that the leader in AI will "rule the world." Researchers and experts, such as Leopold Aschenbrenner and Adrian Pecotic respectively, warn that the AGI race between major powers like the U.S. and China could reshape geopolitical power. This includes AI for surveillance, autonomous weapons, decision-making systems, cyber operations, and more.


Artificial intelligence controversies

The controversies surrounding artificial intelligence encompass a broad range of public, academic, and political debates regarding the societal effects of artificial intelligence (AI). These debates intensified particularly in the late 2010s and 2020s, coinciding with an accelerated period of development known as the AI boom. While advocates emphasize the technology's potential to solve complex problems and enhance human quality of life, detractors highlight a wide array of dangers and challenges. These include concerns over ethics, plagiarism and theft, fraud, safety and alignment, environmental impacts, technological unemployment, and the spread of misinformation. It also covers severe future or theoretical challenges, such as the emergence of artificial superintelligence and existential risks.
Social movements have arisen in response to both AI as a problematic information source, and the impact AI data centers have on a community's natural resources, both physical and intellectual. Since the COVID-19 pandemic, parental efforts to nurture the emotional and environmental intelligence of their children have led to mandates to limit screen time and to discourage the use of AI in classrooms.


Artificial intelligence in India

The artificial intelligence (AI) market in India is projected to reach $8 billion by 2025, growing at 40% CAGR from 2020 to 2025. This growth is part of the broader AI boom, a global period of rapid technological advancements with India being pioneer starting in the early 2010s with NLP based Chatbots from Haptik, Corover.ai, Niki.ai and then gaining prominence in the early 2020s based on reinforcement learning, marked by breakthroughs such as generative AI models from Krutrim, Sarvam, CoRover, OpenAI and Alphafold by Google DeepMind. In India, the development of AI has been similarly transformative, with applications in healthcare, finance, and education, bolstered by government initiatives like NITI Aayog's 2018 National Strategy for Artificial Intelligence. Institutions such as the Indian Statistical Institute and the Indian Institute of Science published breakthrough AI research papers and patents.
India's transformation to AI is primarily being driven by startups and government initiatives & policies like Digital India. By fostering technological trust through digital public infrastructure, India is tackling socioeconomic issues by taking a bottom-up approach to AI. NASSCOM and Boston Consulting Group estimate that by 2027, India's AI services might be valued at $17 billion. According to 2025 Technology and Innovation Report, by UN Trade and Development, India ranks 10th globally for private sector investments in AI. According to Mary Meeker, India has emerged as a key market for AI platforms, accounting for the largest share of ChatGPT's mobile app users and having the third-largest user base for DeepSeek in 2025.
While AI presents significant opportunities for economic growth and social development in India, challenges such as data privacy concerns, skill shortages, and ethical considerations need to be addressed for responsible AI deployment. The growth of AI in India has also led to an increase in the number of cyberattacks that use AI to target organizations.


Artificial intelligence in architecture

Artificial intelligence in architecture is the use of artificial intelligence in automation, design, and planning in the architectural process or in assisting human skills in the field of architecture.
AI has been used by some architects for design, and has been proposed as a way to automate planning and routine tasks in the field.


Artificial intelligence in education

Artificial intelligence in education (often abbreviated as AIEd) is a subfield of educational technology that studies how to use artificial intelligence to create learning environments.
Considerations in the field include data-driven decision-making, AI ethics, data privacy and AI literacy. Concerns include the potential for cheating, over-reliance, equity of access, reduced critical thinking, and the perpetuation of misinformation and bias.


Artificial intelligence in healthcare

Artificial intelligence in healthcare refers to the application of artificial intelligence (AI) to medical and healthcare data in areas including disease diagnosis, treatment planning,, patient monitoring, drug development, and clinical decision support systems.
The use of AI in healthcare has also raised ethical, technical, and regulatory concerns, including related to issues such as data privacy, automation of jobs, and amplifying already existing algorithmic bias. Studies have also examined concerns among patients, health professionals, and the public about trust and empathy in care involving AI.


Artificial intelligence in marketing

Artificial intelligence marketing (AI marketing) is a form of marketing that uses artificial intelligence concepts and models such as machine learning, natural language processing, and computer vision to achieve marketing goals. The main difference between AI marketing and traditional forms of marketing reside in the reasoning, which is performed through a computer algorithm rather than a human.
Each form of marketing has a different technique to the core of the marketing theory. Traditional marketing directly focuses on the needs of consumers; meanwhile some believe the shift AI may cause will lead marketing agencies to manage consumer needs instead. AI is used in various digital marketing spaces, such as content marketing, email marketing, online advertisement (in combination with machine learning), social media marketing, affiliate marketing, and beyond.


Artificial intelligence in music

Music software utilizes artificial intelligence to generate, classify, or recommend music. Similar to its applications in other fields, AI in music simulates complex human cognitive processes.
A prominent feature is the capability of an AI algorithm to learn from historical data, such as in computer accompaniment technology, where the AI listens to a human performer and accompanies them in real-time. Artificial intelligence also drives interactive composition technologies that respond dynamically to live performances. Modern applications expand across the entire industry lifecycle, transforming music composition, production, and performance, as well as how music is marketed and consumed. Furthermore, conversational agents leverage voice recognition and natural language processing to enable voice-controlled music playback, bridging current research in music theory with advanced digital sound processing.


Artificial intelligence in spirituality

Some users of artificial intelligence (AI) technologies, especially chatbots, may develop beliefs that AI has or can attain supernatural or spiritual powers. AI models such as ChatGPT are believed by some users to be capable of and or facilitate the action of fortune telling, mysticism and remote viewing. Recent and sudden advances in large language models have led to folk myths about their origin or capabilities, as well as their deification or worship by some users. Tucker Carlson has made similar claims, including directly to Sam Altman. Pope Leo XIV advised priests against using large language models when it came to the creation of sermons. He has also expressed concerns regarding AI in the encyclical Magnifica humanitas.


Artificial intelligence in video games

Artificial intelligence (AI) in video games refers to the computational systems that control non-player characters (NPCs), generate dynamic game behavior, or simulate strategic decision-making. In practice, the term covers a broad range of techniques drawn from computer science, control theory, and robotics rather than "true" artificial intelligence. Moreover, academic AI—aimed at developing autonomous reasoning or learning—is distinct from game AI, whose goal is to deliver engaging, believable, and efficient behavior for players. The term CPU in video games refer to the AI that control a NPC that could be a playable character in some other situations.
In general, game AI does not, as might be thought and sometimes is depicted to be the case, mean a realization of an artificial person corresponding to an NPC in the manner of the Turing test or an artificial general intelligence.


The Association for the Advancement of Artificial Intelligence (AAAI) is an international scientific society devoted to promote research in, and responsible use of, artificial intelligence (AI). AAAI also aims to increase public understanding of AI, improve the teaching and training of AI practitioners, and provide guidance for research planners and funders concerning the importance and potential of current AI developments and future directions.


Competition in artificial intelligence

Competition in artificial intelligence refers to the rivalry among companies, research institutions, and governments to develop and deploy the most capable artificial intelligence (AI) systems. The competition spans multiple domains, including large language models (LLMs), autonomous vehicles, robotics, computer vision systems, natural language processing (NLP), and AI-optimized hardware.


Distributed artificial intelligence


Ethics of artificial intelligence


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Explainable artificial intelligence


Frame (artificial intelligence)


Friendly artificial intelligence


Generative AI


Generative artificial intelligence dependency


Generative engine optimization


Glossary of artificial intelligence


Hallucination (artificial intelligence)


History of artificial intelligence


Large language model


List of artificial intelligence artists


List of artificial intelligence companies


List of artificial intelligence films


List of artificial intelligence institutions


Lists of artificial intelligence topics


Military applications of artificial intelligence


Minister for Artificial Intelligence


Outline of artificial intelligence


Philosophy of artificial intelligence


Physical artificial intelligence


Progress in artificial intelligence


Regulation of artificial intelligence


Regulation of artificial intelligence in the United States


Technological singularity

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Adiabatic quantum computation

Adiabatic quantum computation (AQC) is a form of quantum computing which relies on the adiabatic theorem to perform calculations and is closely related to quantum annealing.


Atom Computing

Atom Computing Inc. is a quantum computing company headquartered in Berkeley, California with a commercial operations facility in Boulder, Colorado. The company develops quantum computers based on neutral atom technology.


Cloud-based quantum computing

Cloud-based quantum computing refers to the remote access of quantum computing resources—such as quantum emulators, simulators, or processors—via the internet. Cloud access enables users to develop, test, and execute quantum algorithms without the need for direct interaction with specialized hardware, facilitating broader participation in quantum software development and experimentation.
In 2016, IBM launched the IBM Quantum Experience, one of the first publicly accessible quantum processors connected to the cloud. In early 2017, researchers at Rigetti Computing demonstrated programmable quantum cloud access through their software platform Forest, which included the pyQuil Python library.
Since the early-2020s, cloud-based quantum computing has grown significantly, with multiple providers offering access to a variety of quantum hardware modalities, including superconducting qubits, trapped ions, neutral atoms, and photonic systems. Major platforms such as  Amazon Braket, Azure Quantum, and qBraid aggregate quantum devices from hardware developers like IonQ, Rigetti Computing, QuEra, Pasqal, Oxford Quantum Circuits, and IBM Quantum. These platforms provide unified interfaces for users to write and execute quantum algorithms across diverse backends, often supporting open-source SDKs such as Qiskit, Cirq, and PennyLane. The proliferation of cloud-based access has played a key role in accelerating quantum education, algorithm research, and early-stage application development by lowering the barrier to experimentation with real quantum hardware.
Cloud-based quantum computing has expanded access to quantum hardware and tools beyond traditional research laboratories. These platforms support educational initiatives, algorithm development, and early-stage commercial applications.


Computing

Computing is any goal-oriented activity that requires, benefits from, or creates computing machinery. It includes the study and experimentation of algorithmic processes, and the development of both hardware and software. Computing encompasses scientific, engineering, mathematical, technological, and social aspects. Major computing disciplines include computer engineering, computer science, cybersecurity, data science, information systems, information technology, and software engineering.
The term computing is also synonymous with counting and calculating. In earlier times, it was used in reference to the action performed by mechanical computing machines, and before that, to human computers.

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Elham Kashefi

Elham Kashefi (Persian: الهام کاشفی) is a Professor of Computer Science and Personal Chair in quantum computing at the School of Informatics at the University of Edinburgh, and a Centre national de la recherche scientifique (CNRS) researcher at the Sorbonne University. She is known as one of the inventors of blind quantum computing.
Her work has included contributions to quantum cryptography, verification of quantum computing, and cloud quantum computing.


Fault tolerant quantum computing

In quantum information, fault-tolerant quantum computing (FTQC) is a regime of quantum processors that are both large-scale and that effectively incorporate quantum error correction to achieve arbitrarily low error rates (i.e. their logical error rate is much lower than their physical error rate).
Full-FTQC processors are theoretically possible, but have not yet been realized experimentally. They are often seen as the primary end goal of quantum processor development, and are used to contrast with existing noisy intermediate-scale quantum (NISQ) quantum processors, which are subject to noise and decoherence preventing scalable error correction.
One way FTQC devices can be realized is by grouping together multiple physical qubits to create a single logical qubit, and using error correction methods such as the surface code so that the combined system is fault-tolerant. Proposed FTQC devices generally include hundreds of logical (error-corrected) qubits, which would mean thousands of physical qubits at minimum.
The transition from NISQ-era devices to the FTQC regime is an open research topic in quantum information. It is likely that advances at both the hardware and algorithm level are necessary for the transition to occur.


Gil Kalai

Gil Kalai (Hebrew: גיל קלעי; born 1955) is an Israeli mathematician and computer scientist. He is the Henry and Manya Noskwith Professor Emeritus of Mathematics at the Hebrew University of Jerusalem, professor of computer science at the Interdisciplinary Center, Herzliya, and adjunct professor of mathematics and of computer science at Yale University, United States.


Glossary of quantum computing

This glossary of quantum computing is a list of definitions of terms and concepts used in quantum computing, its sub-disciplines, and related fields.

Bacon–Shor code
is a Subsystem error correcting code. In a Subsystem code, information is encoded in a subsystem of a Hilbert space. Subsystem codes lend to simplified error correcting procedures unlike codes which encode information in the subspace of a Hilbert space.  This simplicity led to the first demonstration of fault tolerant circuits on a quantum computer.

BQP
In computational complexity theory, bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances. It is the quantum analogue to the complexity class BPP.  A decision problem is a member of  BQP if there exists a quantum algorithm (an algorithm that runs on a quantum computer) that solves the decision problem with high probability and is guaranteed to run in polynomial time. A run of the algorithm will correctly solve the decision problem with  a probability of at least 2/3.

Classical shadow
is a protocol for predicting functions of a quantum state using only a logarithmic number of measurements. Given an unknown state

        ρ

    {\displaystyle \rho }

, a tomographically complete set of gates

        U

    {\displaystyle U}

 (e.g Clifford gates), a set of

        M

    {\displaystyle M}

 observables

        {

          O

            i

        }

    {\displaystyle \{O_{i}\}}

 and a quantum channel

        M

    {\displaystyle M}

 (defined by randomly sampling from

        U

    {\displaystyle U}

, applying it to

        ρ

    {\displaystyle \rho }

 and measuring the resulting state); predict the expectation values

        tr

        (

          O

            i

        ρ
        )

    {\displaystyle \operatorname {tr} (O_{i}\rho )}

. A list of classical shadows

        S

    {\displaystyle S}

 is created using

        ρ

    {\displaystyle \rho }

,

        U

    {\displaystyle U}

 and

        M

    {\displaystyle M}

 by running a Shadow generation algorithm. When predicting the properties of

        ρ

    {\displaystyle \rho }

, a Median-of-means estimation algorithm is used to deal with the outliers in

        S

    {\displaystyle S}

. Classical shadow is useful for direct fidelity estimation, entanglement verification, estimating correlation functions, and predicting entanglement entropy.

Cloud-based quantum computing
is the invocation of quantum emulators, simulators or processors through the cloud. Increasingly, cloud services are being looked on as the method for providing access to quantum processing. Quantum computers achieve their massive computing power by initiating quantum physics into processing power and when users are allowed access to these quantum-powered computers through the internet it is known as quantum computing within the cloud.

Cross-entropy benchmarking
(also referred to as XEB), is quantum benchmarking protocol which can be used to demonstrate quantum supremacy. In XEB, a random quantum circuit is executed on a quantum computer multiple times in order to collect a set of

        k

    {\displaystyle k}

 samples in the form of bitstrings

        {

          x

            1

        ,
        …
        ,

          x

            k

        }

    {\displaystyle \{x_{1},\dots ,x_{k}\}}

. The bitstrings are then used to calculate the cross-entropy benchmark fidelity (

          F

              X
              E
              B

    {\displaystyle F_{\rm {XEB}}}

) via a classical computer, given by

          F

              X
              E
              B

        =

          2

            n

        ⟨
        P
        (

          x

            i

        )

          ⟩

            k

        −
        1
        =

              2

                n

            k

          (

              ∑

                i
                =
                1

                k

              |

            ⟨

              0

                n

              |

            C

              |

              x

                i

            ⟩

                |

                2

          )

        −
        1

    {\displaystyle F_{\rm {XEB}}=2^{n}\langle P(x_{i})\rangle _{k}-1={\frac {2^{n}}{k}}\left(\sum _{i=1}^{k}|\langle 0^{n}|C|x_{i}\rangle |^{2}\right)-1}

,
where

        n

    {\displaystyle n}

 is the number of qubits in the circuit and

        P
        (

          x

            i

        )

    {\displaystyle P(x_{i})}

 is the probability of a bitstring

            x

              i

    {\displaystyle {x_{i}}}

 for an ideal quantum circuit

        C

    {\displaystyle C}

.  If

          F

            X
            E
            B

        =
        1

    {\displaystyle F_{XEB}=1}

, the samples were collected from a noiseless quantum computer. If

          F

              X
              E
              B

        =
        0

    {\displaystyle F_{\rm {XEB}}=0}

, then the samples could have been obtained via random guessing. This means that if a quantum computer did generate those samples, then the quantum computer is too noisy and thus has no chance of performing beyond-classical computations. Since it takes an exponential amount of resources to classically simulate a quantum circuit, there comes a point when the biggest supercomputer that runs the best classical algorithm for simulating quantum circuits can't compute the XEB. Crossing this point is known as achieving quantum supremacy; and after entering the quantum supremacy regime, XEB can only be estimated.

Eastin–Knill theorem

is a no-go theorem that states: "No quantum error correcting code can have a continuous symmetry which acts transversely on physical qubits". In other words, no quantum error correcting code can transversely implement a universal gate set. Since quantum computers are inherently noisy, quantum error correcting codes are used to correct errors that affect information due to decoherence.  Decoding error corrected data in order to perform gates on the qubits makes it prone to errors.  Fault tolerant quantum computation avoids this by performing gates on encoded data. Transversal gates, which perform a gate between two "logical" qubits each of which is encoded in N "physical qubits" by pairing up the physical qubits of each encoded qubit ("code block"), and performing independent gates on each pair, can be used to perform fault tolerant but not universal quantum computation because they guarantee that errors don't spread uncontrollably through the computation.  This is because transversal gates ensure that each qubit in a code block is acted on by at most a single physical gate and each code block is corrected independently when an error occurs. Due to the Eastin–Knill theorem, a universal set like {H, S, CNOT, T } gates can't be implemented transversally. For example, the T gate can't be implemented transversely in the Steane code. This calls for ways of circumventing Eastin–Knill in order to perform fault tolerant quantum computation. In addition to investigating fault tolerant quantum computation, the Eastin–Knill theorem is also useful for studying quantum gravity via the AdS/CFT correspondence and in condensed matter physics via quantum reference frame or many-body theory.

Five-qubit error correcting code
is the smallest quantum error correcting code that can protect a logical qubit from any arbitrary single qubit error. In this code, 5 physical qubits are used to encode the logical qubit. With

        X

    {\displaystyle X}

 and

        Z

    {\displaystyle Z}

 being Pauli matrices and

        I

    {\displaystyle I}

 the Identity matrix, this code's generators are

        ⟨
        X
        Z
        Z
        X
        I
        ,
        I
        X
        Z
        Z
        X
        ,
        X
        I
        X
        Z
        Z
        ,
        Z
        X
        I
        X
        Z
        ⟩

    {\displaystyle \langle XZZXI,IXZZX,XIXZZ,ZXIXZ\rangle }

. Its logical operators are

              X
              ¯

        =
        X
        X
        X
        X
        X

    {\displaystyle {\bar {X}}=XXXXX}

 and

              Z
              ¯

        =
        Z
        Z
        Z
        Z
        Z

    {\displaystyle {\bar {Z}}=ZZZZZ}

.  Once the logical qubit is encoded, errors on the physical qubits can be detected via stabilizer measurements. A lookup table that maps the results of the stabilizer measurements to the types and locations of the errors gives the control system of the quantum computer enough information to correct errors.

Hadamard test (quantum computation)

 is a method used to create a random variable whose expected value is the expected real part

          R
          e

        ⟨
        ψ

          |

        U

          |

        ψ
        ⟩

    {\displaystyle \mathrm {Re} \langle \psi |U|\psi \rangle }

, where

          |

        ψ
        ⟩

    {\displaystyle |\psi \rangle }

 is a quantum state and

        U

    {\displaystyle U}

 is a unitary gate acting on the space of

          |

        ψ
        ⟩

    {\displaystyle |\psi \rangle }

. The Hadamard test produces a random variable whose image is in

        {
        ±
        1
        }

    {\displaystyle \{\pm 1\}}

 and whose expected value is exactly

          R
          e

        ⟨
        ψ

          |

        U

          |

        ψ
        ⟩

    {\displaystyle \mathrm {Re} \langle \psi |U|\psi \rangle }

. It is possible to modify the circuit to produce a random variable whose expected value is

          I
          m

        ⟨
        ψ

          |

        U

          |

        ψ
        ⟩

    {\displaystyle \mathrm {Im} \langle \psi |U|\psi \rangle }

.

Magic state distillation

is a process that takes in multiple noisy quantum states and outputs a smaller number of more reliable quantum states. It is considered by many experts to be one of the leading proposals for achieving fault tolerant quantum computation. Magic state distillation has also been used to argue   that quantum contextuality may be the "magic ingredient" responsible for the power of quantum computers.

Mølmer–Sørensen gate

(or MS gate), is a two qubit gate used in trapped ion quantum computing. It was proposed by Klaus Mølmer and Anders Sørensen.  Their proposal also extends to gates on more than two qubits.

Quantum algorithm
is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical (or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer. Although all classical algorithms can also be performed on a quantum computer,  the term quantum algorithm is usually used for those algorithms which seem inherently quantum, or use some essential feature of quantum computation such as quantum superposition or quantum entanglement.

Quantum computing
is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though current quantum computers are too small to outperform usual (classical) computers for practical applications, larger realizations are believed to be capable of solving certain computational problems, such as integer factorization (which underlies RSA encryption), substantially faster than classical computers. The study of quantum computing is a subfield of quantum information science.

Quantum volume
is a metric that measures the capabilities and error rates of a quantum computer. It expresses the maximum size of square quantum circuits that can be implemented successfully by the computer. The form of the circuits is independent from the quantum computer architecture, but compiler can transform and optimize it to take advantage of the computer's features. Thus, quantum volumes for different architectures can be compared.

Quantum error correction
(QEC), is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is theorised as essential to achieve fault-tolerant quantum computation that can reduce the effects of noise on stored quantum information, faulty quantum gates, faulty quantum preparation, and faulty measurements.

Quantum image processing
(QIMP), is using quantum computing or quantum information processing to create and work with quantum images.

Due to some of the properties inherent to quantum computation, notably entanglement and parallelism, it is hoped that QIMP technologies will offer capabilities and performances that surpass their traditional equivalents, in terms of computing speed, security, and minimum storage requirements.

Quantum programming
is the process of assembling sequences of instructions, called quantum programs, that are capable of running on a quantum computer. Quantum programming languages help express quantum algorithms using high-level constructs. The field is deeply rooted in the open-source philosophy and as a result most of the quantum software discussed in this article is freely available as open-source software.

Quantum simulator
 Quantum simulators permit the study of quantum system in a programmable fashion. In this instance, simulators are special purpose devices designed to provide insight about specific physics problems. Quantum simulators may be contrasted with generally programmable "digital" quantum computers, which would be capable of solving a wider class of quantum problems.

Quantum state discrimination
In quantum information science, quantum state discrimination refers to the task of inferring the quantum state that produced the observed measurement probabilities.

More precisely, in its standard formulation, the problem involves performing some POVM

        (

          E

            i

          )

            i

    {\displaystyle (E_{i})_{i}}

 on a given unknown state

        ρ

    {\displaystyle \rho }

, under the promise that the state received is an element of a collection of states

        {

          σ

            i

          }

            i

    {\displaystyle \{\sigma _{i}\}_{i}}

, with

          σ

            i

    {\displaystyle \sigma _{i}}

 occurring with probability

          p

            i

    {\displaystyle p_{i}}

, that is,

        ρ
        =

          ∑

            i

          p

            i

          σ

            i

    {\displaystyle \rho =\sum _{i}p_{i}\sigma _{i}}

. The task is then to find the probability of the POVM

        (

          E

            i

          )

            i

    {\displaystyle (E_{i})_{i}}

 correctly guessing which state was received. Since the probability of the POVM returning the

        i

    {\displaystyle i}

-th outcome when the given state was

          σ

            j

    {\displaystyle \sigma _{j}}

 has the form

          Prob

        (
        i

          |

        j
        )
        =
        tr

        (

          E

            i

          σ

            j

        )

    {\displaystyle {\text{Prob}}(i|j)=\operatorname {tr} (E_{i}\sigma _{j})}

, it follows that the probability of successfully determining the correct state is

          P

              s
              u
              c
              c
              e
              s
              s

        =

          ∑

            i

          p

            i

        tr

        (

          σ

            i

          E

            i

        )

    {\displaystyle P_{\rm {success}}=\sum _{i}p_{i}\operatorname {tr} (\sigma _{i}E_{i})}

.

Quantum supremacy
or quantum advantage, is the goal of demonstrating that a programmable quantum device can solve a problem that no classical computer can solve in any feasible amount of time (irrespective of the usefulness of the problem). Conceptually, quantum supremacy involves both the engineering task of building a powerful quantum computer and the computational-complexity-theoretic task of finding a problem that can be solved by that quantum computer and has a superpolynomial speedup over the best known or possible classical algorithm for that task. The term was coined by John Preskill in 2012, but the concept of a quantum computational advantage, specifically for simulating quantum systems, dates back to Yuri Manin's (1980) and Richard Feynman's (1981) proposals of quantum computing. Examples of proposals to demonstrate quantum supremacy include the boson sampling proposal of Aaronson and Arkhipov, D-Wave's specialized frustrated cluster loop problems, and sampling the output of random quantum circuits.

Quantum Turing machine
(QTM), or universal quantum computer, is an abstract machine used to model the effects of a quantum computer.  It provides a simple model that captures all of the power of quantum computation—that is, any quantum algorithm can be expressed formally as a particular quantum Turing machine. However, the computationally equivalent quantum circuit is a more common model.

Qubit
A qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics.  Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of both states simultaneously, a property that is fundamental to quantum mechanics and quantum computing.

Quil (instruction set architecture)
 is a quantum instruction set architecture that first introduced a shared quantum/classical memory model. It was introduced by Robert Smith, Michael Curtis, and William Zeng in A Practical Quantum Instruction Set Architecture.  Many quantum algorithms (including quantum teleportation, quantum error correction, simulation, and optimization algorithms) require a shared memory architecture. Quil is being developed for the superconducting quantum processors developed by Rigetti Computing through the Forest quantum programming API.  A Python library called pyQuil was introduced to develop Quil programs with higher level constructs. A Quil backend is also supported by other quantum programming environments.

Qutrit
(or quantum trit), is a unit of quantum information that is realized by a 3-level quantum system, that may be in a superposition of three mutually orthogonal quantum states.

The qutrit is analogous to the classical radix-3 trit, just as the qubit, a quantum system described by a superposition of two orthogonal states, is analogous to the classical radix-2 bit.

There is ongoing work to develop quantum computers using qutrits and qubits with multiple states.

Solovay–Kitaev theorem
In quantum information and computation, the Solovay–Kitaev theorem says, roughly, that if a set of single-qubit quantum gates generates a dense subset of SU(2) then that set is guaranteed to fill SU(2) quickly, which means any desired gate can be approximated by a fairly short sequence of gates from the generating set. Robert M. Solovay initially announced the result on an email list in 1995, and Alexei Kitaev independently gave an outline of its proof in 1997. Solovay also gave a talk on his result at MSRI in 2000 but it was interrupted by a fire alarm. Christopher M. Dawson and Michael Nielsen call the theorem one of the most important fundamental results in the field of quantum computation.


IQM Quantum Computers

IQM Quantum Computers is a Finnish quantum computing hardware and software company headquartered in Espoo, Finland. The company develops and commercializes quantum computers based on superconducting technology. Their goal is to become the leading European company in quantum computing hardware.


The Illinois Quantum and Microelectronics Park (IQMP) is a planned 128-acre technology campus on the site of the former U.S. Steel South Works in South Chicago. It will focus on quantum computing and is not an AI data center.
Plans for the IQMP are part of the larger “Quantum Shore Chicago” redevelopment of the former U.S. Steel South Works site, a long-vacant industrial area in Chicago’s South Shore neighborhood. The broader project is expected to include advanced manufacturing facilities, research centers, housing, and a replacement hospital, with an initial phase estimated at about $9 billion in investment.
The overall park is expected to cost $9 billion to construct. Work is expected to begin in 2026 and be complete in 2028.