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In mathematics, the truncated power function with exponent n {\displaystyle n} is defined as x + n = { x n : x > 0 0 : x ≤ 0. {\displaystyle
Truncated_power_function
Functional relationship between two quantities
cannot be a probability distribution, but a distribution that is a truncated power function is possible: p ( x ) = C x − α {\displaystyle p(x)=Cx^{-\alpha
Power_law
Mathematical function
{\displaystyle x,y\geq 1} , the beta function may be written in terms of a convolution involving the truncated power function t ↦ t + x {\displaystyle t\mapsto
Beta_function
Computational operation
then the truncated, floored, and Euclidean definitions agree. If the dividend is positive and the divisor is negative, then the truncated and Euclidean
Modulo
Replacing a number with a simpler value
digits. In contrast, truncation does not suffer from this problem; for example, a simple string search for "3.1415", which is π truncated to four digits, will
Rounding
'Best' approximation of a function by a rational function of given order
rational approximations of power series. The Padé approximant often gives better approximation of the function than truncating its Taylor series, and it
Padé_approximant
Probability distribution
known as the power-normal distribution) is the distribution of a random variable X for which the Box–Cox transformation on X follows a truncated normal distribution
Box–Cox_distribution
B-spline Box spline — multivariate generalization of B-splines Truncated power function De Boor's algorithm — generalizes De Casteljau's algorithm Non-uniform
List of numerical analysis topics
List_of_numerical_analysis_topics
series are built from Bessel functions depending on the eccentricity e. Note that while these series can be presented in truncated form, they represent a sum
Equation_of_the_center
Series of functions in mathematics
tail. The expansion's underlying function is the sum of this computed remainder and the truncated series. When a truncated series has a factorially divergent
Asymptotic_expansion
Password-based key derivation function
would be truncated at 4 bytes rather than truncated at 72 bytes. When OpenBSD fixed this issue, they changed the version to $2b$. The bcrypt function below
Bcrypt
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
Family of functions to transform data
In statistics, a power transform is a family of functions applied to create a monotonic transformation of data using power functions. It is a data transformation
Power_transform
Mathematical function used in signal processing
function is named after the Austrian meteorologist Julius von Hann. It is a window function used to perform Hann smoothing or hanning. The function,
Hann_function
Mathematical relation assigning a probability event to a cost
optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one
Loss_function
Special function defined by an integral
is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its argument
Exponential_integral
Set of cryptographic hash functions
are truncated versions of SHA-256 and SHA-512 respectively, computed with different initial values. SHA-512/224 and SHA-512/256 are also truncated versions
SHA-2
Number taken as representative of a list of numbers
similar approach to the power mean is the f {\displaystyle f} -mean, also known as the quasi-arithmetic mean. For an injective function f : I → R {\displaystyle
Average
The Heaviside function is refinable with respect to 1 2 ⋅ δ {\displaystyle {\frac {1}{2}}\cdot \delta } . The truncated power functions with exponent
Refinable_function
Authenticated encryption mode for block ciphers
constructed by feeding blocks of data into the GHASH function and encrypting the result. This GHASH function is defined by GHASH ( H , A , C ) = X m + n +
Galois/Counter_Mode
Extension of the factorial function
in the OEIS. The values presented here are truncated rather than rounded.) The complex-valued gamma function is undefined for non-positive integers, but
Gamma_function
Probability of survival beyond any specified time
certain time. The survival function is also known as the survivor function or reliability function. The term reliability function is common in engineering
Survival_function
Digital signal generator
output word must be truncated to M bits as shown in Figure 1. However, the truncated bits can be used for interpolation. Truncation of the phase output
Numerically controlled oscillator
Numerically_controlled_oscillator
Product of numbers from 1 to n
mathematical analysis, factorials are used in power series for the exponential function and other functions, and they also have applications in algebra
Factorial
Type of signal filter
windowing function. Design and choice of real filters involves understanding and minimizing these artifacts. For example, simple truncation of the sinc
Low-pass_filter
Probability distribution
Consider the truncated distribution defined by restricting the standard Cauchy distribution to the interval [−10100, 10100]. Such a truncated distribution
Cauchy_distribution
Block cipher
256bit Ciphers - CLEFIA Reference implementation and derived code Sony Introduces CLEFIA Implementation of 128-bit CLEFIA codec and hash function v t e
CLEFIA
wedges. Such a gradual reduction should follow a power-law function of the propagation distance, with the power-law exponent being equal or larger than two
Acoustic_black_hole_effect
Cryptography construction
similar operations, and both consist of iteratively running a function called a "round function" a fixed number of times. Many modern symmetric block ciphers
Feistel_cipher
Inverse of the gamma function
mathematics, the inverse gamma function Γ − 1 ( x ) {\displaystyle \Gamma ^{-1}(x)} is the inverse function of the gamma function. In other words, y = Γ − 1
Inverse_gamma_function
Block cipher
tweakable block cipher designed as part of the Skein hash function, an entry in the NIST hash function competition. Threefish uses no S-boxes or other table
Threefish
Logarithm to the base of the mathematical constant e
infinity. Nowadays, more formally, one can prove that the harmonic series truncated at N is close to the logarithm of N, when N is large, with the difference
Natural_logarithm
Cryptographic attack
compiler optimizations. Countermeasures include blinding and constant-time functions. Many cryptographic algorithms can be implemented (or masked by a proxy)
Timing_attack
Cryptographic algorithm
Arguably the most obvious way to arrange the ciphertext is to transmit the truncated penultimate block, followed by the full final block. This is not convenient
Ciphertext_stealing
Matrix of second derivatives
minor consisting of the truncated first 2 m + 1 {\displaystyle 2m+1} rows and columns, the next consisting of the truncated first 2 m + 2 {\displaystyle
Hessian_matrix
Family of authenticated ciphers
Ascon is a family of lightweight authenticated ciphers and hash functions that have been selected by the U.S. National Institute of Standards and Technology
Ascon_(cipher)
Block cipher
code omitted redundant parentheses, using C precedence to write the round function as e.g. v1 += (v0<<4 ^ v0>>5) + v0 ^ sum + k[sum>>11 & 3]; The recommended
XTEA
Study of mathematical algorithms for optimization problems
solutions. The function f is variously called an objective function, criterion function, loss function, cost function (minimization), utility function or fitness
Mathematical_optimization
Function related to statistics and probability theory
A likelihood function (often simply called the likelihood) gives the relative merit of various statistical models for describing a data set. Often the
Likelihood_function
Block cipher
elements S[4][256] // S-boxes: 4 arrays of 256 elements function f(x): // Calculates a function f on a 32-bit input x, using S-boxes and bit manipulation
Blowfish_(cipher)
of the Poisson distribution with an adjustable rate of decay. The zero-truncated Poisson distribution, for processes in which zero counts are not observed
List of probability distributions
List_of_probability_distributions
Block cipher
though all are Feistel ciphers, and make use of the same basic round function and operate on a 64-bit block. One of the earliest designs is now termed
FEAL
Standard for the encryption of electronic data
algebraic properties, the S-box is constructed by combining the inverse function with an invertible affine transformation. The S-box is also chosen to avoid
Advanced_Encryption_Standard
Statistical technique correcting sampling bias
correct bias from non-randomly selected samples or otherwise incidentally truncated dependent variables, a pervasive issue in quantitative social sciences
Heckman_correction
Nearest integers from a number
"integer part" is ambiguous, as it can also mean truncation towards zero, which differs from the floor function for negative numbers. For an integer n, ⌊n⌋
Floor_and_ceiling_functions
Statistical test comparing two probability distributions
the statistic whose weight function can be chosen to improve power. These methods are implemented in the KS2sample function of the KSgeneral package. Note
Kolmogorov–Smirnov_test
Effect in signal processing
simply truncate the sequence (effectively w [ N ] = 0 {\displaystyle w[N]=0} ), and compute an N {\displaystyle N} -length DFT. The truncated sequence
Spectral_leakage
Approximation of a function by a polynomial
polynomial. For a smooth function, the Taylor polynomial is the truncation at the order k {\textstyle k} of the Taylor series of the function. The first-order
Taylor's_theorem
Block cipher
block cipher is a truncated differential cryptanalysis of the full 16-round version. The paper claims that the probability of truncated differentials is
Twofish
Authenticated encryption mode for block ciphers
block size, and for any size of cryptographically strong pseudo-random function (since in both counter mode and CBC-MAC, the block cipher is only ever
CCM_mode
Cryptanalytic method for unauthorized users to access data
Cryptographic key length Distributed.net Hail Mary Cloud Key derivation function MD5CRK Metasploit Express Side-channel attack TWINKLE and TWIRL Unicity
Brute-force_attack
Indefinite integral
1}} and the series is truncated to 8 terms. Figure 2 shows the graph of an approximation to the antiderivative G(x), also truncated to 8 terms. On the other
Antiderivative
Method used in statistics, pattern recognition, and other fields
discriminant analysis (NDA), canonical variates analysis (CVA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method
Linear_discriminant_analysis
Expression of a function as an infinite sum of simpler functions
functions.[verification needed] There are several kinds of series expansions, listed below. A Taylor series is a power series based on a function's derivatives
Series_expansion
Concept in cryptography
cryptographic algorithms, typically block ciphers and cryptographic hash functions, wherein if an input is changed slightly (for example, flipping a single
Avalanche_effect
Term in statistical hypothesis testing
(the difference between the two distributions being a function of the effect size), the power of the test would be the probability, under H 1 {\displaystyle
Power_(statistics)
Software programming optimization technique
remembered'), usually truncated as memo in American English, and thus carries the meaning of 'turning [the results of] a function into something to be
Memoization
Signal (re-)construction algorithm
sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real numbers. The formula dates back to the works of
Whittaker–Shannon interpolation formula
Whittaker–Shannon_interpolation_formula
Correlation of a signal with a time-shifted copy of itself, as a function of shift
Wiener–Khinchin theorem relates the autocorrelation function R X X {\displaystyle \operatorname {R} _{XX}} to the power spectral density S X X {\displaystyle S_{XX}}
Autocorrelation
Describes approximate behavior of a function
error when truncating a power series and expresses the quality of approximation of a real or complex valued function by a simpler function. Often, big
Big_O_notation
Type of cipher
defined to be the inverse function of encryption, i.e., D = E−1. More formally, a block cipher is specified by an encryption function E K ( P ) := E ( K ,
Block_cipher
Condition in which the value of a measurement or observation is only partially known
probability of the censored data points as a function of the model parameters given a model, i.e. a function of CDF(s) instead of the density or probability
Censoring_(statistics)
Number of orderings allowing ties
reinterpreting the sequence as the coefficients of a power series and working with the function that results from summing this series can provide useful
Ordered_Bell_number
Chinese block cipher
X_{i+2}\oplus X_{i+3}\oplus rk_{i})} Where F {\displaystyle F} is a substitution function composed of a non-linear transform, the S-box and linear transform L {\displaystyle
SM4_(cipher)
Cryptographic algorithm
the new international standard for lightweight cryptographic methods. A truncated differential attack on 26 out of 31 rounds of PRESENT was suggested in
PRESENT
Early unclassified symmetric-key block cipher
exclusive-OR (XOR) operation. The F-function scrambles half a block together with some of the key. The output from the F-function is then combined with the other
Data_Encryption_Standard
General form of cryptanalysis applicable primarily to block ciphers
primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in information
Differential_cryptanalysis
Basic component of symmetric key algorithms
of confusion. Mathematically, an S-box is a nonlinear vectorial Boolean function. In general, an S-box takes some number of input bits, m, and transforms
S-box
Block cipher
when it was designed, but the availability of increasing computational power made brute-force attacks feasible. Triple DES provides a relatively simple
Triple_DES
Function computable with bounded loops
primitive recursive functions if we extend the set of initial functions with truncated subtraction x ∸ y. We get all primitive recursive functions if we additionally
Primitive_recursive_function
Cryptographic algorithm
standard. Another application is to build hash functions from block ciphers. See one-way compression function for descriptions of several such methods. Many
Symmetric-key_algorithm
How efficiently a source produces visible light
range of human visual sensitivity. Integral of truncated Planck function times photopic luminosity function times 683.002 lm/W. Omits the part of the spectrum
Luminous_efficacy
Hash function that is suitable for use in cryptography
A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with a fixed size of n {\displaystyle n}
Cryptographic_hash_function
Generalization of the one-dimensional normal distribution to higher dimensions
E(X_{2}\mid X_{2}<z)} and then using the properties of the expectation of a truncated normal distribution. To obtain the marginal distribution over a subset
Multivariate normal distribution
Multivariate_normal_distribution
Block cipher
implementation of BaseKing to such an attack. Joan Daemen (1994), Cipher and Hash Function Design: Strategies based on linear and differential cryptanalysis (Ph.D
BaseKing
Smooth function in statistics
the variance function is a smooth function that depicts the variance of a random quantity as a function of its mean. The variance function is a measure
Variance_function
Model for generating observable data in probability and statistics
{\displaystyle P(Y\mid X)} can also be interpreted as a (non-deterministic) target function f : X → Y {\displaystyle f\colon X\to Y} , considering X as inputs and
Generative_model
Partial correlation of a time series with its lagged values
In time series analysis, the partial autocorrelation function (PACF) gives the partial correlation of a stationary time series with its own lagged values
Partial autocorrelation function
Partial_autocorrelation_function
Authenticated encryption mode for block ciphers
attack Gröbner attack Linear (Piling-up lemma) Differential Impossible Truncated Higher-order Differential-linear Distinguishing (Known-key) Integral/Square
EAX_mode
Mathematical function for the probability a given outcome occurs in an experiment
often described by functions such as cumulative distribution functions, probability mass functions, or probability density functions. Which description
Probability_distribution
Class of statistical models
response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized
Generalized_linear_model
Covariance and correlation
processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as
Cross-correlation
Algorithm for generating pseudo-randomized numbers
power of 2, then c must be odd), so the value c=1 is commonly chosen. The sequence produced by other choices of c can be written as a simple function
Linear_congruential_generator
Soviet/Russian national standard block cipher
12-2015, specifies that it may be referred to as Magma. The GOST hash function is based on this cipher. The new standard also specifies a new 128-bit
GOST_(block_cipher)
Process of developing the AES standard
Competition – Competition to design authenticated encryption schemes NIST hash function competition Post-Quantum Cryptography Standardization "cryptology:: The
Advanced Encryption Standard process
Advanced_Encryption_Standard_process
Authenticated encryption mode with resistance against nonce reuse
integrity even if nonces are repeated. To accomplish this, encryption is a function of a nonce, the plaintext message, and optional additional associated data
AES-GCM-SIV
Cryptanalytic attacks using a system of multivariate equations
set of algebraic equations can be used to solve a cryptographic Boolean function that has a low degree or a high degree of non linearity. The main objective
Algebraic_attack
Distribution function associated with the empirical measure of a sample
an empirical distribution function (a.k.a. an empirical cumulative distribution function, eCDF) is the distribution function associated with the empirical
Empirical distribution function
Empirical_distribution_function
Probability distribution
sections of the density functions of different normal distributions and rescaling the density to integrate to one. The truncated normal distribution results
Normal_distribution
Wide-block cipher
in 2018 by Paul Crowley and Eric Biggers at Google specifically for low-powered mobile devices running Android Go. It has been included in the Linux kernel
Adiantum_(cipher)
Value that appears most often in a set of data
random variable, the mode is the value x at which the probability mass function P(X) takes its maximum value, i.e., x = argmaxxi P(X = xi). In other words
Mode_(statistics)
Implementations of Advanced Encryption Standard
provides developers with well known published block ciphers, one-way hash functions, chaining modes, pseudo-random number generators, public key cryptography
AES_implementations
Approximation for factorials
a coincidence between the resultant power series and the Taylor series expansion of the hyperbolic sine function. This approximation is good to more than
Stirling's_approximation
Adding data to a message prior to encryption to hide its length
Most modern cryptographic hash functions process messages in fixed-length blocks; all but the earliest hash functions include some sort of padding scheme
Padding_(cryptography)
Data transformation of statistics into rank
provides two ranking functions, the Rank.EQ function which assigns competition ranks in the case of ties, and the Rank.AVG function which assigns fractional
Ranking_(statistics)
Cryptographic hardware
attack Gröbner attack Linear (Piling-up lemma) Differential Impossible Truncated Higher-order Differential-linear Distinguishing (Known-key) Integral/Square
EFF_DES_cracker
Probabilistic problem-solving algorithm
with significant input uncertainties, e.g. risk assessments for nuclear power plants. Monte Carlo methods are often implemented using computer simulations
Monte_Carlo_method
Probability distribution
that X is greater than some number x, i.e., the survival function (also called tail function), is given by F ¯ ( x ) = Pr ( X > x ) = { ( x m x ) α x
Pareto_distribution
Length of bit string processed by a cipher
attack Gröbner attack Linear (Piling-up lemma) Differential Impossible Truncated Higher-order Differential-linear Distinguishing (Known-key) Integral/Square
Block_size_(cryptography)
Statistical transformation
(r),} where "ln" is the natural logarithm function and "artanh" is the inverse hyperbolic tangent function. If (X, Y) has a bivariate normal distribution
Fisher_transformation
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TRUNCATED POWER-FUNCTION
TRUNCATED POWER-FUNCTION
TRUNCATED POWER-FUNCTION
TRUNCATED POWER-FUNCTION
TRUNCATED POWER-FUNCTION
TRUNCATED POWER-FUNCTION
TRUNCATED POWER-FUNCTION
TRUNCATED POWER-FUNCTION
TRUNCATED POWER-FUNCTION
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