2019/03/07 by Antonino Leonardis, Leonardis, Antonino
Computer Science · Mathematics · #13A18 11Y65 11Y40 68W20 #Chaos-based Image/Signal Encryption #Computability, Logic, AI Algorithms #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1903.03200
openalex publication_date 2019/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper continues the author's previous studies on continued fractions and\nHeron's algorithm, as from his former JMM2017 presentation (see\n citeCF.HA). par medskip Extending the notion of continued fraction to the\np-adic fields, one can find continued fractions which converge in both real\nand p-adic topologies to the `same' quadratic irrational number, some of\nwhich are given by the Heron's algorithm using a generalized version of an\nauthor's theorem from the cited JMM presentation. The definition can be\npossibly generalized to other global fields, as left as an open question. We\nwill end the part on hybrid convergence with many numerical examples. After\nthat, we will recall the basic algorithms on the p-adic fields studied by the\nauthor and see some applications of theirs to computer science: applying\nHeron's algorithm to quickly compute p-adic square roots, finding new\nelementary cryptography procedures and some methods to get pseudo-random\nnumbers, calculate last digits of some peculiar very big numbers.\n