COUNTING FIXED POINTS, TWO-CYCLES, AND COLLISIONS OF THE DISCRETE EXPONENTIAL FUNCTION USING p-ADIC METHODS

DOI10.1017/S1446788712000262zbMath1278.11005arXiv1105.5346MaRDI QIDQ4899948

Margaret M. Robinson, Joshua Brandon Holden

Publication date: 10 January 2013

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.5346

zbMATH Keywords

fixed pointsp-adic interpolationcollisionsdiscrete logarithmHensel's lemmatwo-cyclesBrizolisdiscrete exponential

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Congruences; primitive roots; residue systems (11A07) Algebraic number theory: local fields (11S99)

Related Items (3)

Statistics for fixed points of the self-power map ⋮ Soficity, short cycles, and the Higman group ⋮ Counting fixed points and rooted closed walks of the singular map \(x \mapsto x^{x^n}\) modulo powers of a prime

Cites Work

• Short cycles in repeated exponentiation modulo a prime
• Fixed Points for Discrete Logarithms
• On the number of solutions of exponential congruences
• Some heuristics and results for small cycles of the discrete logarithm
• Unsolved problems in number theory

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