On the cycle structure of repeated exponentiation modulo a prime

DOI10.1016/j.jnt.2004.04.005zbMath1060.11059OpenAlexW2041524352MaRDI QIDQ1876236

Igor E. Shparlinski, Wun-Seng Chou

Publication date: 16 August 2004

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2004.04.005

zbMATH Keywords

primes in arithmetic progressionscycle structurerepeated powering

Mathematics Subject Classification ID

Rate of growth of arithmetic functions (11N56) Power residues, reciprocity (11A15)

Related Items (26)

Power maps in finite groups ⋮ Periodic points and tail lengths of split polynomial maps modulo primes ⋮ Cycle structure of iterating Rédei functions ⋮ A probabilistic heuristic for counting components of functional graphs of polynomials over finite fields ⋮ Functional graphs of families of quadratic polynomials ⋮ On the iterations of certain maps \(X \mapsto K \cdot(X + X^{- 1})\) over finite fields of odd characteristic ⋮ Functional graphs of polynomials over finite fields ⋮ Graphs associated with the map \(x\mapsto x+x^{-1}\) in finite fields of characteristic three and five ⋮ On a bijection between a finite group and cyclic group ⋮ On the power generator and its multivariate analogue ⋮ The Carlitz rank of permutations of finite fields: a survey ⋮ On the functional graph of \(f(X)=c(X^{q+1} + aX^2)\) over quadratic extensions of finite fields ⋮ The graph structure of Chebyshev polynomials over finite fields and applications ⋮ The functional graph of linear maps over finite fields and applications ⋮ Iteration entropy ⋮ The structure of isomorphic digraph from powers modulo \(p^e\) ⋮ On the cycle structure of permutation polynomials ⋮ Discriminants of simplest \(3^n\)-tic extensions ⋮ GRAPH COMPONENTS AND DYNAMICS OVER FINITE FIELDS ⋮ On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators ⋮ Connected components of the graph generated by power maps in prime finite fields ⋮ On the heuristic of approximating polynomials over finite fields by random mappings ⋮ The structure of digraphs associated with the congruence x k ≡ y (mod n) ⋮ Noncommutative algebraic dynamics: ergodic theory for profinite groups ⋮ Sequences of irreducible polynomials without prescribed coefficients over odd prime fields ⋮ A note on Low Order assumptions in RSA groups

Cites Work

• On the iteration of certain quadratic maps over GF(\(p\)).
• On zeros of Dirichlet's \(L\)-series
• Primes in progressions to prime-power modulus
• On the linear complexity profile of the power generator
• On the distribution of the power generator
• Period of the power generator and small values of Carmichael’s function
• A Simple Unpredictable Pseudo-Random Number Generator
• On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators
• Character sums with exponential functions
• Some doubly exponential sums over Z_m
• On the linear complexity of the power generator
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