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I am trying to create an encryption algorithm for educational purpose. Where I use Henon map to encrypt a message. In the Wikipedia section I got, "The map depends on two parameters, $a$ and $b$, which for the classical Hénon map have values of $a = 1.4$ and $b = 0.3$"

And I use that value, which seems OK. But is there any range where the chaotic nature hold? How to predict the range?

Another question is, how to pick initial guess $(x_0,y_0)$ for that map? Is there any dependency between their initial guess with the values of $a,b$? I am asking because some of random initial guess give me OverflowError in python code. One more thing, how to check sensitivity of Henon map for a small change in key $(a,b)$ or $(x_0,y_0)$?

WhyMeasureTheory
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  • For choosing starting points whose orbits remain bounded, use a trapping region. See https://math.stackexchange.com/questions/4063271/finding-a-trapping-region-for-the-hénon-map – lhf Oct 14 '21 at 21:12
  • Thanks for the link, @lhf. But those seem heavy mathematics for me now. I need an answer which is accessible for beginner, like only mention the range explicitly with some insight. Thanks again. – WhyMeasureTheory Oct 15 '21 at 12:14

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