The Harris corner detector is a corner detection operator that is commonly used in computer vision algorithms to extract corners and infer features of an image. It was first introduced by Chris Harris and Mike Stephens in 1988 upon the improvement of Moravec's corner detector. Compared to its predecessor, Harris' corner detector takes the differential of the corner score into account with reference to direction directly, instead of using shifting patches for every 45 degree angles, and has been proved to be more accurate in distinguishing between edges and corners. Since then, it has been improved and adopted in many algorithms to preprocess images for subsequent applications. == Introduction == A corner is a point whose local neighborhood stands in two dominant and different edge directions. In other words, a corner can be interpreted as the junction of two edges, where an edge is a sudden change in image brightness. Corners are the important features in the image, and they are generally termed as interest points which are invariant to translation, rotation and illumination. Although corners are only a small percentage of the image, they contain the most important features in restoring image information, and they can be used to minimize the amount of processed data for motion tracking, image stitching, building 2D mosaics, stereo vision, image representation and other related computer vision areas. In order to capture the corners from the image, researchers have proposed many different corner detectors including the Kanade-Lucas-Tomasi (KLT) operator and the Harris operator which are most simple, efficient and reliable for use in corner detection. These two popular methodologies are both closely associated with and based on the local structure matrix. Compared to the Kanade-Lucas-Tomasi corner detector, the Harris corner detector provides good repeatability under changing illumination and rotation, and therefore, it is more often used in stereo matching and image database retrieval. Although there still exist drawbacks and limitations, the Harris corner detector is still an important and fundamental technique for many computer vision applications. == Development of Harris corner detection algorithm == Source: Without loss of generality, we will assume a grayscale 2-dimensional image is used. Let this image be given by I {\displaystyle I} . Consider taking an image patch ( x , y ) ∈ W {\displaystyle (x,y)\in W} (window) and shifting it by ( Δ x , Δ y ) {\displaystyle (\Delta x,\Delta y)} . The sum of squared differences (SSD) between these two patches, denoted f {\displaystyle f} , is given by: f ( Δ x , Δ y ) = ∑ ( x k , y k ) ∈ W ( I ( x k , y k ) − I ( x k + Δ x , y k + Δ y ) ) 2 {\displaystyle f(\Delta x,\Delta y)={\underset {(x_{k},y_{k})\in W}{\sum }}\left(I(x_{k},y_{k})-I(x_{k}+\Delta x,y_{k}+\Delta y)\right)^{2}} I ( x + Δ x , y + Δ y ) {\displaystyle I(x+\Delta x,y+\Delta y)} can be approximated by a Taylor expansion. Let I x {\displaystyle I_{x}} and I y {\displaystyle I_{y}} be the partial derivatives of I {\displaystyle I} , such that I ( x + Δ x , y + Δ y ) ≈ I ( x , y ) + I x ( x , y ) Δ x + I y ( x , y ) Δ y {\displaystyle I(x+\Delta x,y+\Delta y)\approx I(x,y)+I_{x}(x,y)\Delta x+I_{y}(x,y)\Delta y} This produces the approximation f ( Δ x , Δ y ) ≈ ∑ ( x , y ) ∈ W ( I x ( x , y ) Δ x + I y ( x , y ) Δ y ) 2 , {\displaystyle f(\Delta x,\Delta y)\approx {\underset {(x,y)\in W}{\sum }}\left(I_{x}(x,y)\Delta x+I_{y}(x,y)\Delta y\right)^{2},} which can be written in matrix form: f ( Δ x , Δ y ) ≈ ( Δ x Δ y ) M ( Δ x Δ y ) , {\displaystyle f(\Delta x,\Delta y)\approx {\begin{pmatrix}\Delta x&\Delta y\end{pmatrix}}M{\begin{pmatrix}\Delta x\\\Delta y\end{pmatrix}},} where M is the structure tensor, M = ∑ ( x , y ) ∈ W [ I x 2 I x I y I x I y I y 2 ] = [ ∑ ( x , y ) ∈ W I x 2 ∑ ( x , y ) ∈ W I x I y ∑ ( x , y ) ∈ W I x I y ∑ ( x , y ) ∈ W I y 2 ] {\displaystyle M={\underset {(x,y)\in W}{\sum }}{\begin{bmatrix}I_{x}^{2}&I_{x}I_{y}\\I_{x}I_{y}&I_{y}^{2}\end{bmatrix}}={\begin{bmatrix}{\underset {(x,y)\in W}{\sum }}I_{x}^{2}&{\underset {(x,y)\in W}{\sum }}I_{x}I_{y}\\{\underset {(x,y)\in W}{\sum }}I_{x}I_{y}&{\underset {(x,y)\in W}{\sum }}I_{y}^{2}\end{bmatrix}}} == Process of Harris corner detection algorithm == Commonly, Harris corner detector algorithm can be divided into five steps. Color to grayscale Spatial derivative calculation Structure tensor setup Harris response calculation Non-maximum suppression === Color to grayscale === If we use Harris corner detector in a color image, the first step is to convert it into a grayscale image, which will enhance the processing speed. The value of the gray scale pixel can be computed as a weighted sums of the values R, B and G of the color image, ∑ C ∈ { R , G , B } w C ⋅ C {\displaystyle \sum _{C\,\in \,\{R,G,B\}}w_{C}\cdot C} , where, e.g., w R = 0.299 , w G = 0.587 , w B = 1 − ( w R + w G ) = 0.114. {\displaystyle w_{R}=0.299,\ w_{G}=0.587,\ w_{B}=1-(w_{R}+w_{G})=0.114.} === Spatial derivative calculation === Next, we are going to find the derivative with respect to x and the derivative with respect to y, I x ( x , y ) {\displaystyle I_{x}(x,y)} and I y ( x , y ) {\displaystyle I_{y}(x,y)} . This can be approximated by applying Sobel operators. === Structure tensor setup === With I x ( x , y ) {\displaystyle I_{x}(x,y)} , I y ( x , y ) {\displaystyle I_{y}(x,y)} , we can construct the structure tensor M {\displaystyle M} . === Harris response calculation === For x ≪ y {\displaystyle x\ll y} , one has x ⋅ y x + y = x 1 1 + x / y ≈ x . {\displaystyle {\tfrac {x\cdot y}{x+y}}=x{\tfrac {1}{1+x/y}}\approx x.} In this step, we compute the smallest eigenvalue of the structure tensor using that approximation: λ min ≈ λ 1 λ 2 ( λ 1 + λ 2 ) = det ( M ) tr ( M ) {\displaystyle \lambda _{\min }\approx {\frac {\lambda _{1}\lambda _{2}}{(\lambda _{1}+\lambda _{2})}}={\frac {\det(M)}{\operatorname {tr} (M)}}} with the trace t r ( M ) = m 11 + m 22 {\displaystyle \mathrm {tr} (M)=m_{11}+m_{22}} . Another commonly used Harris response calculation is shown as below, R = λ 1 λ 2 − k ( λ 1 + λ 2 ) 2 = det ( M ) − k tr ( M ) 2 {\displaystyle R=\lambda _{1}\lambda _{2}-k(\lambda _{1}+\lambda _{2})^{2}=\det(M)-k\operatorname {tr} (M)^{2}} where k {\displaystyle k} is an empirically determined constant; k ∈ [ 0.04 , 0.06 ] {\displaystyle k\in [0.04,0.06]} . === Non-maximum suppression === In order to pick up the optimal values to indicate corners, we find the local maxima as corners within the window which is a 3 by 3 filter. == Improvement == Sources: Harris-Laplace Corner Detector Differential Morphological Decomposition Based Corner Detector Multi-scale Bilateral Structure Tensor Based Corner Detector == Applications == Image Alignment, Stitching and Registration 2D Mosaics Creation 3D Scene Modeling and Reconstruction Motion Detection Object Recognition Image Indexing and Content-based Retrieval Video Tracking
Pixorial
Pixorial was a cloud-based consumer photo sharing, video sharing and video editing platform. The company was formed in 2007 in Centennial, Colorado as a media conversion service. In 2013, Pixorial was chosen as one of two video storage companies to partner with the launch of Google Drive. Pixorial allowed users to edit and share videos on social channels by connecting through their Pixorial account. The company closed on July 18, 2014, and its assets were acquired by LifeLogger Technologies Corp in November 2015. == History == The company was founded in 2007 and launched in 2009 by former Netscape employee Andres Espineira. Changing its focus to video editing software in 2009, Pixorial began developing an app that would be launched for iOS and Android devices in 2011. Later developments in the app in 2012 would also included real time filters, which were later removed. With the launch of Google Drive in 2012, Pixorial was chosen as an integrated video partner. This integration with Google Drive allowed users to access videos stored in Google Drive within the web app of Pixorial. After the Google Drive launch, Pixorial developed a crowdsourced, location-based video sharing app, Krowds. The app was cited in July 2012 by PC Magazine as one of "The 8 Best Apps for Making and Sharing Videos on Your iPhone". In late July, Pixorial replaced its original mobile app with the MyPlayer HD app that optimized HD video viewing for large screen viewing including tablets and smart televisions. Pixorial's services terminated on July 18, 2014. == Products == === Krowds App === Pixorial's app was launched in April 2013 for iOS, and in May for Android, as a tool to aggregate event videos through location based collections. The app was launched to generally positive reviews. === Movie Creator === Launched July 12, 2012 Pixorial's Movie Creator allowed users to edit movies in a simple story-telling platform Movie Creator's features include transitions, text boxes, access to free music tracks, credits, and social media sharing capabilities. The Pixorial platform allowed users to view, share, and edit videos without modifying the original. Movie Creator integrated pictures and video to create user movies. == Awards == 2012 Apex Award from the Colorado Technology Association, for Best Technology Project of the Year 2010 Computerworld Laureate for Media, Arts and Entertainment
Information leakage
Information leakage happens whenever a system that is designed to be closed to an eavesdropper reveals some information to unauthorized parties nonetheless. In other words: Information leakage occurs when secret information correlates with, or can be correlated with, observable information. For example, when designing an encrypted instant messaging network, a network engineer without the capacity to crack encryption codes could see when messages are transmitted, even if he could not read them. == Risk vectors == A modern example of information leakage is the leakage of secret information via data compression, by using variations in data compression ratio to reveal correlations between known (or deliberately injected) plaintext and secret data combined in a single compressed stream. Another example is the key leakage that can occur when using some public-key systems when cryptographic nonce values used in signing operations are insufficiently random. Bad randomness cannot protect proper functioning of a cryptographic system, even in a benign circumstance, it can easily produce crackable keys that cause key leakage. Information leakage can sometimes be deliberate: for example, an algorithmic converter may be shipped that intentionally leaks small amounts of information, in order to provide its creator with the ability to intercept the users' messages, while still allowing the user to maintain an illusion that the system is secure. This sort of deliberate leakage is sometimes known as a subliminal channel. Generally, only very advanced systems employ defenses against information leakage. Following are the commonly implemented countermeasures : Use steganography to hide the fact that a message is transmitted at all. Use chaffing to make it unclear to whom messages are transmitted (but this does not hide from others the fact that messages are transmitted). For busy re-transmitting proxies, such as a Mixmaster node: randomly delay and shuffle the order of outbound packets - this will assist in disguising a given message's path, especially if there are multiple, popular forwarding nodes, such as are employed with Mixmaster mail forwarding. When a data value is no longer going to be used, erase it from the memory.
Social media therapy
Social media therapy is a form of expressive therapy. It uses the act of creating and sharing user-generated content as a way of connecting with and understanding people. Social media therapy combines different expressive therapy aspects of talk therapy, art therapy, writing therapy, and drama therapy and applies them to the web domain. Within social media therapy, synchronous or asynchronous dialogue occurs through exchanges of audio, text or visual information. The digital content is published online to serve as a form of therapy. == Background == Time spent online via email, websites, instant messaging and social media has increased: since 1999, more than 2,554 million people have become internet users. This alters the way people communicate with each other, and alters the connotation of certain words. The concepts of "identity", "friend", "like" and "connected" have adapted alongside technology. People are influenced by data sharing, social marketing, and technological tools. There are multiple therapeutic services offered through the internet. E-therapy, online counseling, cyber therapy, and social media therapy are similar in that each utilizes the internet in order to provide therapy for patients. == Controversy == There are pros and cons when it comes to the subject of online therapy. Criticism of providing therapy through online methods comes from concerns over the lack of physical contact. There are important features of therapy created through face-to-face therapy such as transference and countertransference that can not be created through online therapy. Patricia R. Recupero and Samara E. Rainey stated in their article "Informed Consent to E-Therapy" of American Journal of Psychotherapy that the lack of face-to-face interaction increased the risk of misdiagnosis and misunderstanding between the E-therapist and patient, thereby increasing the risk of uncertainty for the clinician. There are also concerns over the internet creating a distraction from the therapy itself. Confidentiality and privacy concerns have been raised as well. However, several systematic reviews have found that online psychotherapy can produce clinical outcomes comparable to face-to-face treatment, suggesting that physical distance does not inherently reduce therapeutic effectiveness.
Social film
A social film is a type of interactive film that is presented through the lens of social media. A social film is distributed digitally and integrates with a social networking service, such as Facebook or YouTube. It combines features of web video, social network games and social media. == Key elements == Social films are a more recent phenomenon, and, in turn, there are few precedents for their format. Although there are not many examples of this genre of film, the medium has certain identifiable elements: Casual entertainment Social media User-generated content Game mechanics Using just one of these factors or a combination of them, a social film engages viewers to interact directly with the work. This can be done through usual social media functionality like comments and ranking or adding directly to the narrative itself. Just as with memes, social film distribution relies on the viral spread enabled by social media. This is based on the viral expansion loops model, in which a viewer benefits from sharing the application with friends, exponentially creating new viewers compelled to share the application. == History == One of the first social films to be created was from the YouTube channel lonelygirl15. This social film started in 2006 and was created by Miles Beckett , Mesh Flinders, and Greg Goodfried. They used YouTube posts to create an interactive video series about a fictional character who showcased her life in a vlog format. As the videos went on, more bizarre things would keep happening to the main character, Bree, before she just stopped uploading. This channel was not only the first viral social film, but went on to be one of the first viral YouTube channels to be created. It did take a few years to see any more films in this genre, but 2011 saw many people start to try their hand at making these films. The first social film in this year was a film called Him, Her and Them which was produced and released by Murmur in April 2011. It was distributed exclusively through Facebook and promoted as the first “Facebook film.” The film is composed of short video clips and interactive slideshows, integrating Facebook's Social Graph API. Users participate via text-based additions to the story, which are viewable only by friends within their social network. In May 2011, Canon and Ron Howard teamed up to create Project Imagin8ion, which was a photo contest where photographers submitted photos and the top 8 photos would be the inspiration for a short film. This short film was called "When You Find Me" and could be found exclusively on YouTube. In July 2011, Intel and Toshiba partnered together to create Hollywood's first Social Film experience, a thriller called Inside, directed by D.J. Caruso and starring Emmy Rossum. The project is broken up into several segments across multiple social media platforms including Facebook, YouTube, and Twitter. In this instance, the audience is challenged to help Emmy Rossum's character, Christina, safely make it out of the room she's been trapped in. This particular form of social film is a major undertaking in that it combines social media activity with A-list acting talent to create a user experience that all happens in real time. Although not quite the same idea, Hollywood also started experimenting with the idea of interactive and crowd-sourced films. One of the first examples of this was a short film called "Life In A Day" directed by Kevin Macdonald and produced by Ridley Scott. Kevin asked people from all over the world to submit videos onto YouTube of what they were doing on July 24th, 2010. They combined all of the best videos that were submitted together to create one film of people doing different things all around the world, no matter how boring or simple those things seemed. They took this short to film festivals before releasing it to the public on YouTube in 2011. In August 2012, Intel and Toshiba partnered again to create The Beauty Inside, directed by Drake Doremus, starring Mary Elizabeth Winstead and Topher Grace. It's Hollywood's first social film that gives everyone in the audience a chance to play Alex, the lead role. The experience will be broken up into six filmed episodes interspersed with real-time interactive storytelling that all takes place on Alex's Facebook timeline. In August 2013, Intel and Toshiba released their third entry into the category, The Power Inside, directed by Will Speck and Josh Gordon and starring Harvey Keitel, Analeigh Tipton, and Craig Roberts. It's Hollywood's first social film that asks the audience to audition to help save or destroy the world. The experience is broken up into six filmed episodes interspersed with user-generated content and interactive storytelling on the main character's Facebook timeline. In 2015, Intel partnered with Dell for their fourth entry, What Lives Inside directed by Robert Stromberg and starring Colin Hanks, Catherine O'Hara, and J. K. Simmons. The first of four episodes was released on Hulu on March 25, 2015.
Framebuffer
A framebuffer (frame buffer, or sometimes framestore) is a portion of random-access memory (RAM) containing a bitmap that drives a video display. It is a memory buffer containing data representing all the pixels in a complete video frame. Modern video cards contain framebuffer circuitry in their cores. This circuitry converts an in-memory bitmap into a video signal that can be displayed on a computer monitor. In computing, a screen buffer is a part of computer memory used by a computer application for the representation of the content to be shown on the computer display. The screen buffer may also be called the video buffer, the regeneration buffer, or regen buffer for short. The phrase "screen buffer” refers to a logical function, while video memory refers to a hardware storage location. In particular, the screen buffer may be placed in the main RAM, the video memory, or some other hardware location. To reduce latency and avoid screen tearing, multiple frames can be buffered, and this technique is called multiple buffering. When this is so, at any time, only one frame would be visible, and the others would not be. The currently invisible frames are located in the off-screen buffer. The information in the buffer typically consists of color values for every pixel to be shown on the display. Color values are commonly stored in 1-bit binary (monochrome), 4-bit palettized, 8-bit palettized, 16-bit high color and 24-bit true color formats. An additional alpha channel is sometimes used to retain information about pixel transparency. The total amount of memory required for the framebuffer depends on the resolution of the output signal, and on the color depth or palette size. == History == Computer researchers had long discussed the theoretical advantages of a framebuffer but were unable to produce a machine with sufficient memory at an economically practicable cost. In 1947, the Manchester Baby computer used a Williams tube, later the Williams-Kilburn tube, to store 1024 bits on a cathode-ray tube (CRT) memory and displayed on a second CRT. Other research labs were exploring these techniques with MIT Lincoln Laboratory achieving a 4096 display in 1950. A color-scanned display was implemented in the late 1960s, called the Brookhaven RAster Display (BRAD), which used a drum memory and a television monitor. In 1969, A. Michael Noll of Bell Telephone Laboratories, Inc. implemented a scanned display with a frame buffer, using magnetic-core memory. A year or so later, the Bell Labs system was expanded to display an image with a color depth of three bits on a standard color TV monitor. The vector graphics used in the computer had to be converted for the scanned graphics of a TV display. In the early 1970s, the development of MOS memory (metal–oxide–semiconductor memory) integrated-circuit chips, particularly high-density DRAM (dynamic random-access memory) chips with at least 1 kb memory, made it practical to create, for the first time, a digital memory system with framebuffers capable of holding a standard video image. This led to the development of the SuperPaint system by Richard Shoup at Xerox PARC in 1972. Shoup was able to use the SuperPaint framebuffer to create an early digital video-capture system. By synchronizing the output signal to the input signal, Shoup was able to overwrite each pixel of data as it shifted in. Shoup also experimented with modifying the output signal using color tables. These color tables allowed the SuperPaint system to produce a wide variety of colors outside the range of the limited 8-bit data it contained. This scheme would later become commonplace in computer framebuffers. In 1974, Evans & Sutherland released the first commercial framebuffer, the Picture System, costing about $15,000. It was capable of producing resolutions of up to 512 by 512 pixels in 8-bit grayscale, and became a boon for graphics researchers who did not have the resources to build their own framebuffer. The New York Institute of Technology would later create the first 24-bit color system using three of the Evans & Sutherland framebuffers. Each framebuffer was connected to an RGB color output (one for red, one for green and one for blue), with a Digital Equipment Corporation PDP 11/04 minicomputer controlling the three devices as one. In 1975, the UK company Quantel produced the first commercial full-color broadcast framebuffer, the Quantel DFS 3000. It was first used in TV coverage of the 1976 Montreal Olympics to generate a picture-in-picture inset of the Olympic flaming torch while the rest of the picture featured the runner entering the stadium. The rapid improvement of integrated-circuit technology made it possible for many of the home computers of the late 1970s to contain low-color-depth framebuffers. Today, nearly all computers with graphical capabilities utilize a framebuffer for generating the video signal. Amiga computers, created in the 1980s, featured special design attention to graphics performance and included a unique Hold-And-Modify framebuffer capable of displaying 4096 colors. Framebuffers also became popular in high-end workstations and arcade system boards throughout the 1980s. SGI, Sun Microsystems, HP, DEC and IBM all released framebuffers for their workstation computers in this period. These framebuffers were usually of a much higher quality than could be found in most home computers, and were regularly used in television, printing, computer modeling and 3D graphics. Framebuffers were also used by Sega for its high-end arcade boards, which were also of a higher quality than on home computers. == Display modes == Framebuffers used in personal and home computing often had sets of defined modes under which the framebuffer can operate. These modes reconfigure the hardware to output different resolutions, color depths, memory layouts and refresh rate timings. In the world of Unix machines and operating systems, such conveniences were usually eschewed in favor of directly manipulating the hardware settings. This manipulation was far more flexible in that any resolution, color depth and refresh rate was attainable – limited only by the memory available to the framebuffer. An unfortunate side-effect of this method was that the display device could be driven beyond its capabilities. In some cases, this resulted in hardware damage to the display. More commonly, it simply produced garbled and unusable output. Modern CRT monitors fix this problem through the introduction of protection circuitry. When the display mode is changed, the monitor attempts to obtain a signal lock on the new refresh frequency. If the monitor is unable to obtain a signal lock or if the signal is outside the range of its design limitations, the monitor will ignore the framebuffer signal and possibly present the user with an error message. LCD monitors tend to contain similar protection circuitry, but for different reasons. Since the LCD must digitally sample the display signal (thereby emulating an electron beam), any signal that is out of range cannot be physically displayed on the monitor. == Color palette == Framebuffers have traditionally supported a wide variety of color modes. Due to the expense of memory, most early framebuffers used 1-bit (2 colors per pixel), 2-bit (4 colors), 4-bit (16 colors) or 8-bit (256 colors) color depths. The problem with such small color depths is that a full range of colors cannot be produced. The solution to this problem was indexed color, which adds a lookup table to the framebuffer. Each color stored in framebuffer memory acts as a color index. The lookup table serves as a palette with a limited number of different colors, while the rest is used as an index table. Here is a typical indexed 256-color image and its own palette (shown as a rectangle of swatches): In some designs, it was also possible to write data to the lookup table (or switch between existing palettes) on the fly, allowing dividing the picture into horizontal bars with their own palette and thus rendering an image that had a far wider palette. For example, viewing an outdoor shot photograph, the picture could be divided into four bars: the top one with emphasis on sky tones, the next with foliage tones, the next with skin and clothing tones, and the bottom one with ground colors. This required each palette to have overlapping colors, but, carefully done, allowed great flexibility. == Memory access == While framebuffers are commonly accessed via a memory mapping directly to the CPU memory space, this is not the only method by which they may be accessed. Framebuffers have varied widely in the methods used to access memory. Some of the most common are: Mapping the entire framebuffer to a given memory range. Port commands to set each pixel, range of pixels or palette entry. Mapping a memory range smaller than the framebuffer memory, then bank switching as necessary. The framebuffer organization may be packed pixel or planar. The framebuffer may be all
Ciphertext
In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext that is unreadable by a human or computer without the proper cipher to decrypt it. This process prevents the loss of sensitive information via hacking. Decryption, the inverse of encryption, is the process of turning ciphertext into readable plaintext. Ciphertext is not to be confused with codetext, because the latter is a result of a code, not a cipher. == Conceptual underpinnings == Let m {\displaystyle m\!} be the plaintext message that Alice wants to secretly transmit to Bob and let E k {\displaystyle E_{k}\!} be the encryption cipher, where k {\displaystyle _{k}\!} is a cryptographic key. Alice must first transform the plaintext into ciphertext, c {\displaystyle c\!} , in order to securely send the message to Bob, as follows: c = E k ( m ) . {\displaystyle c=E_{k}(m).\!} In a symmetric-key system, Bob knows Alice's encryption key. Once the message is encrypted, Alice can safely transmit it to Bob (assuming no one else knows the key). In order to read Alice's message, Bob must decrypt the ciphertext using E k − 1 {\displaystyle {E_{k}}^{-1}\!} which is known as the decryption cipher, D k : {\displaystyle D_{k}:\!} D k ( c ) = D k ( E k ( m ) ) = m . {\displaystyle D_{k}(c)=D_{k}(E_{k}(m))=m.\!} Alternatively, in a non-symmetric key system, everyone, not just Alice and Bob, knows the encryption key; but the decryption key cannot be inferred from the encryption key. Only Bob knows the decryption key D k , {\displaystyle D_{k},} and decryption proceeds as D k ( c ) = m . {\displaystyle D_{k}(c)=m.} == Types of ciphers == The history of cryptography began thousands of years ago. Cryptography uses a variety of different types of encryption. Earlier algorithms were performed by hand and are substantially different from modern algorithms, which are generally executed by a machine. === Historical ciphers === Historical pen and paper ciphers used in the past are sometimes known as classical ciphers. They include: Substitution cipher: the units of plaintext are replaced with ciphertext (e.g., Caesar cipher and one-time pad) Polyalphabetic substitution cipher: a substitution cipher using multiple substitution alphabets (e.g., Vigenère cipher and Enigma machine) Polygraphic substitution cipher: the unit of substitution is a sequence of two or more letters rather than just one (e.g., Playfair cipher) Transposition cipher: the ciphertext is a permutation of the plaintext (e.g., rail fence cipher) Historical ciphers are not generally used as a standalone encryption technique because they are quite easy to crack. Many of the classical ciphers, with the exception of the one-time pad, can be cracked using brute force. === Modern ciphers === Modern ciphers are more secure than classical ciphers and are designed to withstand a wide range of attacks. An attacker should not be able to find the key used in a modern cipher, even if they know any specifics about the plaintext and its corresponding ciphertext. Modern encryption methods can be divided into the following categories: Private-key cryptography (symmetric key algorithm): one shared key is used for encryption and decryption Public-key cryptography (asymmetric key algorithm): two different keys are used for encryption and decryption In a symmetric key algorithm (e.g., DES, AES), the sender and receiver have a shared key established in advance: the sender uses the shared key to perform encryption; the receiver uses the shared key to perform decryption. Symmetric key algorithms can either be block ciphers or stream ciphers. Block ciphers operate on fixed-length groups of bits, called blocks, with an unvarying transformation. Stream ciphers encrypt plaintext digits one at a time on a continuous stream of data, with the transformation of successive digits varying during the encryption process. In an asymmetric key algorithm (e.g., RSA), there are two different keys: a public key and a private key. The public key is published, thereby allowing any sender to perform encryption. The private key is kept secret by the receiver, thereby allowing only the receiver to correctly perform decryption. == Cryptanalysis == Cryptanalysis (also referred to as codebreaking or cracking the code) is the study of applying various methodologies to obtain the meaning of encrypted information, without having access to the cipher required to correctly decrypt the information. This typically involves gaining an understanding of the system design and determining the cipher. Cryptanalysts can follow one or more attack models to crack a cipher, depending upon what information is available and the type of cipher being analyzed. Ciphertext is generally the most easily obtained part of a cryptosystem and therefore is an important part of cryptanalysis. === Attack models === Ciphertext-only: the cryptanalyst has access only to a collection of ciphertexts or code texts. This is the weakest attack model because the cryptanalyst has limited information. Modern ciphers rarely fail under this attack. Known-plaintext: the attacker has a set of ciphertexts to which they know the corresponding plaintext Chosen-plaintext attack: the attacker can obtain the ciphertexts corresponding to an arbitrary set of plaintexts of their own choosing Batch chosen-plaintext attack: where the cryptanalyst chooses all plaintexts before any of them are encrypted. This is often the meaning of an unqualified use of "chosen-plaintext attack". Adaptive chosen-plaintext attack: where the cryptanalyst makes a series of interactive queries, choosing subsequent plaintexts based on the information from the previous encryptions. Chosen-ciphertext attack: the attacker can obtain the plaintexts corresponding to an arbitrary set of ciphertexts of their own choosing Adaptive chosen-ciphertext attack Indifferent chosen-ciphertext attack Related-key attack: similar to a chosen-plaintext attack, except the attacker can obtain ciphertexts encrypted under two different keys. The keys are unknown, but the relationship between them is known (e.g., two keys that differ in the one bit). == Famous ciphertexts == The Babington Plot ciphers The Shugborough inscription The Zimmermann Telegram The Magic Words are Squeamish Ossifrage The cryptogram in "The Gold-Bug" Beale ciphers Kryptos Zodiac Killer ciphers