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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. Thes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudorandom Number Generator
A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random number generation, random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's ''random seed, seed'' (which may include truly random values). Although sequences that are closer to truly random can be generated using hardware random number generators, ''pseudorandom number generators'' are important in practice for their speed in number generation and their reproducibility. PRNGs are central in applications such as simulations (e.g. for the Monte Carlo method), electronic games (e.g. for procedural generation), and cryptography. Cryptographic applications require the output not to be predictable from earlier outputs, and more cryptographically-secure pseudorandom number generator, elabora ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
One-way Function
In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input. Here, "easy" and "hard" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems. This has nothing to do with whether the function is one-to-one; finding any one input with the desired image is considered a successful inversion. (See , below.) The existence of such one-way functions is still an open conjecture. Their existence would prove that the complexity classes P and NP are not equal, thus resolving the foremost unsolved question of theoretical computer science.Oded Goldreich (2001). Foundations of Cryptography: Volume 1, Basic Toolsdraft availablefrom author's site). Cambridge University Press. . See als The converse is not known to be true, i.e. the existence of a proof that P ≠ NP would not directly imply the existence of one-way functions. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yongge Wang
Yongge Wang (born 1967) is a computer science professor at the University of North Carolina at Charlotte specialized in algorithmic complexity and cryptography. He is the inventor of IEEE P1363 cryptographic standards SRP5 and WANG-KE and has contributed to the mathematical theory of algorithmic randomness. He co-authored a paper demonstrating that a recursively enumerable real number In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every re ... is an algorithmically random sequence if and only if it is a Chaitin's constant for some encoding of programs. He also showed the separation of Schnorr randomness from recursive randomness. He also invented a distance based statistical testing technique to improve NIST SP800-22 testing in randomness tests. In cryptographic research, he is known fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randomness Tests
A randomness test (or test for randomness), in data evaluation, is a test used to analyze the distribution of a set of data to see whether it can be described as random (patternless). In stochastic modeling, as in some computer simulations, the hoped-for randomness of potential input data can be verified, by a formal test for randomness, to show that the data are valid for use in simulation runs. In some cases, data reveals an obvious non-random pattern, as with so-called "runs in the data" (such as expecting random 0–9 but finding "4 3 2 1 0 4 3 2 1..." and rarely going above 4). If a selected set of data fails the tests, then parameters can be changed or other randomized data can be used which does pass the tests for randomness. Background The issue of randomness is an important philosophical and theoretical question. Tests for randomness can be used to determine whether a data set has a recognisable pattern, which would indicate that the process that generated it is sig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correlation Function
A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. If one considers the correlation function between random variables representing the same quantity measured at two different points, then this is often referred to as an autocorrelation function, which is made up of autocorrelations. Correlation functions of different random variables are sometimes called cross-correlation functions to emphasize that different variables are being considered and because they are made up of cross-correlations. Correlation functions are a useful indicator of dependencies as a function of distance in time or space, and they can be used to assess the distance required between sample points for the values to be effectively uncorrelated. In addition, they can form the basis of rules for interpolating values at points for which there are no observations. Correlation functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Walk
In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some Space (mathematics), mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating random walk hypothesis, stock and the financial status of a gambler. Random walks have applications to engineering and many scientific fields including ecology, psychology, computer science, physics, chemistry, biology, economics, and sociology. The term ''random walk'' was first introduced by Karl Pearson in 1905. Realizations of random walks can be obtained by Monte Carlo Simulation, Monte Carlo simulation. Lattice random ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ising Model
The Ising model (or Lenz–Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical models in physics, mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent Nuclear magnetic moment, magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a Graph (abstract data type), graph, usually a lattice (group), lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors. Neighboring spins that agree have a lower energy than those that disagree; the system tends to the lowest energy but heat disturbs this tendency, thus creating the possibility of different structural phases.The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition. Though it is a highly simplified model of a magnetic material, the Ising model can sti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Transition
In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic State of matter, states of matter: solid, liquid, and gas, and in rare cases, plasma (physics), plasma. A phase of a thermodynamic system and the states of matter have uniform physical property, physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point. Types of phase transition States of matter Phase transitions commonly refer to when a substance tran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudorandom Function Family
In cryptography, a pseudorandom function family, abbreviated PRF, is a collection of efficiently-computable functions which emulate a random oracle in the following way: no efficient algorithm can distinguish (with significant advantage) between a function chosen randomly from the PRF family and a random oracle (a function whose outputs are fixed completely at random). Pseudorandom functions are vital tools in the construction of cryptographic primitives, especially secure encryption schemes. Pseudorandom functions are not to be confused with pseudorandom generators (PRGs). The guarantee of a PRG is that a ''single'' output appears random if the input was chosen at random. On the other hand, the guarantee of a PRF is that ''all its outputs'' appear random, regardless of how the corresponding inputs were chosen, as long as the ''function'' was drawn at random from the PRF family. A pseudorandom function family can be constructed from any pseudorandom generator, using, for exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric-key Algorithm
Symmetric-key algorithms are algorithms for cryptography that use the same cryptographic keys for both the encryption of plaintext and the decryption of ciphertext. The keys may be identical, or there may be a simple transformation to go between the two keys. The keys, in practice, represent a shared secret between two or more parties that can be used to maintain a private information link. The requirement that both parties have access to the secret key is one of the main drawbacks of symmetric-key encryption, in comparison to public-key encryption (also known as asymmetric-key encryption). However, symmetric-key encryption algorithms are usually better for bulk encryption. With exception of the one-time pad they have a smaller key size, which means less storage space and faster transmission. Due to this, asymmetric-key encryption is often used to exchange the secret key for symmetric-key encryption. Types Symmetric-key encryption can use either stream ciphers or block ci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stream Cipher
stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream ( keystream). In a stream cipher, each plaintext digit is encrypted one at a time with the corresponding digit of the keystream, to give a digit of the ciphertext stream. Since encryption of each digit is dependent on the current state of the cipher, it is also known as ''state cipher''. In practice, a digit is typically a bit and the combining operation is an exclusive-or (XOR). The pseudorandom keystream is typically generated serially from a random seed value using digital shift registers. The seed value serves as the cryptographic key for decrypting the ciphertext stream. Stream ciphers represent a different approach to symmetric encryption from block ciphers. Block ciphers operate on large blocks of digits with a fixed, unvarying transformation. This distinction is not always clear-cut: in some modes of operation, a block cipher primitive is used in such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semantic Security
In cryptography, a semantically secure cryptosystem is one where only negligible information about the plaintext can be feasibly extracted from the ciphertext. Specifically, any probabilistic, polynomial-time algorithm (PPTA) that is given the ciphertext of a certain message m (taken from any distribution of messages), and the message's length, cannot determine any partial information on the message with probability non-negligibly higher than all other PPTA's that only have access to the message length (and not the ciphertext). S. Goldwasser and S. MicaliProbabilistic encryption & how to play mental poker keeping secret all partial information Annual ACM Symposium on Theory of Computing, 1982. This concept is the computational complexity analogue to Shannon's concept of perfect secrecy. Perfect secrecy means that the ciphertext reveals no information at all about the plaintext, whereas semantic security implies that any information revealed cannot be feasibly extracted. Goldreic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
