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Quantum image processing
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. == Background == A. Y. Vlasov's work in 1997 focused on using a quantum system to recognize orthogonal images. This was followed by efforts using quantum algorithms to search specific patterns in binary images and detect the posture of certain targets. Notably, more optics-based interpretations for quantum imaging were initially experimentally demonstrated in and formalized in after seven years. In 2003, Salvador Venegas-Andraca and S. Bose presented Qubit Lattice, the first published general model for storing, processing and retrieving images using quantum systems. Later on, in 2005, Latorre proposed another kind of representation, called the Real Ket, whose purpose was to encode quantum images as a basis for further applications in QIMP. Furthermore, in 2010 Venegas-Andraca and Ball presented a method for storing and retrieving binary geometrical shapes in quantum mechanical systems in which it is shown that maximally entangled qubits can be used to reconstruct images without using any additional information. Technically, these pioneering efforts with the subsequent studies related to them can be classified into three main groups: Quantum-assisted digital image processing (QDIP): These applications aim at improving digital or classical image processing tasks and applications. Optics-based quantum imaging (OQI) Classically inspired quantum image processing (QIMP) A survey of quantum image representation has been published in. Furthermore, the recently published book Quantum Image Processing provides a comprehensive introduction to quantum image processing, which focuses on extending conventional image processing tasks to the quantum computing frameworks. It summarizes the available quantum image representations and their operations, reviews the possible quantum image applications and their implementation, and discusses the open questions and future development trends. == Quantum image representations == There are various approaches for quantum image representation, that are usually based on the encoding of color information. A common representation is FRQI (Flexible Representation for Quantum Images), that captures the color and position at every pixel of the image, and defined as: | I ⟩ = 1 2 n ∑ i = 0 2 2 n − 1 | c i ⟩ ⊗ | i ⟩ {\displaystyle \vert I\rangle ={\frac {1}{2^{n}}}\sum _{i=0}^{2^{2n-1}}\vert c_{i}\rangle \otimes \vert i\rangle } where | i ⟩ {\textstyle |i\rangle } is the position and | c i ⟩ = c o s θ i | 0 ⟩ + s i n θ i | 1 ⟩ {\textstyle \vert c_{i}\rangle =cos\theta _{i}\vert 0\rangle +sin\theta _{i}\vert 1\rangle } the color with a vector of angles θ i ∈ [ 0 , π / 2 ] {\textstyle \theta _{i}\in \left[0,\pi /2\right]} . As it can be seen, | c i ⟩ {\textstyle \vert c_{i}\rangle } is a regular qubit state of the form | ψ ⟩ = α | 0 ⟩ + β | 1 ⟩ {\displaystyle \vert \psi \rangle =\alpha \vert 0\rangle +\beta \vert 1\rangle } , with basis states | 0 ⟩ = ( 1 0 ) {\textstyle \vert 0\rangle ={\begin{pmatrix}1\\0\end{pmatrix}}} and | 1 ⟩ = ( 0 1 ) {\textstyle \vert 1\rangle ={\begin{pmatrix}0\\1\end{pmatrix}}} , as well as amplitudes α {\textstyle \alpha } and β {\textstyle \beta } that satisfy | α | 2 + | β | 2 = 1 {\textstyle \left|\alpha \right|^{2}+\left|\beta \right|^{2}=1} . Another common representation is MCQI (Multi-Channel Representation for Quantum Images), that uses the RGB channels with quantum states and following FRQI definition: | I ⟩ = 1 2 n + 1 ∑ i = 0 2 2 n − 1 | C R G B i ⟩ ⊗ | i ⟩ {\displaystyle \vert I\rangle ={\frac {1}{2^{n+1}}}\sum _{i=0}^{2^{2n-1}}\vert C_{RGB}^{i}\rangle \otimes \vert i\rangle } | C R G B i ⟩ = cos θ R i | 000 ⟩ + cos θ G i | 001 ⟩ + cos θ B i | 010 ⟩ + sin θ R i | 100 ⟩ + sin θ G i | 101 ⟩ + sin θ B i | 110 ⟩ + cos θ α | 011 ⟩ + sin θ α | 111 ⟩ {\displaystyle {\begin{aligned}{\begin{aligned}\vert C_{RGB}^{i}\rangle &={\cos \theta _{R}^{i}\vert 000\rangle }+{\cos \theta _{G}^{i}\vert 001\rangle }+{\cos \theta _{B}^{i}\vert 010\rangle }\\&\quad +{\sin \theta _{R}^{i}\vert 100\rangle }+{\sin \theta _{G}^{i}\vert 101\rangle }+{\sin \theta _{B}^{i}\vert 110\rangle }\\&\quad +{\cos {\theta _{\alpha }}\vert 011\rangle }+{\sin \theta _{\alpha }\vert 111\rangle }\end{aligned}}\end{aligned}}} Departing from the angle-based approach of FRQI and MCQI, and using a qubit sequence, NEQR (Novel Enhanced Representation for Quantum Images) is another representation approach, that uses a function f ( y , x ) = C y x q − 1 C y x q − 2 … C y x 1 C y x 0 {\textstyle f\left(y,x\right)=C_{yx}^{q-1}C_{yx}^{q-2}\ldots C_{yx}^{1}C_{yx}^{0}} to encode color values for a 2 n × 2 n {\displaystyle 2^{n}\times 2^{n}} image: | I ⟩ = 1 2 n ∑ y = 0 2 n − 1 ∑ x = 0 2 n − 1 | f ( y , x ) ⟩ | y x ⟩ {\displaystyle \vert I\rangle ={\frac {1}{2^{n}}}\sum _{y=0}^{2^{n}-1}\sum _{x=0}^{2^{n}-1}\vert f\left(y,x\right)\rangle \vert yx\rangle } == Quantum image manipulations == A lot of the effort in QIMP has been focused on designing algorithms to manipulate the position and color information encoded using flexible representation of quantum images (FRQI) and its many variants. For instance, FRQI-based fast geometric transformations including (two-point) swapping, flip, (orthogonal) rotations and restricted geometric transformations to constrain these operations to a specified area of an image were initially proposed. Recently, NEQR-based quantum image translation to map the position of each picture element in an input image into a new position in an output image and quantum image scaling to resize a quantum image were discussed. While FRQI-based general form of color transformations were first proposed by means of the single qubit gates such as X, Z, and H gates. Later, Multi-Channel Quantum Image-based channel of interest (CoI) operator to entail shifting the grayscale value of the preselected color channel and the channel swapping (CS) operator to swap the grayscale values between two channels have been fully discussed. To illustrate the feasibility and capability of QIMP algorithms and application, researchers always prefer to simulate the digital image processing tasks on the basis of the QIRs that we already have. By using the basic quantum gates and the aforementioned operations, so far, researchers have contributed to quantum image feature extraction, quantum image segmentation, quantum image morphology, quantum image comparison, quantum image filtering, quantum image classification, quantum image stabilization, among others. In particular, QIMP-based security technologies have attracted extensive interest of researchers as presented in the ensuing discussions. Similarly, these advancements have led to many applications in the areas of watermarking, encryption, and steganography etc., which form the core security technologies highlighted in this area. In general, the work pursued by the researchers in this area are focused on expanding the applicability of QIMP to realize more classical-like digital image processing algorithms; propose technologies to physically realize the QIMP hardware; or simply to note the likely challenges that could impede the realization of some QIMP protocols. == Quantum image transform == By encoding and processing the image information in quantum-mechanical systems, a framework of quantum image processing is presented, where a pure quantum state encodes the image information: to encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states. Given an image F = ( F i , j ) M × L {\displaystyle F=(F_{i,j})_{M\times L}} , where F i , j {\displaystyle F_{i,j}} represents the pixel value at position ( i , j ) {\displaystyle (i,j)} with i = 1 , … , M {\displaystyle i=1,\dots ,M} and j = 1 , … , L {\displaystyle j=1,\dots ,L} , a vector f → {\displaystyle {\vec {f}}} with M L {\displaystyle ML} elements can be formed by letting the first M {\displaystyle M} elements of f → {\displaystyle {\vec {f}}} be the first column of F {\displaystyle F} , the next M {\displaystyle M} elements the second column, etc. A large class of image operations is linear, e.g., unitary transformations, convolutions, and linear filtering. In the quantum computing, the linear transformation can be represented as | g ⟩ = U ^ | f ⟩ {\displaystyle |g\rangle ={\hat {U}}|f\rangle } with the input image state | f ⟩ {\displaystyle |f\rangle } and the output image state | g ⟩ {\displaystyle |g\rangle } . A unitary transformation can be implemented as a unitary evolution. Some basic and commonly used image transforms (e.g., the Fourier, Hadamard, an
Consistency (database systems)
In database systems, consistency (or correctness) refers to the requirement that any given database transaction must change affected data only in allowed ways. Any data written to the database must be valid according to all defined rules, including constraints, cascades, triggers, and any combination thereof. This does not guarantee correctness of the transaction in all ways the application programmer might have wanted (that is the responsibility of application-level code) but merely that any programming errors cannot result in the violation of any defined database constraints. In a distributed system, referencing CAP theorem, consistency can also be understood as after a successful write, update or delete of a Record, any read request immediately receives the latest value of the Record. == As an ACID guarantee == Consistency is one of the four guarantees that define ACID transactions; however, significant ambiguity exists about the nature of this guarantee. It is defined variously as: The guarantee that database constraints are not violated, particularly once a transaction commits. The guarantee that any transactions started in the future necessarily see the effects of other transactions committed in the past. As these various definitions are not mutually exclusive, it is possible to design a system that guarantees "consistency" in every sense of the word, as most relational database management systems in common use today arguably do. == As a CAP trade-off == The CAP theorem is based on three trade-offs, one of which is "atomic consistency" (shortened to "consistency" for the acronym), about which the authors note, "Discussing atomic consistency is somewhat different than talking about an ACID database, as database consistency refers to transactions, while atomic consistency refers only to a property of a single request/response operation sequence. And it has a different meaning than the Atomic in ACID, as it subsumes the database notions of both Atomic and Consistent." In the CAP theorem, you can only have two of the following three properties: consistency, availability, or partition tolerance. Therefore, consistency may have to be traded off in some database systems.
Interplanetary Internet
The interplanetary Internet is a conceived computer network in space, consisting of a set of network nodes that can communicate with each other. These nodes are the planet's orbiters and landers, and the Earth ground stations. For example, the orbiters collect the scientific data from the Curiosity rover on Mars through near-Mars communication links, transmit the data to Earth through direct links from the Mars orbiters to the Earth ground stations via the NASA Deep Space Network, and finally the data routed through Earth's internal internet. Interplanetary communication is greatly delayed by interplanetary distances, as data transmission can only go as fast as the speed of light, so a new set of protocols and technologies that are tolerant to large delays and errors are required. The interplanetary Internet has been envisioned as a store and forward network of internets that is often disconnected, has a wireless backbone fraught with error-prone links and delays ranging from tens of minutes to even hours, even when there is a connection. As of 2024 agencies and companies working towards bringing the network to fruition include NASA, ESA, SpaceX and Blue Origin. == Challenges and reasons == In the core implementation of Interplanetary Internet, satellites orbiting a planet communicate to other planet's satellites. Simultaneously, these planets revolve around the Sun with long distances, and thus many challenges face the communications. The reasons and the resultant challenges are: The motion and long distances between planets: The interplanetary communication is greatly delayed due to the interplanetary distances and the motion of the planets. The delay is variable and long, ranging from a couple of minutes (Earth-to-Mars), to a couple of hours (Pluto-to-Earth), depending on their relative positions. The interplanetary communication also suspends due to the solar conjunction, when the sun's radiation hinders the direct communication between the planets. As such, the communication characterizes lossy links and intermittent link connectivity. Low embeddable payload: Satellites can only carry a small payload, which poses challenges to the power, mass, size, and cost for communication hardware design. An asymmetric bandwidth would be the result of this limitation. This asymmetry reaches ratios up to 1000:1 as downlink:uplink bandwidth portion. Absence of fixed infrastructure: The graph of participating nodes in a specific planet-to-planet communication keeps changing over time, due to the constant motion. The routes of the planet-to-planet communication are planned and scheduled rather than being opportunistic. The Interplanetary Internet design must address these challenges to operate successfully and achieve good communication with other planets. It also must use the few available resources efficiently in the system. == Development == Space communication technology has steadily evolved from expensive, one-of-a-kind point-to-point architectures, to the re-use of technology on successive missions, to the development of standard protocols agreed upon by space agencies of many countries. This last phase has gone on since 1982 through the efforts of the Consultative Committee for Space Data Systems (CCSDS), a body composed of the major space agencies of the world. It has 11 member agencies, 32 observer agencies, and over 119 industrial associates. The evolution of space data system standards has gone on in parallel with the evolution of the Internet, with conceptual cross-pollination where fruitful, but largely as a separate evolution. Since the late 1990s, familiar Internet protocols and CCSDS space link protocols have integrated and converged in several ways; for example, the successful FTP file transfer to Earth-orbiting STRV 1B on January 2, 1996, which ran FTP over the CCSDS IPv4-like Space Communications Protocol Specifications (SCPS) protocols. Internet Protocol use without CCSDS has taken place on spacecraft, e.g., demonstrations on the UoSAT-12 satellite, and operationally on the Disaster Monitoring Constellation. Having reached the era where networking and IP on board spacecraft have been shown to be feasible and reliable, a forward-looking study of the bigger picture was the next phase. The Interplanetary Internet study at NASA's Jet Propulsion Laboratory (JPL) was started by a team of scientists at JPL led by internet pioneer Vinton Cerf and the late Adrian Hooke. Cerf was appointed as a distinguished visiting scientist at JPL in 1998, while Hooke was one of the founders and directors of CCSDS. While IP-like SCPS protocols are feasible for short hops, such as ground station to orbiter, rover to lander, lander to orbiter, probe to flyby, and so on, delay-tolerant networking is needed to get information from one region of the Solar System to another. It becomes apparent that the concept of a region is a natural architectural factoring of the Interplanetary Internet. A region is an area where the characteristics of communication are the same. Region characteristics include communications, security, the maintenance of resources, perhaps ownership, and other factors. The Interplanetary Internet is a "network of regional internets". What is needed then, is a standard way to achieve end-to-end communication through multiple regions in a disconnected, variable-delay environment using a generalized suite of protocols. Examples of regions might include the terrestrial Internet as a region, a region on the surface of the Moon or Mars, or a ground-to-orbit region. The recognition of this requirement led to the concept of a "bundle" as a high-level way to address the generalized Store-and-Forward problem. Bundles are an area of new protocol development in the upper layers of the OSI model, above the Transport Layer with the goal of addressing the issue of bundling store-and-forward information so that it can reliably traverse radically dissimilar environments constituting a "network of regional internets". Delay-tolerant networking (DTN) was designed to enable standardized communications over long distances and through time delays. At its core is the Bundle Protocol (BP), which is similar to the Internet Protocol, or IP, that serves as the heart of the Internet here on Earth. The big difference between the regular Internet Protocol (IP) and the Bundle Protocol is that IP assumes a seamless end-to-end data path, while BP is built to account for errors and disconnections — glitches that commonly plague deep-space communications. Bundle Service Layering, implemented as the Bundling protocol suite for delay-tolerant networking, will provide general-purpose delay-tolerant protocol services in support of a range of applications: custody transfer, segmentation and reassembly, end-to-end reliability, end-to-end security, and end-to-end routing among them. The Bundle Protocol was first tested in space on the UK-DMC satellite in 2008. An example of one of these end-to-end applications flown on a space mission is the CCSDS File Delivery Protocol (CFDP), used on the Deep Impact comet mission. CFDP is an international standard for automatic, reliable file transfer in both directions. CFDP should not be confused with Coherent File Distribution Protocol, which has the same acronym and is an IETF-documented experimental protocol for rapidly deploying files to multiple targets in a highly networked environment. In addition to reliably copying a file from one entity (such as a spacecraft or ground station) to another entity, CFDP has the capability to reliably transmit arbitrarily small messages defined by the user, in the metadata accompanying the file, and to reliably transmit commands relating to file system management that are to be executed automatically on the remote end-point entity (such as a spacecraft) upon successful reception of a file. == Protocol == The Consultative Committee for Space Data Systems (CCSDS) packet telemetry standard defines the protocol used for the transmission of spacecraft instrument data over the deep-space channel. Under this standard, an image or other data sent from a spacecraft instrument is transmitted using one or more packets. === CCSDS packet definition === A packet is a block of data with length that can vary between successive packets, ranging from 7 to 65,542 bytes, including the packet header. Packetized data is transmitted via frames, which are fixed-length data blocks. The size of a frame, including frame header and control information, can range up to 2048 bytes. Packet sizes are fixed during the development phase. Because packet lengths are variable but frame lengths are fixed, packet boundaries usually do not coincide with frame boundaries. === Telecom processing notes === Data in a frame is typically protected from channel errors by error-correcting codes. Even when the channel errors exceed the correction capability of the error-correcting code, the presence of errors is nearly always detected by the e
Visual cryptography
Visual cryptography is a cryptographic technique which allows visual information (pictures, text, etc.) to be encrypted in such a way that the decrypted information appears as a visual image. One of the best-known techniques has been credited to Moni Naor and Adi Shamir, who developed it in 1994. They demonstrated a visual secret sharing scheme, where a binary image was broken up into n shares so that only someone with all n shares could decrypt the image, while any n − 1 shares revealed no information about the original image. Each share was printed on a separate transparency, and decryption was performed by overlaying the shares. When all n shares were overlaid, the original image would appear. There are several generalizations of the basic scheme including k-out-of-n visual cryptography, and using opaque sheets but illuminating them by multiple sets of identical illumination patterns under the recording of only one single-pixel detector, which exposed the image. Using a similar idea, transparencies can be used to implement a one-time pad encryption, where one transparency is a shared random pad, and another transparency acts as the ciphertext. Normally, there is an expansion of space requirement in visual cryptography. But if one of the two shares is structured recursively, the efficiency of visual cryptography can be increased to 100%. Some antecedents of visual cryptography are in patents from the 1960s. Other antecedents are in the work on perception and secure communication. Visual cryptography can be used to protect biometric templates in which decryption does not require any complex computations. == Example == In this example, the binary image has been split into two component images. Each component image has a pair of pixels for every pixel in the original image. These pixel pairs are shaded black or white according to the following rule: if the original image pixel was black, the pixel pairs in the component images must be complementary; randomly shade one ■□, and the other □■. When these complementary pairs are overlapped, they will appear dark gray. On the other hand, if the original image pixel was white, the pixel pairs in the component images must match: both ■□ or both □■. When these matching pairs are overlapped, they will appear light gray. So, when the two component images are superimposed, the original image appears. However, without the other component, a component image reveals no information about the original image; it is indistinguishable from a random pattern of ■□ / □■ pairs. Moreover, if you have one component image, you can use the shading rules above to produce a counterfeit component image that combines with it to produce any image at all. == (2, n) visual cryptography sharing case == Sharing a secret with an arbitrary number of people, n, such that at least 2 of them are required to decode the secret is one form of the visual secret sharing scheme presented by Moni Naor and Adi Shamir in 1994. In this scheme we have a secret image which is encoded into n shares printed on transparencies. The shares appear random and contain no decipherable information about the underlying secret image, however if any 2 of the shares are stacked on top of one another the secret image becomes decipherable by the human eye. Every pixel from the secret image is encoded into multiple subpixels in each share image using a matrix to determine the color of the pixels. In the (2, n) case, a white pixel in the secret image is encoded using a matrix from the following set, where each row gives the subpixel pattern for one of the components: {all permutations of the columns of} : C 0 = [ 1 0 . . . 0 1 0 . . . 0 . . . 1 0 . . . 0 ] . {\displaystyle \mathbf {C_{0}=} {\begin{bmatrix}1&0&...&0\\1&0&...&0\\...\\1&0&...&0\end{bmatrix}}.} While a black pixel in the secret image is encoded using a matrix from the following set: {all permutations of the columns of} : C 1 = [ 1 0 . . . 0 0 1 . . . 0 . . . 0 0 . . . 1 ] . {\displaystyle \mathbf {C_{1}=} {\begin{bmatrix}1&0&...&0\\0&1&...&0\\...\\0&0&...&1\end{bmatrix}}.} For instance in the (2,2) sharing case (the secret is split into 2 shares and both shares are required to decode the secret) we use complementary matrices to share a black pixel and identical matrices to share a white pixel. Stacking the shares we have all the subpixels associated with the black pixel now black while 50% of the subpixels associated with the white pixel remain white. == Cheating the (2, n) visual secret sharing scheme == Horng et al. proposed a method that allows n − 1 colluding parties to cheat an honest party in visual cryptography. They take advantage of knowing the underlying distribution of the pixels in the shares to create new shares that combine with existing shares to form a new secret message of the cheaters choosing. We know that 2 shares are enough to decode the secret image using the human visual system. But examining two shares also gives some information about the 3rd share. For instance, colluding participants may examine their shares to determine when they both have black pixels and use that information to determine that another participant will also have a black pixel in that location. Knowing where black pixels exist in another party's share allows them to create a new share that will combine with the predicted share to form a new secret message. In this way a set of colluding parties that have enough shares to access the secret code can cheat other honest parties. == Visual steganography == 2×2 subpixels can also encode a binary image in each component image. For example, each white pixel of each component image could be represented by two black subpixels, while each black pixel represented by three black subpixels. When overlaid, each white pixel of the secret image is represented by three black subpixels, while each black pixel is represented by all four subpixels black. Each corresponding pixel in the component images is randomly rotated to avoid orientation leaking information about the secret image. == In popular culture == In "Do Not Forsake Me Oh My Darling", a 1967 episode of TV series The Prisoner, the protagonist uses a visual cryptography overlay of multiple transparencies to reveal a secret message – the location of a scientist friend who had gone into hiding.
Event condition action
Event condition action (ECA) is a short-cut for referring to the structure of active rules in event-driven architecture and active database systems. Such a rule traditionally consisted of three parts: The event part specifies the signal that triggers the invocation of the rule The condition part is a logical test that, if satisfied or evaluates to true, causes the action to be carried out The action part consists of updates or invocations on the local data This structure was used by the early research in active databases which started to use the term ECA. Current state of the art ECA rule engines use many variations on rule structure. Also other features not considered by the early research is introduced, such as strategies for event selection into the event part. In a memory-based rule engine, the condition could be some tests on local data and actions could be updates to object attributes. In a database system, the condition could simply be a query to the database, with the result set (if not null) being passed to the action part for changes to the database. In either case, actions could also be calls to external programs or remote procedures. Note that for database usage, updates to the database are regarded as internal events. As a consequence, the execution of the action part of an active rule can match the event part of the same or another active rule, thus triggering it. The equivalent in a memory-based rule engine would be to invoke an external method that caused an external event to trigger another ECA rule. ECA rules can also be used in rule engines that use variants of the Rete algorithm for rule processing. == ECA rule engines == Rulecore Concurrent Rules Apart Database Detect Invocation Rules ConceptBase ECArules
List of cryptosystems
A cryptosystem is a set of cryptographic algorithms that map ciphertexts and plaintexts to each other. == Private-key cryptosystems == Private-key cryptosystems use the same key for encryption and decryption. Caesar cipher Substitution cipher Enigma machine Data Encryption Standard Twofish Serpent Camellia Salsa20 ChaCha20 Blowfish CAST5 Kuznyechik RC4 3DES Skipjack Safer IDEA Advanced Encryption Standard, also known as AES and Rijndael. == Public-key cryptosystems == Public-key cryptosystems use a public key for encryption and a private key for decryption. Diffie–Hellman key exchange RSA encryption Rabin cryptosystem Schnorr signature ElGamal encryption Elliptic-curve cryptography Lattice-based cryptography McEliece cryptosystem Multivariate cryptography Isogeny-based cryptography