On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators
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Publication:3584787
DOI10.1090/S0025-5718-09-02271-6zbMath1227.11093arXiv0902.3884OpenAlexW3099946464MaRDI QIDQ3584787
Alina Ostafe, Igor E. Shparlinski
Publication date: 30 August 2010
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0902.3884
Exponential sums (11T23) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Pseudo-random numbers; Monte Carlo methods (11K45)
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Cites Work
- Unnamed Item
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- Sequences, discrepancies and applications
- The Laurent phenomenon
- Exponential sums with Dickson polynomials
- On a problem of Arnold on uniform distribution
- Variation of periods modulo \(p\) in arithmetic dynamics
- Inferring sequences produced by a linear congruential generator on elliptic curves missing high-order bits
- Lattice reduction: a toolbox for the cryptoanalyst
- Heights of polynomials and entropy in algebraic dynamics
- Fermat-Euler dynamical systems and the statistics of arithmetics of geometric progressions
- On the iteration of certain quadratic maps over GF(\(p\)).
- Number-theoretical turbulence in Fermat-Euler arithmetics and large Young diagrams geometry statistics
- On the average distribution of inversive pseudorandom numbers
- On the cycle structure of repeated exponentiation modulo a prime
- On the distribution and lattice structure of nonlinear congruential pseudorandom numbers
- On some dynamical systems in finite fields and residue rings
- Exponential sums of nonlinear congruential pseudorandom number generators with Rédei functions
- Exponential sums for nonlinear recurring sequences
- On the distribution of inversive congruential pseudorandom numbers in parts of the period
- On the distribution of the power generator
- Period of the power generator and small values of Carmichael’s function
- The density of prime divisors in the arithmetic dynamics of quadratic polynomials
- Attacking the Pollard Generator
- Reconstructing Truncated Integer Variables Satisfying Linear Congruences
- How to predict congruential generators
- Quasi-Monte Carlo methods and pseudo-random numbers
- Sur la dynamique arithmétique des automorphismes de l’espace affine
- The dynamics of linearized polynomials
- Mordell’s exponential sum estimate revisited
- Predicting nonlinear pseudorandom number generators
- Character sums with exponential functions
- The iterated Carmichael λ-function and the number of cycles of the power generator
- Cryptography and Coding
- Information Security and Privacy
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