Sieve of Pritchard

In mathematics, the sieve of Pritchard is an algorithm for finding all prime numbers up to a specified bound. Like the ancient sieve of Eratosthenes, it has a simple conceptual basis in number theory. It is especially suited to quick hand computation for small bounds. Whereas the sieve of Eratosthenes marks off each non-prime for each of its prime factors, the sieve of Pritchard avoids considering almost all non-prime numbers by building progressively larger wheels, which represent the pattern of numbers not divisible by any of the primes processed thus far. It thereby achieves a better asymptotic complexity, and was the first sieve with a running time sublinear in the specified bound. Its asymptotic running-time has not been improved on, and it deletes fewer composites than any other known sieve. It was created in 1979 by Paul Pritchard. Since Pritchard has created a number of other sieve algorithms for finding prime numbers, the sieve of Pritchard is sometimes singled out by being called the wheel sieve (by Pritchard himself) or the dynamic wheel sieve. == Overview == A prime number is a natural number that has no natural number divisors other than the number 1 and itself. To find all the prime numbers less than or equal to a given integer N, a sieve algorithm examines a set of candidates in the range 2, 3, …, N, and eliminates those that are not prime, leaving the primes at the end. The sieve of Eratosthenes examines all of the range, first removing all multiples of the first prime 2, then of the next prime 3, and so on. The sieve of Pritchard instead examines a subset of the range consisting of numbers that occur on successive wheels, which represent the pattern of numbers left after each successive prime is processed by the sieve of Eratosthenes. For i > 0, the ith wheel Wi represents this pattern. It is the set of numbers between 1 and the product Pi = p1 · p2 ⋯ pi of the first i prime numbers that are not divisible by any of these prime numbers (and is said to have an associated length Pi). This is because adding Pi to a number does not change whether it is divisible by one of the first i prime numbers, since the remainder on division by any one of these primes is unchanged. So W1 = {1} with length P1 = 2 represents the pattern of odd numbers; W2 = {1,5} with length P2 = 6 represents the pattern of numbers not divisible by 2 or 3; etc. Wheels are so-called because Wi can be usefully visualized as a circle of circumference Pi with its members marked at their corresponding distances from an origin. Then rolling the wheel along the number line marks points corresponding to successive numbers not divisible by one of the first i prime numbers. The animation shows W2 being rolled up to 30. It is useful to define Wi → n for n > 0 to be the result of rolling Wi up to n. Then the animation generates W2 → 30 = {1,5,7,11,13,17,19,23,25,29}. Note that up to 52 − 1 = 24, this consists only of 1 and the primes between 5 and 25. The sieve of Pritchard is derived from the observation that this holds generally: for all i > 0, the values in Wi → (p2i+1 − 1) are 1 and the primes between pi+1 and p2i+1. It even holds for i = 0, where the wheel has length 1 and contains just 1 (representing all the natural numbers). So the sieve of Pritchard starts with the trivial wheel W0 and builds successive wheels until the square of the wheel's first member after 1 is at least N. Wheels grow very quickly, but only their values up to N are needed and generated. It remains to find a method for generating the next wheel. Note in the animation that W3 = {1,5,7,11,13,17,19,23,25,29} − {5 · 1 , 5 · 5} can be obtained by rolling W2 up to 30 and then removing 5 times each member of W2.This also holds generally: for all i ≥ 0, Wi+1 = (Wi → Pi+1) − {pi+1 · w | w ∈ Wi}. Rolling Wi past Pi just adds values to Wi, so the current wheel is first extended by getting each successive member starting with w = 1, adding Pi to it, and inserting the result in the set. Then the multiples of pi+1 are deleted. Care must be taken to avoid a number being deleted that itself needs to be multiplied by pi+1. The sieve of Pritchard as originally presented does so by first skipping past successive members until finding the maximum one needed, and then doing the deletions in reverse order by working back through the set. This is the method used in the first animation above. A simpler approach is just to gather the multiples of pi+1 in a list, and then delete them. Another approach is given by Gries and Misra. If the main loop terminates with a wheel whose length is less than N, it is extended up to N to generate the remaining primes. The algorithm, for finding all primes up to N, is therefore as follows: Start with a set W = {1} and length = 1 representing wheel 0, and prime p = 2. As long as p2 ≤ N, do the following: if length < N, then extend W by repeatedly getting successive members w of W starting with 1 and inserting length + w into W as long as it does not exceed p · length or N; increase length to the minimum of p · length and N. repeatedly delete p times each member of W by first finding the largest ≤ length and then working backwards. note the prime p, then set p to the next member of W after 1 (or 3 if p was 2). if length < N, then extend W to N by repeatedly getting successive members w of W starting with 1 and inserting length + w into W as long as it does not exceed N; On termination, the rest of the primes up to N are the members of W after 1. === Example === To find all the prime numbers less than or equal to 150, proceed as follows. Start with wheel 0 with length 1, representing all natural numbers 1, 2, 3...: 1 The first number after 1 for wheel 0 (when rolled) is 2; note it as a prime. Now form wheel 1 with length 2 × 1 = 2 by first extending wheel 0 up to 2 and then deleting 2 times each number in wheel 0, to get: 1 2 The first number after 1 for wheel 1 (when rolled) is 3; note it as a prime. Now form wheel 2 with length 3 × 2 = 6 by first extending wheel 1 up to 6 and then deleting 3 times each number in wheel 1, to get 1 2 3 5 The first number after 1 for wheel 2 is 5; note it as a prime. Now form wheel 3 with length 5 × 6 = 30 by first extending wheel 2 up to 30 and then deleting 5 times each number in wheel 2 (in reverse order), to get 1 2 3 5 7 11 13 17 19 23 25 29 The first number after 1 for wheel 3 is 7; note it as a prime. Now wheel 4 has length 7 × 30 = 210, so we only extend wheel 3 up to our limit 150. (No further extending will be done now that the limit has been reached.) We then delete 7 times each number in wheel 3 until we exceed our limit 150, to get the elements in wheel 4 up to 150: 1 2 3 5 7 11 13 17 19 23 25 29 31 37 41 43 47 49 53 59 61 67 71 73 77 79 83 89 91 97 101 103 107 109 113 119 121 127 131 133 137 139 143 149 The first number after 1 for this partial wheel 4 is 11; note it as a prime. Since we have finished with rolling, we delete 11 times each number in the partial wheel 4 until we exceed our limit 150, to get the elements in wheel 5 up to 150: 1 2 3 5 7 11 13 17 19 23 25 29 31 37 41 43 47 49 53 59 61 67 71 73 77 79 83 89 91 97 101 103 107 109 113 119 121 127 131 133 137 139 143 149 The first number after 1 for this partial wheel 5 is 13. Since 13 squared is at least our limit 150, we stop. The remaining numbers (other than 1) are the rest of the primes up to our limit 150. Just 8 composite numbers are removed, once each. The rest of the numbers considered (other than 1) are prime. In comparison, the natural version of Eratosthenes sieve (stopping at the same point) removes composite numbers 184 times. == Pseudocode == The sieve of Pritchard can be expressed in pseudocode, as follows: algorithm Sieve of Pritchard is input: an integer N >= 2. output: the set of prime numbers in {1,2,...,N}. let W and Pr be sets of integer values, and all other variables integer values. k, W, length, p, Pr := 1, {1}, 2, 3, {2}; {invariant: p = pk+1 and W = Wk ∩ {\displaystyle \cap } {1,2,...,N} and length = minimum of Pk,N and Pr = the primes up to pk} while p2 <= N do if (length < N) then Extend W,length to minimum of plength,N; Delete multiples of p from W; Insert p into Pr; k, p := k+1, next(W, 1) if (length < N) then Extend W,length to N; return Pr ∪ {\displaystyle \cup } W - {1}; where next(W, w) is the next value in the ordered set W after w. procedure Extend W,length to n is {in: W = Wk and length = Pk and n > length} {out: W = Wk → {\displaystyle \rightarrow } n and length = n} integer w, x; w, x := 1, length+1; while x <= n do Insert x into W; w := next(W,w); x := length + w; length := n; procedure Delete multiples of p from W,length is integer w; w := p; while pw <= length do w := next(W,w); while w > 1 do w := prev(W,w); Remove pw from W; where prev(W, w) is the previous value in the ordered set W before w. The algorithm can be initialized with W0 instead of W1 at the minor complication of making next(W, 1) a special case when k = 0. This a

Digital image correlation and tracking

Digital image correlation and tracking is an optical method that employs tracking and image registration techniques for accurate 2D and 3D measurements of changes in 2D images or 3D volumes. This method is often used to measure full-field displacement and strains, and it is widely applied in many areas of science and engineering. Compared to strain gauges and extensometers, digital image correlation methods provide finer details about deformation, due to the ability to provide both local and average data. == Overview == Digital image correlation (DIC) techniques have been increasing in popularity, especially in micro- and nano-scale mechanical testing applications due to their relative ease of implementation and use. Advances in computer technology and digital cameras have been the enabling technologies for this method and while white-light optics has been the predominant approach, DIC can be and has been extended to almost any imaging technology. The concept of using cross-correlation to measure shifts in datasets has been known for a long time, and it has been applied to digital images since at least the early 1970s. The present-day applications are almost innumerable, including image analysis, image compression, velocimetry, and strain estimation. Much early work in DIC in the field of mechanics was led by researchers at the University of South Carolina in the early 1980s and has been optimized and improved in recent years. Commonly, DIC relies on finding the maximum of the correlation array between pixel intensity array subsets on two or more corresponding images, which gives the integer translational shift between them. It is also possible to estimate shifts to a finer resolution than the resolution of the original images, which is often called "sub-pixel" registration because the measured shift is smaller than an integer pixel unit. For sub-pixel interpolation of the shift, other methods do not simply maximize the correlation coefficient. An iterative approach can also be used to maximize the interpolated correlation coefficient by using non-linear optimization techniques. The non-linear optimization approach tends to be conceptually simpler and can handle large deformations more accurately, but as with most nonlinear optimization techniques, it is slower. The two-dimensional discrete cross correlation r i j {\displaystyle r_{ij}} can be defined in several ways, one possibility being: r i j = ∑ m ∑ n [ f ( m + i , n + j ) − f ¯ ] [ g ( m , n ) − g ¯ ] ∑ m ∑ n [ f ( m , n ) − f ¯ ] 2 ∑ m ∑ n [ g ( m , n ) − g ¯ ] 2 . {\displaystyle r_{ij}={\frac {\sum _{m}\sum _{n}[f(m+i,n+j)-{\bar {f}}][g(m,n)-{\bar {g}}]}{\sqrt {\sum _{m}\sum _{n}{[f(m,n)-{\bar {f}}]^{2}}\sum _{m}\sum _{n}{[g(m,n)-{\bar {g}}]^{2}}}}}.} Here f(m, n) is the pixel intensity or the gray-scale value at a point (m, n) in the original image, g(m, n) is the gray-scale value at a point (m, n) in the translated image, f ¯ {\displaystyle {\bar {f}}} and g ¯ {\displaystyle {\bar {g}}} are mean values of the intensity matrices f and g respectively. However, in practical applications, the correlation array is usually computed using Fourier-transform methods, since the fast Fourier transform is a much faster method than directly computing the correlation. F = F { f } , G = F { g } . {\displaystyle \mathbf {F} ={\mathcal {F}}\{f\},\quad \mathbf {G} ={\mathcal {F}}\{g\}.} Then taking the complex conjugate of the second result and multiplying the Fourier transforms together elementwise, we obtain the Fourier transform of the correlogram, R {\displaystyle \ R} : R = F ∘ G ∗ , {\displaystyle R=\mathbf {F} \circ \mathbf {G} ^{},} where ∘ {\displaystyle \circ } is the Hadamard product (entry-wise product). It is also fairly common to normalize the magnitudes to unity at this point, which results in a variation called phase correlation. Then the cross-correlation is obtained by applying the inverse Fourier transform: r = F − 1 { R } . {\displaystyle \ r={\mathcal {F}}^{-1}\{R\}.} At this point, the coordinates of the maximum of r i j {\displaystyle r_{ij}} give the integer shift: ( Δ x , Δ y ) = arg ⁡ max ( i , j ) { r } . {\displaystyle (\Delta x,\Delta y)=\arg \max _{(i,j)}\{r\}.} == Deformation mapping == For deformation mapping, the mapping function that relates the images can be derived from comparing a set of subwindow pairs over the whole images. (Figure 1). The coordinates or grid points (xi, yj) and (xi, yj) are related by the translations that occur between the two images. If the deformation is small and perpendicular to the optical axis of the camera, then the relation between (xi, yj) and (xi, yj) can be approximated by a 2D affine transformation such as: x ∗ = x + u + ∂ u ∂ x Δ x + ∂ u ∂ y Δ y , {\displaystyle x^{}=x+u+{\frac {\partial u}{\partial x}}\Delta x+{\frac {\partial u}{\partial y}}\Delta y,} y ∗ = y + v + ∂ v ∂ x Δ x + ∂ v ∂ y Δ y . {\displaystyle y^{}=y+v+{\frac {\partial v}{\partial x}}\Delta x+{\frac {\partial v}{\partial y}}\Delta y.} Here u and v are translations of the center of the sub-image in the X and Y directions respectively. The distances from the center of the sub-image to the point (x, y) are denoted by Δ x {\displaystyle \Delta x} and Δ y {\displaystyle \Delta y} . Thus, the correlation coefficient rij is a function of displacement components (u, v) and displacement gradients ∂ u ∂ x , ∂ u ∂ y , ∂ v ∂ x , ∂ v ∂ y . {\displaystyle {\frac {\partial u}{\partial x}},{\frac {\partial u}{\partial y}},{\frac {\partial v}{\partial x}},{\frac {\partial v}{\partial y}}.} DIC has proven to be very effective at mapping deformation in macroscopic mechanical testing, where the application of specular markers (e.g. paint, toner powder) or surface finishes from machining and polishing provide the needed contrast to correlate images well. However, these methods for applying surface contrast do not extend to the application of free-standing thin films for several reasons. First, vapor deposition at normal temperatures on semiconductor grade substrates results in mirror-finish quality films with RMS roughnesses that are typically on the order of several nanometers. No subsequent polishing or finishing steps are required, and unless electron imaging techniques are employed that can resolve microstructural features, the films do not possess enough useful surface contrast to adequately correlate images. Typically this challenge can be circumvented by applying paint that results in a random speckle pattern on the surface, although the large and turbulent forces resulting from either spraying or applying paint to the surface of a free-standing thin film are too high and would break the specimens. In addition, the sizes of individual paint particles are on the order of μms, while the film thickness is only several hundred nanometers, which would be analogous to supporting a large boulder on a thin sheet of paper. == Digital volume correlation == Digital Volume Correlation (DVC, and sometimes called Volumetric-DIC) extends the 2D-DIC algorithms into three dimensions to calculate the full-field 3D deformation from a pair of 3D images. This technique is distinct from 3D-DIC, which only calculates the 3D deformation of an exterior surface using conventional optical images. The DVC algorithm is able to track full-field displacement information in the form of voxels instead of pixels. The theory is similar to above except that another dimension is added: the z-dimension. The displacement is calculated from the correlation of 3D subsets of the reference and deformed volumetric images, which is analogous to the correlation of 2D subsets described above. DVC can be performed using volumetric image datasets. These images can be obtained using confocal microscopy, X-ray computed tomography, Magnetic Resonance Imaging or other techniques. Similar to the other DIC techniques, the images must exhibit a distinct, high-contrast 3D "speckle pattern" to ensure accurate displacement measurement. DVC was first developed in 1999 to study the deformation of trabecular bone using X-ray computed tomography images. Since then, applications of DVC have grown to include granular materials, metals, foams, composites and biological materials. To date it has been used with images acquired by MRI imaging, Computer Tomography (CT), micro-CT, confocal microscopy, and lightsheet microscopy. DVC is currently considered to be ideal in the research world for 3D quantification of local displacements, strains, and stress in biological specimens. It is preferred because of the non-invasiveness of the method over traditional experimental methods. Two of the key challenges are improving the speed and reliability of the DVC measurement. The 3D imaging techniques produce noisier images than conventional 2D optical images, which reduces the quality of the displacement measurement. Computational speed is restricted by the file sizes of 3D images, which are significantly larger than 2D images. For example, an

Key-agreement protocol

In cryptography, a key-agreement protocol is a protocol whereby two (or more) parties generate a cryptographic key as a function of information provided by each honest party so that no party can predetermine the resulting value. In particular, all honest participants influence the outcome. A key-agreement protocol is a specialisation of a key-exchange protocol. At the completion of the protocol, all parties share the same key. A key-agreement protocol precludes undesired third parties from forcing a key choice on the agreeing parties. A secure key agreement can ensure confidentiality and data integrity in communications systems, ranging from simple messaging applications to complex banking transactions. Secure agreement is defined relative to a security model, for example the Universal Model. More generally, when evaluating protocols, it is important to state security goals and the security model. For example, it may be required for the session key to be authenticated. A protocol can be evaluated for success only in the context of its goals and attack model. An example of an adversarial model is the Dolev–Yao model. In many key exchange systems, one party generates the key, and sends that key to the other party; the other party has no influence on the key. == Exponential key exchange == The first publicly known public-key agreement protocol that meets the above criteria was the Diffie–Hellman key exchange, in which two parties jointly exponentiate a generator with random numbers, in such a way that an eavesdropper cannot feasibly determine what the resultant shared key is. Exponential key agreement in and of itself does not specify any prior agreement or subsequent authentication between the participants. It has thus been described as an anonymous key agreement protocol. == Symmetric key agreement == Symmetric key agreement (SKA) is a method of key agreement that uses solely symmetric cryptography and cryptographic hash functions as cryptographic primitives. It is related to symmetric authenticated key exchange. SKA may assume the use of initial shared secrets or a trusted third party with whom the agreeing parties share a secret is assumed. If no third party is present, then achieving SKA can be trivial: we tautologically assume that two parties that share an initial secret and have achieved SKA. SKA contrasts with key-agreement protocols that include techniques from asymmetric cryptography, such as key encapsulation mechanisms. The initial exchange of a shared key must be done in a manner that is private and integrity-assured. Historically, this was achieved by physical means, such as by using a trusted courier. An example of a SKA protocol is the Needham–Schroeder protocol. It establishes a session key between two parties on the same network, using a server as a trusted third party. The original Needham–Schroeder protocol is vulnerable to a replay attack. Timestamps and nonces are included to fix this attack. It forms the basis for the Kerberos protocol. === Types of key agreement === Boyd et al. classify two-party key agreement protocols according to two criteria as follows: whether a pre-shared key already exists or not the method of generating the session key. The pre-shared key may be shared between the two parties, or each party may share a key with a trusted third party. If there is no secure channel (as may be established via a pre-shared key), it is impossible to create an authenticated session key. The session key may be generated via: key transport, key agreement and hybrid. If there is no trusted third party, then the cases of key transport and hybrid session key generation are indistinguishable. SKA is concerned with protocols in which the session key is established using only symmetric primitives. == Authentication == Anonymous key exchange, like Diffie–Hellman, does not provide authentication of the parties, and is thus vulnerable to man-in-the-middle attacks. A wide variety of cryptographic authentication schemes and protocols have been developed to provide authenticated key agreement to prevent man-in-the-middle and related attacks. These methods generally mathematically bind the agreed key to other agreed-upon data, such as the following: public–private key pairs shared secret keys passwords === Public keys === A widely used mechanism for defeating such attacks is the use of digitally signed keys that must be integrity-assured: if Bob's key is signed by a trusted third party vouching for his identity, Alice can have considerable confidence that a signed key she receives is not an attempt to intercept by Eve. When Alice and Bob have a public-key infrastructure, they may digitally sign an agreed Diffie–Hellman key, or exchanged Diffie–Hellman public keys. Such signed keys, sometimes signed by a certificate authority, are one of the primary mechanisms used for secure web traffic (including HTTPS, SSL or TLS protocols). Other specific examples are MQV, YAK and the ISAKMP component of the IPsec protocol suite for securing Internet Protocol communications. However, these systems require care in endorsing the match between identity information and public keys by certificate authorities in order to work properly. === Hybrid systems === Hybrid systems use public-key cryptography to exchange secret keys, which are then used in a symmetric-key cryptography systems. Most practical applications of cryptography use a combination of cryptographic functions to implement an overall system that provides all of the four desirable features of secure communications (confidentiality, integrity, authentication, and non-repudiation). === Passwords === Password-authenticated key agreement protocols require the separate establishment of a password (which may be smaller than a key) in a manner that is both private and integrity-assured. These are designed to resist man-in-the-middle and other active attacks on the password and the established keys. For example, DH-EKE, SPEKE, and SRP are password-authenticated variations of Diffie–Hellman. === Other tricks === If one has an integrity-assured way to verify a shared key over a public channel, one may engage in a Diffie–Hellman key exchange to derive a short-term shared key, and then subsequently authenticate that the keys match. One way is to use a voice-authenticated read-out of the key, as in PGPfone. Voice authentication, however, presumes that it is infeasible for a man-in-the-middle to spoof one participant's voice to the other in real-time, which may be an undesirable assumption. Such protocols may be designed to work with even a small public value, such as a password. Variations on this theme have been proposed for Bluetooth pairing protocols. In an attempt to avoid using any additional out-of-band authentication factors, Davies and Price proposed the use of the interlock protocol of Ron Rivest and Adi Shamir, which has been subject to both attack and subsequent refinement.

Unknown key-share attack

As defined by Blake-Wilson & Menezes (1999), an unknown key-share (UKS) attack on an authenticated key agreement (AK) or authenticated key agreement with key confirmation (AKC) protocol is an attack whereby an entity A {\displaystyle A} ends up believing she shares a key with B {\displaystyle B} , and although this is in fact the case, B {\displaystyle B} mistakenly believes the key is instead shared with an entity E ≠ A {\displaystyle E\neq A} . In other words, in a UKS, an opponent, say Eve, coerces honest parties Alice and Bob into establishing a secret key where at least one of Alice and Bob does not know that the secret key is shared with the other. For example, Eve may coerce Bob into believing he shares the key with Eve, while he actually shares the key with Alice. The “key share” with Alice is thus unknown to Bob.

Memory-hard function

In cryptography, a memory-hard function (MHF) is a function that costs a significant amount of memory to efficiently evaluate. It differs from a memory-bound function, which incurs cost by slowing down computation through memory latency. MHFs have found use in key stretching and proof of work as their increased memory requirements significantly reduce the computational efficiency advantage of custom hardware over general-purpose hardware compared to non-MHFs. == Introduction == MHFs are designed to consume large amounts of memory on a computer in order to reduce the effectiveness of parallel computing. In order to evaluate the function using less memory, a significant time penalty is incurred. As each MHF computation requires a large amount of memory, the number of function computations that can occur simultaneously is limited by the amount of available memory. This reduces the efficiency of specialised hardware, such as application-specific integrated circuits and graphics processing units, which utilise parallelisation, in computing a MHF for a large number of inputs, such as when brute-forcing password hashes or mining cryptocurrency. == Motivation and examples == Bitcoin's proof-of-work uses repeated evaluation of the SHA-256 function, but modern general-purpose processors, such as off-the-shelf CPUs, are inefficient when computing a fixed function many times over. Specialized hardware, such as application-specific integrated circuits (ASICs) designed for Bitcoin mining, can use 30,000 times less energy per hash than x86 CPUs whilst having much greater hash rates. This led to concerns about the centralization of mining for Bitcoin and other cryptocurrencies. Because of this inequality between miners using ASICs and miners using CPUs or off-the shelf hardware, designers of later proof-of-work systems utilised hash functions for which it was difficult to construct ASICs that could evaluate the hash function significantly faster than a CPU. As memory cost is platform-independent, MHFs have found use in cryptocurrency mining, such as for Litecoin, which uses scrypt as its hash function. They are also useful in password hashing because they significantly increase the cost of trying many possible passwords against a leaked database of hashed passwords without significantly increasing the computation time for legitimate users. == Measuring memory hardness == There are various ways to measure the memory hardness of a function. One commonly seen measure is cumulative memory complexity (CMC). In a parallel model, CMC is the sum of the memory required to compute a function over every time step of the computation. Other viable measures include integrating memory usage against time and measuring memory bandwidth consumption on a memory bus. Functions requiring high memory bandwidth are sometimes referred to as "bandwidth-hard functions". == Variants == MHFs can be categorized into two different groups based on their evaluation patterns: data-dependent memory-hard functions (dMHF) and data-independent memory-hard functions (iMHF). As opposed to iMHFs, the memory access pattern of a dMHF depends on the function input, such as the password provided to a key derivation function. Examples of dMHFs are scrypt and Argon2d, while examples of iMHFs are Argon2i and catena. Many of these MHFs have been designed to be used as password hashing functions because of their memory hardness. A notable problem with dMHFs is that they are prone to side-channel attacks such as cache timing. This has resulted in a preference for using iMHFs when hashing passwords. However, iMHFs have been mathematically proven to have weaker memory hardness properties than dMHFs.

KE Software

KE Software is a formerly Australian-owned computer software company based in Manchester, United Kingdom, which specialises in collection management programs for museums, galleries and archives. The Axiell Group acquired the firm in 2014. == History == KE Software had its origins in investigations into electronic systems for managing natural science collections conducted in the late 1970s under a joint program of the University of Melbourne, the then National Museum of Victoria and the Australian Museum, which led to the development of the Titan Database in 1984. Much of the credit for the development of the project was due to the work of Martin Hallett of the Museum of Victoria which evolved into Textpress, and by 2000, the KE EMu database program. KE Software was bought by Axiell in 2014 and the team merged with the Axiell staff. Axiell continues to sell and support EMu. == Products == The firm has two main products: the Ke EMu Electronic Museum management system, a collections management system for museums; and Vitalware Vital Records Management System. The first version of Ke EMu was launched in 1997 and uses the Texpress database engine with client/server architecture on a Windows or Unix/Linux server. Ke Emu is consistent with the Dublin Core / Darwin Core standards for archive and museum catalogue metadata. "The company’s clients include the three largest museums in the world.: == KE EMu == KE EMu is considered one of the more effective and purpose-designed museum cataloguing programs. particularly in the creation of public interfaces to museum catalogue data. KE EMu was further developed in 1997 as a multilingual platform, which has been utilised in bilingual institutions such as the Canadian Museum of Civilisation. Subsequently this evolved into Texpress and KE EMu (standing for Electronic MUseum) in 2000, which is "now used across the world in natural science museums with huge collections'". KE EMu is used by a large number of museums and galleries around the world, including the Smithsonian Anthropological Collection, American Museum of Natural HistoryVancouver Art Gallery, New York Botanical Garden, the University of Chicago Research Archives, the University of Pennsylvania Museum in Philadelphia, the National Museum of Australia, the Australian Museum, Museum of Victoria, University of Melbourne Archives, and the Alexander Turnbull Library, National Library of New Zealand. There are over 300 clients, and more than 5000 users of the EMu software worldwide. The program has been described as providing "...comprehensive museum management (collection management plus other administrative needs for a museum), workflow and project management, flexible metadata, various stats and metrics, and comprehensive web interface with support for mobile devices and kiosks" == KE Vitalware == The firm's vitalware software is used by a number of governments and commercial organisations for managing and accessing large data sets, such as the birth records of the Trinidad and Tobago Registrar General, the Government of Anguilla, Ministry for Infrastructure, Communications, Utility and Housing, and the Mississippi Department of Information Technology Services. == Further development == A specialist tracking component for KE EMu has been developed by Forbes Hawkins of Museum Victoria. This enables locations to be barcoded, and data to be updated as items are moved around the stores, or between venues, display, laboratories and other locations. This system has been considered by Museums around the world. The company has been working with Australian government agencies to digitize birth deaths and marriage registers in order to cross match identity data. The program has also been used for managing the Australian Plant Disease Database and the Australian Plant Pest Database as the program "...has several features that have proven to be invaluable for a plant disease database".

Code (cryptography)

In cryptology, a code is a method used to encrypt a message that operates at the level of meaning; that is, words or phrases are converted into something else. A code might transform "change" into "CVGDK" or "cocktail lounge". The U.S. National Security Agency defined a code as "A substitution cryptosystem in which the plaintext elements are primarily words, phrases, or sentences, and the code equivalents (called "code groups") typically consist of letters or digits (or both) in otherwise meaningless combinations of identical length." A codebook is needed to encrypt, and decrypt the phrases or words. By contrast, ciphers encrypt messages at the level of individual letters, or small groups of letters, or even, in modern ciphers, individual bits. Messages can be transformed first by a code, and then by a cipher. Such multiple encryption, or "superencryption" aims to make cryptanalysis more difficult. Another comparison between codes and ciphers is that a code typically represents a letter or groups of letters directly without the use of mathematics. As such the numbers are configured to represent these three values: 1001 = A, 1002 = B, 1003 = C, ... . The resulting message, then would be 1001 1002 1003 to communicate ABC. Ciphers, however, utilize a mathematical formula to represent letters or groups of letters. For example, A = 1, B = 2, C = 3, ... . Thus the message ABC results by multiplying each letter's value by 13. The message ABC, then would be 13 26 39. Codes have a variety of drawbacks, including susceptibility to cryptanalysis and the difficulty of managing the cumbersome codebooks, so ciphers are now the dominant technique in modern cryptography. In contrast, because codes are representational, they are not susceptible to mathematical analysis of the individual codebook elements. In the example, the message 13 26 39 can be cracked by dividing each number by 13 and then ranking them alphabetically. However, the focus of codebook cryptanalysis is the comparative frequency of the individual code elements matching the same frequency of letters within the plaintext messages using frequency analysis. In the above example, the code group, 1001, 1002, 1003, might occur more than once and that frequency might match the number of times that ABC occurs in plain text messages. (In the past, or in non-technical contexts, code and cipher are often used to refer to any form of encryption). == One- and two-part codes == Codes are defined by "codebooks" (physical or notional), which are dictionaries of codegroups listed with their corresponding plaintext. Codes originally had the codegroups assigned in 'plaintext order' for convenience of the code designed, or the encoder. For example, in a code using numeric code groups, a plaintext word starting with "a" would have a low-value group, while one starting with "z" would have a high-value group. The same codebook could be used to "encode" a plaintext message into a coded message or "codetext", and "decode" a codetext back into plaintext message. In order to make life more difficult for codebreakers, codemakers designed codes with no predictable relationship between the codegroups and the ordering of the matching plaintext. In practice, this meant that two codebooks were now required, one to find codegroups for encoding, the other to look up codegroups to find plaintext for decoding. Such "two-part" codes required more effort to develop, and twice as much effort to distribute (and discard safely when replaced), but they were harder to break. The Zimmermann Telegram in January 1917 used the German diplomatic "0075" two-part code system which contained upwards of 10,000 phrases and individual words. == One-time code == A one-time code is a prearranged word, phrase or symbol that is intended to be used only once to convey a simple message, often the signal to execute or abort some plan or confirm that it has succeeded or failed. One-time codes are often designed to be included in what would appear to be an innocent conversation. Done properly they are almost impossible to detect, though a trained analyst monitoring the communications of someone who has already aroused suspicion might be able to recognize a comment like "Aunt Bertha has gone into labor" as having an ominous meaning. Famous example of one time codes include: In the Bible, Jonathan prearranges a code with David, who is going into hiding from Jonathan's father, King Saul. If, during archery practice, Jonathan tells the servant retrieving arrows "the arrows are on this side of you," David may safely return to court; if the command is "the arrows are beyond you," David must flee. "One if by land; two if by sea" in "Paul Revere's Ride" made famous in the poem by Henry Wadsworth Longfellow "Climb Mount Niitaka" - the signal to Japanese planes to begin the attack on Pearl Harbor During World War II the British Broadcasting Corporation's overseas service frequently included "personal messages" as part of its regular broadcast schedule. The seemingly nonsensical stream of messages read out by announcers were actually one time codes intended for Special Operations Executive (SOE) agents operating behind enemy lines. An example might be "The princess wears red shoes" or "Mimi's cat is asleep under the table". Each code message was read out twice. By such means, the French Resistance were instructed to start sabotaging rail and other transport links the night before D-day. "Over all of Spain, the sky is clear" was a signal (broadcast on radio) to start the nationalist military revolt in Spain on July 17, 1936. Sometimes messages are not prearranged and rely on shared knowledge hopefully known only to the recipients. An example is the telegram sent to U.S. President Harry Truman, then at the Potsdam Conference to meet with Soviet premier Joseph Stalin, informing Truman of the first successful test of an atomic bomb. "Operated on this morning. Diagnosis not yet complete but results seem satisfactory and already exceed expectations. Local press release necessary as interest extends great distance. Dr. Groves pleased. He returns tomorrow. I will keep you posted." == Idiot code == An idiot code is a code that is created by the parties using it. This type of communication is akin to the hand signals used by armies in the field. Example: Any sentence where 'day' and 'night' are used means 'attack'. The location mentioned in the following sentence specifies the location to be attacked. Plaintext: Attack X. Codetext: We walked day and night through the streets but couldn't find it! Tomorrow we'll head into X. An early use of the term appears to be by George Perrault, a character in the science fiction book Friday by Robert A. Heinlein: The simplest sort [of code] and thereby impossible to break. The first ad told the person or persons concerned to carry out number seven or expect number seven or it said something about something designated as seven. This one says the same with respect to code item number ten. But the meaning of the numbers cannot be deduced through statistical analysis because the code can be changed long before a useful statistical universe can be reached. It's an idiot code... and an idiot code can never be broken if the user has the good sense not to go too often to the well. Terrorism expert Magnus Ranstorp said that the men who carried out the September 11 attacks on the United States used basic e-mail and what he calls "idiot code" to discuss their plans. == Cryptanalysis of codes == While solving a monoalphabetic substitution cipher is easy, solving even a simple code is difficult. Decrypting a coded message is a little like trying to translate a document written in a foreign language, with the task basically amounting to building up a "dictionary" of the codegroups and the plaintext words they represent. One fingerhold on a simple code is the fact that some words are more common than others, such as "the" or "a" in English. In telegraphic messages, the codegroup for "STOP" (i.e., end of sentence or paragraph) is usually very common. This helps define the structure of the message in terms of sentences, if not their meaning, and this is cryptanalytically useful. Further progress can be made against a code by collecting many codetexts encrypted with the same code and then using information from other sources spies newspapers diplomatic cocktail party chat the location from where a message was sent where it was being sent to (i.e., traffic analysis) the time the message was sent, events occurring before and after the message was sent the normal habits of the people sending the coded messages etc. For example, a particular codegroup found almost exclusively in messages from a particular army and nowhere else might very well indicate the commander of that army. A codegroup that appears in messages preceding an attack on a particular location may very well stand for that location. Cribs can be an immediate giveaway to the definiti