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Inversive congruential generator information


Inversive congruential generators are a type of nonlinear congruential pseudorandom number generator, which use the modular multiplicative inverse (if it exists) to generate the next number in a sequence. The standard formula for an inversive congruential generator, modulo some prime q is:

Such a generator is denoted symbolically as ICG(q, a, c, seed) and is said to be an ICG with parameters q, a, c and seed seed.

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Inversive congruential generator

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Inversive congruential generators are a type of nonlinear congruential pseudorandom number generator, which use the modular multiplicative inverse (if...

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Linear congruential generator

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used for variants of LCG and LFSR generators Permuted congruential generator Full cycle Inversive congruential generator Multiply-with-carry Lehmer RNG (sometimes...

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Modular multiplicative inverse

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multiplicative inverse figures prominently in the definition of the Kloosterman sum. Inversive congruential generator – a pseudo-random number generator that uses...

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Generalized inversive congruential pseudorandom numbers

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to nonlinear congruential methods of generating uniform pseudorandom numbers in the interval [0,1) is the Inversive congruential generator with prime modulus...

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List of random number generators

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Eichenauer, Jürgen; Lehn, Jürgen (1986). "A nonlinear congruential pseudorandom number generator". Statistische Hefte. 27: 315–326. doi:10.1007/BF02932576...

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Pseudorandom number generator

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number generators. In the second half of the 20th century, the standard class of algorithms used for PRNGs comprised linear congruential generators. The...

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ICG

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Crisis Group, a non-profit organisation Internet Capital Group Inversive congruential generator Intra-character gap (or inter-character gap) in American Morse...

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Inversive geometry

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In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines...

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Bruce Saran

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Chester County Eye Care where he performs angiography with the inversive congruential generator, ultrasound and tomography to treat conditions such as macular...

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Affine cipher

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linear congruential generators, a type of pseudorandom number generator. This generator is not a cryptographically secure pseudorandom number generator for...

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Isometry

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In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed...

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Multiplicative group of integers modulo n

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Prime number

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Prime numbers are also used in pseudorandom number generators including linear congruential generators and the Mersenne Twister. Prime numbers are of central...

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Gaussian integer

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the same ideal. As all the generators of an ideal have the same norm, the norm of an ideal is the norm of any of its generators. In some circumstances, it...

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Reduction

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row space Reduced word, in a free group, a word with no adjacent generator-inverse pairs Variance reduction, a procedure used to increase the precision...

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List of named matrices

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matrices; these matrices are one notable representation of the infinitesimal generators of the special unitary group SU(3). Hamiltonian matrix — a matrix used...

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Main conjecture of Iwasawa theory

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Natural number

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commutative monoid with identity element 0. It is a free monoid on one generator. This commutative monoid satisfies the cancellation property, so it can...

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Affine symmetric group

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at positions not congruent to i or j modulo n. In the geometric action of S ~ n {\displaystyle {\widetilde {S}}_{n}} , the generator s i {\displaystyle...

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Rolling hash

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modulus n {\displaystyle n} is typically a prime number. See linear congruential generator for more discussion. Removing and adding characters simply involves...

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Universal hashing

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{\displaystyle a\neq 0} . (This is a single iteration of a linear congruential generator.) To see that H = { h a , b } {\displaystyle H=\{h_{a,b}\}} is a...

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varying statistical quality): ACORN generator Blum Blum Shub Lagged Fibonacci generator Linear congruential generator Mersenne Twister Coloring algorithm:...

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Lemniscate elliptic functions

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{\displaystyle \delta _{\beta }} is any β {\displaystyle \beta } -torsion generator (i.e. δ β ∈ ( 1 / β ) L {\displaystyle \delta _{\beta }\in (1/\beta )L}...

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Torus

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