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Pseudo-randomness
A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable process. Background The generation of random numbers has many uses, such as for random sampling, Monte Carlo methods, board games, or gambling. In physics, however, most processes, such as gravitational acceleration, are deterministic, meaning that they always produce the same outcome from the same starting point. Some notable exceptions are radioactive decay and quantum measurement, which are both modeled as being truly random processes in the underlying physics. Since these processes are not practical sources of random numbers, people use pseudorandom numbers, which ideally have the unpredictability of a truly random sequence, despite being generated by a deterministic process. In many applications, the deterministic process is a computer algorithm called a pseudorandom number generator, which must first be provided wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Randomness
A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal dice roll or the digits of π exhibit statistical randomness. Statistical randomness does not necessarily imply "true" randomness, i.e., objective unpredictability. Pseudorandomness is sufficient for many uses, such as statistics, hence the name ''statistical'' randomness. ''Global randomness'' and ''local randomness'' are different. Most philosophical conceptions of randomness are global—because they are based on the idea that "in the long run" a sequence looks truly random, even if certain sub-sequences would ''not'' look random. In a "truly" random sequence of numbers of sufficient length, for example, it is probable there would be long sequences of nothing but repeating numbers, though on the whole the sequence might be random. ''Local'' randomness refers to the idea that there can be minimum sequence lengths in which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roulette
Roulette is a casino game named after the French word meaning ''little wheel'' which was likely developed from the Italian game Biribi''.'' In the game, a player may choose to place a bet on a single number, various groupings of numbers, the color red or black, whether the number is odd or even, or if the numbers are high (19–36) or low (1–18). To determine the winning number, a croupier spins a wheel in one direction, then spins a ball in the opposite direction around a tilted circular track running around the outer edge of the wheel. The ball eventually loses momentum, passes through an area of deflectors, and falls onto the wheel and into one of thirty-seven (single-zero, French or European style roulette) or thirty-eight (double-zero, American style roulette) or thirty-nine (triple-zero, "Sands Roulette") colored and numbered pockets on the wheel. The winnings are then paid to anyone who has placed a successful bet. History The first form of roulette was devised in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudorandom Ensemble
In cryptography, a pseudorandom ensemble is a family of variables meeting the following criteria: Let U = \_ be a uniform ensemble and X = \_ be an ensemble Ensemble may refer to: Art * Architectural ensemble * ''Ensemble'' (album), Kendji Girac 2015 album * Ensemble (band), a project of Olivier Alary * Ensemble cast (drama, comedy) * Ensemble (musical theatre), also known as the chorus * ''En .... The ensemble X is called pseudorandom if X and U are indistinguishable in polynomial time. References * Goldreich, Oded (2001). ''Foundations of Cryptography: Volume 1, Basic Tools''. Cambridge University Press. . Fragments available at theauthor's web site Algorithmic information theory Pseudorandomness Cryptography {{crypto-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudorandom Binary Sequence
A pseudorandom binary sequence (PRBS), pseudorandom binary code or pseudorandom bitstream is a binary sequence that, while generated with a deterministic algorithm, is difficult to predict and exhibits statistical behavior similar to a truly random sequence. PRBS generators are used in telecommunication, such as in analog-to-information conversion, but also in encryption, simulation, correlation technique and time-of-flight spectroscopy. The most common example is the maximum length sequence generated by a (maximal) linear feedback shift register (LFSR). Other examples are Gold sequences (used in CDMA and GPS), Kasami sequences and JPL sequences, all based on LFSRs. In telecommunications, pseudorandom binary sequences are known as pseudorandom noise codes (PN or PRN codes) due to their application as pseudorandom noise. Details A binary sequence (BS) is a sequence a_0,\ldots, a_ of N bits, i.e. :a_j\in \ for j=0,1,...,N-1. A BS consists of m=\sum a_j ones and N-m zeros. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Random Number Generators
Random number generators are important in many kinds of technical applications, including physics, engineering or mathematical computer studies (e.g., Monte Carlo simulations), cryptography and gambling (on game servers). This list includes many common types, regardless of quality. Pseudorandom number generators (PRNGs) Whenever using a pseudorandom number generator, keep in mind John von Neumann's dictum "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin." The following algorithms are pseudorandom number generators. Cryptographic algorithms Cipher algorithms and cryptographic hashes can be used as very high-quality pseudorandom number generators. However, generally they are considerably slower (typically by a factor 2-10) than fast, non-cryptographic random number generators. These include: * Stream ciphers. Popular choices are Salsa20 or ChaCha (often with the number of rounds reduced to 8 for speed), ISAAC, HC-128 an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptographically Secure Pseudorandom Number Generator
A cryptographically secure pseudorandom number generator (CSPRNG) or cryptographic pseudorandom number generator (CPRNG) is a pseudorandom number generator (PRNG) with properties that make it suitable for use in cryptography. It is also loosely known as a cryptographic random number generator (CRNG) (see Random number generation § "True" vs. pseudo-random numbers). Most cryptographic applications require random numbers, for example: * key generation * nonces * salts in certain signature schemes, including ECDSA, RSASSA-PSS The "quality" of the randomness required for these applications varies. For example, creating a nonce in some protocols needs only uniqueness. On the other hand, the generation of a master key requires a higher quality, such as more entropy. And in the case of one-time pads, the information-theoretic guarantee of perfect secrecy only holds if the key material comes from a true random source with high entropy, and thus any kind of pseudorandom number genera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudorandom Generator
In theoretical computer science and cryptography, a pseudorandom generator (PRG) for a class of statistical tests is a deterministic procedure that maps a random seed to a longer pseudorandom string such that no statistical test in the class can distinguish between the output of the generator and the uniform distribution. The random seed itself is typically a short binary string drawn from the uniform distribution. Many different classes of statistical tests have been considered in the literature, among them the class of all Boolean circuits of a given size. It is not known whether good pseudorandom generators for this class exist, but it is known that their existence is in a certain sense equivalent to (unproven) circuit lower bounds in computational complexity theory. Hence the construction of pseudorandom generators for the class of Boolean circuits of a given size rests on currently unproven hardness assumptions. Definition Let \mathcal A = \ be a class of functions. These ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Distribution (discrete)
In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein a finite number of values are equally likely to be observed; every one of ''n'' values has equal probability 1/''n''. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen". A simple example of the discrete uniform distribution is throwing a fair dice. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform because not all sums have equal probability. Although it is convenient to describe discrete uniform distributions over integers, such as this, one can also consider discrete uniform distributions over any finite set. For instance, a random permutation is a permutation generated uniformly from the permutations of a given length, and a unif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Total Variation Distance
In probability theory, the total variation distance is a distance measure for probability distributions. It is an example of a statistical distance metric, and is sometimes called the statistical distance, statistical difference or variational distance. Definition Consider a measurable space (\Omega, \mathcal) and probability measures P and Q defined on (\Omega, \mathcal). The total variation distance between P and Q is defined as: :\delta(P,Q)=\sup_\left, P(A)-Q(A)\. Informally, this is the largest possible difference between the probabilities that the two probability distributions can assign to the same event. Properties Relation to other distances The total variation distance is related to the Kullback–Leibler divergence by Pinsker’s inequality: :\delta(P,Q) \le \sqrt. One also has the following inequality, due to Bretagnolle and Huber (see, also, Tsybakov), which has the advantage of providing a non-vacuous bound even when D_(P\parallel Q)>2: :\delta(P,Q) \le \sqrt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security ( data confidentiality, data integrity, authentication, and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications. Cryptography prior to the modern age was effectively synonymo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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