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Method of bit-shuffling used to diffuse bits across S-box inputs
In cryptography, a permutation box (or P-box) is a method of bit-shuffling used to permute or transpose bits across S-boxes inputs, creating diffusion
Permutation_box
Cipher design construction
layers of substitution boxes (S-boxes) and permutation boxes (P-boxes) to produce the ciphertext block. The S-boxes and P-boxes transform (sub-)blocks
Substitution–permutation network
Substitution–permutation_network
mathematical permutations. Alternating permutation Circular shift Cyclic permutation Derangement Even and odd permutations—see Parity of a permutation Josephus
List_of_permutation_topics
Basic component of symmetric key algorithms
Boolean function Nothing-up-my-sleeve number Permutation box (P-box) Permutation cipher Rijndael S-box Substitution cipher Daemen & Rijmen 2013, p. 22
S-box
Topics referred to by the same term
P-box may refer to: permutation box probability box privacy box, used by the Winston Smith Project#P-Box project P. Box (band) This disambiguation page
P-box
Topics referred to by the same term
algorithms such as AES Permutation box, a cryptography method of bit shuffling used to permute or transpose bits across S-boxes Permutation (music), as a concept
Permutation_(disambiguation)
Type of cipher
depend on every input bit. A permutation box (P-box) is a permutation of all the bits: it takes the outputs of all the S-boxes of one round, permutes the
Block_cipher
Class of functions in cryptography
cryptography, a pseudorandom permutation (PRP) is a function that cannot be distinguished from a random permutation (that is, a permutation selected at random with
Pseudorandom_permutation
both the permutation groups and the matrix groups. The upper bound on the order of G given by |G| ≤ 2N shows that G is finite. The black box groups were
Black_box_group
Systematic classification of 12 related enumerative problems concerning two finite sets
one box, while requiring f {\displaystyle f} to be surjective means insisting that every box contain at least one ball. Counting modulo permutations of
Twelvefold_way
Group of symmetries of an n-dimensional hypercube
version of the symmetric groups, with their elements given by signed permutations. Algebraically, each hyperoctahedral group may be realized as a wreath
Hyperoctahedral_group
Exact statistical hypothesis test
A permutation test (also called re-randomization test or shuffle test) is an exact statistical hypothesis test. A permutation test involves two or more
Permutation_test
Data visualization
quartiles. In addition to the box on a box plot, there can be lines (which are called whiskers) extending from the box indicating variability outside
Box_plot
Mathematics problem
of the permutation. Every permutation can be decomposed into disjoint cycles, that is, cycles which have no common elements. The permutation of the first
100_prisoners_problem
Properties of the operation of a secure cipher
columns of the cipher. In substitution–permutation networks, diffusion is provided by permutation boxes (a.k.a. permutation layer). In the beginning of the 21st
Confusion_and_diffusion
Tables for the Data Encryption Standard
1 is always the most significant bit. This table specifies the input permutation on a 64-bit block. The meaning is as follows: the first bit of the output
DES_supplementary_material
Concept in combinatorics
The statistics of random permutations, such as the cycle structure of a random permutation, are of fundamental importance in the analysis of algorithms
Random_permutation_statistics
Cryptographic structure used in block ciphers
{\displaystyle x\mapsto \sigma (x)-x} are permutations (in the mathematical sense, that is, a bijection – not a permutation box). Since there are no orthomorphisms
Lai–Massey_scheme
Simple performance space with black walls
stage was not a traditional black box, the idea was still a revolutionary one. This venue, and two subsequent permutations, are known as the Playbox Theatre
Black_box_theater
Area of mathematics
irreducible representation can in fact be realized over the integers (every permutation acting by a matrix with integer entries); it can be explicitly constructed
Representation theory of the symmetric group
Representation_theory_of_the_symmetric_group
Block cipher
achieve quick diffusion. The permutation step swaps the positions of the words according to a constant pattern. Bit-level permutation is not achieved in this
Threefish
Cryptographic model of a random function
random permutation. In the ideal permutation model, an additional oracle access is given to the ideal permutation and its inverse. The ideal permutation model
Random_oracle
Logic-based number-placement puzzle
essentially different solutions, when symmetries such as rotation, reflection, permutation, and relabelling are taken into account, is much smaller, 5,472,730,538
Sudoku
Lock using symbols rather than a key
ISBN 978-1-58839-589-4. "Fragment of a box with a combination lock". Permutation padlock. Found in Google Books. [1] Improvement in permutation padlocks Google Books.[2]
Combination_lock
Discrete mathematics decomposition
known bijections between equivalence classes of rectangulations and permutation classes. In the following table p 1 {\displaystyle p_{1}} and p 2 {\displaystyle
Rectangulations
Block cipher
32-round substitution–permutation network operating on a block of four 32-bit words. Each round applies one of eight 4-bit to 4-bit S-boxes 32 times in parallel
Serpent_(cipher)
2009 box set by Graham Nash
3-CD box set by British singer-songwriter Graham Nash including solo material, highlights from groups including The Hollies and various permutations of
Reflections (Graham Nash album)
Reflections_(Graham_Nash_album)
Standard for the encryption of electronic data
attack, against AES-like permutations, which view two consecutive rounds of permutation as the application of a so-called Super-S-box. It works on the 8-round
Advanced_Encryption_Standard
Family of statistical methods based on sampling of available data
are: Permutation tests (also re-randomization tests) for generating counterfactual samples Bootstrapping Cross validation Jackknife Permutation tests
Resampling_(statistics)
Statistical test
The Ljung–Box test (named for Greta M. Ljung and George E. P. Box) is a type of statistical test of whether any of a group of autocorrelations of a time
Ljung–Box_test
Experimental designs for response surface methodology
In statistics, Box–Behnken designs are experimental designs for response surface methodology, devised by George E. P. Box and Donald Behnken in 1960, to
Box–Behnken_design
Early unclassified symmetric-key block cipher
S-boxes are rearranged according to a fixed permutation, the P-box. This is designed so that, after permutation, the bits from the output of each S-box
Data_Encryption_Standard
Block cipher
with the addition of a key-dependent bit permutation in the round function. The key-dependent bit permutation is implemented efficiently in software. The
ICE_(cipher)
Type of cipher
combines a sequence of simple transformations such as substitution (S-box), permutation (P-box), and modular arithmetic. The concept of product ciphers is due
Product_cipher
Sufficiently long sequences of numbers have long monotonic subsequences
any permutation of three numbers has an increasing subsequence of length three or a decreasing subsequence of length two. Among the six permutations of
Erdős–Szekeres_theorem
Measure of linear correlation
are a permutation of the set {1,...,n}. The permutation i′ is selected randomly, with equal probabilities placed on all n! possible permutations. This
Pearson correlation coefficient
Pearson_correlation_coefficient
Cryptography construction
the block cipher a pseudorandom permutation, while 4 rounds are sufficient to make it a "strong" pseudorandom permutation (which means that it remains pseudorandom
Feistel_cipher
Measure of statistical dispersion
used as a robust measure of scale. It can be clearly visualized by the box on a box plot. Unlike total range, the interquartile range has a breakdown point
Interquartile_range
Type of matrix factorization
multiplication and matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of
LU_decomposition
Study of mathematical groups by means of computers
theory include: the Schreier–Sims algorithm for finding the order of a permutation group the Todd–Coxeter algorithm and Knuth–Bendix algorithm for coset
Computational_group_theory
Cryptographic hash function
a pair of 512- or 1024-bit permutation functions P and Q, and is defined as: f(h, m) = P(h ⊕ m) ⊕ Q(m) ⊕ h The permutation functions P and Q are heavily
Grøstl
DC Studios film by James Gunn
perceived as old-fashioned by many? There have been so many different permutations of the character throughout the years, so how could you do it for a modern
Superman_(2025_film)
Intersection graph of trapezoids between parallel lines
a class of co-comparability graphs that contain interval graphs and permutation graphs as subclasses. A graph is a trapezoid graph if there exists a
Trapezoid_graph
3D combination puzzle
preceding figure is limited to permutations that can be reached solely by turning the sides of the cube. If the permutations reached through disassembly
Rubik's_Cube
Probabilistic problem-solving algorithm
approximate randomization and permutation tests. An approximate randomization test is based on a specified subset of all permutations (which entails potentially
Monte_Carlo_method
Algorithms to complete a sudoku
partial permutation of N. Let T = { X : X is a row, column, or block of Q }, so T has 27 elements. An arrangement is either a partial permutation or a permutation
Sudoku_solving_algorithms
transformed using an S-box. The tweak for each round is updated using h , ω {\displaystyle h,\omega } : h {\displaystyle h} is a cell permutation from MANTIS ([
QARMA
2016 film by Andrew Stanton
enduring parent-child bond, and the special embrace of family, in all its permutations", but added: "it is approached with such charm and warmth that it hardly
Finding_Dory
American mathematician (born 1969)
Berkeley Math Circle, and an expert in the combinatorial enumeration of permutations with forbidden patterns. Stankova was born in Ruse, Bulgaria (then the
Zvezdelina_Stankova
American singer and actor (1935–1977)
recordings reworked pop and country songs, but in markedly different permutations. His stylistic range now began to embrace a more contemporary rock sound
Elvis_Presley
Earliest civilian block ciphers
blocks. The cipher is a substitution–permutation network and uses two 4-bit S-boxes. The key selects which S-boxes are used. The patent describes the execution
Lucifer_(cipher)
Method of plotting numeric data
statistical graphic for comparing probability distributions. It is similar to a box plot, but has enhanced information with the addition of a rotated kernel
Violin_plot
Empirical law on the variance of species in a habitat
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Taylor's_law
2009 Film by Zack Snyder
2016. All DVD and Blu-ray editions of the three cuts come in various permutations, with varying quantities of extra features. Watchmen debuted at the top
Watchmen_(2009_film)
3D symmetry group
symmetric group or the group of permutations of four objects, since there is exactly one such symmetry for each permutation of the four diagonals of the
Octahedral_symmetry
2006 box set by David Crosby
3-CD box set by David Crosby. It features highlights from his career as a solo artist and with groups including The Byrds, various permutations of CSN&Y
Voyage_(David_Crosby_album)
2002 film by Steve Beck
the same old tired stuff we've seen a hundred times before in various permutations." Jamie Russell of the BBC awarded the film two out of five stars, but
Ghost_Ship_(2002_film)
Unit of information
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Data
Counting technique in combinatorics
example, there are 12 = 2(3!) permutations with property P1, 6 = 3! permutations with property P2 and no permutations have properties P3 or P4 as there
Inclusion–exclusion_principle
U.S. conscription procedure during the Vietnam War
prepared 78 random permutations of the numbers 1 to 366 using random numbers selected from published tables. From the 78 permutations, 25 were selected
Vietnam_War_draft
Experiment methodology
Academy. Archived from the original on 5 January 2015. Retrieved 22 July 2014. Box, Joan Fisher (1987). "Guinness, Gosset, Fisher, and Small Samples". Statistical
A/B_testing
1965 film directed by Sergio Leone
Dolores Martinez (25 May 2009). Remaking Kurosawa: Translations and Permutations in Global Cinema. Palgrave Macmillan US. pp. 206–. ISBN 978-0-230-62167-1
For_a_Few_Dollars_More
Block cipher
diffusion called raking, and a substitution step using the permutation tables as S-boxes. The shredding step can either permute all 8 bit-planes independently
BassOmatic
1983–1991 British musical collective
a band, but a unique collaboration of musicians recording in various permutations, the brainchild of 4AD kingpin Ivo Watts-Russell. The idea was to allow
This_Mortal_Coil
AI whose outputs can be understood by humans
estimates how important a feature is for the model. It is usually done using permutation importance, which measures the performance decrease when the feature
Explainable artificial intelligence
Explainable_artificial_intelligence
On packing congruent rectangular bricks (of any dimension) into larger rectangular boxes
a_{d}b_{d}} are a permutation of A 1 , A 2 , … , A d {\displaystyle A_{1},A_{2},\dots ,A_{d}} , the box is called a multiple of the brick. The box can then be
De_Bruijn's_theorem
Decryption of World War II cipher
Rejewski at the Polish General Staff's Cipher Bureau, using mathematical permutation group theory combined with French-supplied intelligence material obtained
Cryptanalysis_of_the_Enigma
Number taken as representative of a list of numbers
strictly increasing in each argument, and symmetric (invariant under permutation of the arguments). The average y is then the value that, when replacing
Average
Statistical property
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Standard_error
Mathematics of number-placement puzzle
C_{2}} act on two copies of that group, one for the row permutations and one for the column permutations. This is S 3 ≀ S 3 ≀ C 2 {\displaystyle S_{3}\wr S_{3}\wr
Mathematics_of_Sudoku
1988 film by Hayao Miyazaki
sequence was not storyboarded; "The sequence was determined through permutations and combinations determined by the time sheets. Each element was made
My_Neighbor_Totoro
Statistical hypothesis test
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Chi-squared_test
Complexity class
they are strongly related to cryptographic primitives such as one-way permutations and collision-resistant hash functions. PPP is the set of all function
PPP_(complexity)
Type of logic puzzle
consider, and by comparing them with entries that cross them, the proper permutation—or part of it—can be derived. The simplest example is where a 3-in-two
Kakuro
The permutations that achieve this are the Garnir elements. Suppose we want to eliminate a row descent from box ( x , y ) {\displaystyle (x,y)} to box (
Garnir_relations
2000 film directed by Ed Bye
public-humiliation and hating-your-parents gags, working through the most obvious permutations and a scatter of clever ones. Fans of Harry Enfield and Kathy Burke's
Kevin_&_Perry_Go_Large
Collection of statistical models
closely approximate the permutation test's p-values: The approximation is particularly close when the design is balanced. Such permutation tests characterize
Analysis_of_variance
System of phonetic notation
complex tones, one may combine three or four tone diacritics in any permutation. Chao tone letters are required for finer detail (e˧˥˧, e˩˨˩, e˦˩˧, e˨˩˦
International Phonetic Alphabet
International_Phonetic_Alphabet
Middle quantile of a data set or probability distribution
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Median
Study of health and disease within a population
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Epidemiology
Range to estimate an unknown parameter
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Confidence_interval
Numerical measure of a statistical relationship between variables
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Correlation_coefficient
Statistical measure of how far values spread from their average
variants known. Other tests of the equality of variances include the Box test, the Box–Anderson test and the Moses test. Resampling methods, which include
Variance
Form of cryptanalysis
substitution–permutation network, analysis is concentrated primarily on the S-boxes, the only nonlinear part of the cipher (i.e. the operation of an S-box cannot
Linear_cryptanalysis
Selection of data points in statistics
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Sampling_(statistics)
Study of collection and analysis of data
popularity of computationally intensive methods based on resampling, such as permutation tests and the bootstrap, while techniques such as Gibbs sampling have
Statistics
2007 film by Robert Benton
Feast of Love by Charles Baxter. The movie deals with love and its many permutations, set within a community of friends in Portland, Oregon. Harry Stevenson
Feast_of_Love
Cryptologic device
Bureau's German section (BS-4), to catalog the cycle structure of Enigma permutations, thereby facilitating the decryption of German Enigma ciphertext. With
Cyclometer
English art rock band
four members contributed to songwriting, working together in various permutations. Godley and Creme’s songwriting has been said to be inspired by art and
10cc
Algorithm that arranges lists in order
previous element, according to the required order). The output is a permutation (a reordering, yet retaining all of the original elements) of the input
Sorting_algorithm
Set of statistical processes for estimating the relationships among variables
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Regression_analysis
Block diagonal matrix of Jordan blocks
( K ) {\displaystyle \mathbb {M} _{n}(K)} , which is unique up to a permutation of its diagonal blocks themselves. J is called the Jordan normal form
Jordan_matrix
Block cypher operating mode
prewhitening key, apply a publicly known unkeyed permutation (in practice, a pseudorandom permutation) to the result, and then XOR a postwhitening key
Xor–encrypt–xor
Method of data analysis
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Principal_component_analysis
Numbers obtained by adding the two previous ones
Repdigit Repunit Self-descriptive Smarandache–Wellin Undulating Digit-permutation related Cyclic Digit-reassembly Parasitic Primeval Transposable Divisor-related
Fibonacci_sequence
Australian science fiction author and mathematician
Angle (1983), ISBN 0-909106-12-6 Quarantine (1992), ISBN 0-7126-9870-1 Permutation City (1994), ISBN 1-85798-174-X Distress (1995), ISBN 1-85798-286-X Diaspora
Greg_Egan
Fundamental theorem in probability theory and statistics
Jackknife Testing hypotheses 1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood-ratio
Central_limit_theorem
Mathematical function generalizing the determinant and permanent
{\displaystyle \operatorname {sgn} } , of Sn, defined by the parity of a permutation. The permanent is the case where χ λ {\displaystyle \chi _{\lambda }}
Immanant
2004 film by Mamoru Oshii
"Anatomy of Permutational Desire: Perversion in Hans Bellmer and Oshii Mamoru", Mechademia 5 (2010), 285–309 Monnet, Livia, "Anatomy of Permutational Desire
Ghost in the Shell 2: Innocence
Ghost_in_the_Shell_2:_Innocence
preserving transformations: row permutations within a band, column permutations within a stack, band permutations, stack permutations, and "reflection, transposition
Glossary_of_Sudoku
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