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I will venture myself into studying chaotic cryptography. However, I find it hard to explain what chaotic cryptography entails to those that have some knowledge of cryptography. Neither can I explain it - at a more basic level - to those that don't know what cryptography is.

Can you help me explain chaotic cryptography to others?

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    $\begingroup$ I've edited your post substantially, hopefully making it easier to read. However, if you think too much of the original intent has been removed, don't hesitate to roll it back (by looking at the revision history). $\endgroup$
    – Maarten Bodewes ♦
    Commented Dec 10, 2018 at 0:47
  • $\begingroup$ there are some references on the wikipedia page (en.wikipedia.org/wiki/Chaotic_cryptology). have you already skimmed some of them? $\endgroup$
    – ddddavidee
    Commented Dec 10, 2018 at 8:17

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  1. Explain the problem that the solution of "chaotic cryptography" is intended to solve
    • You have the question tagged with encryption, cryptanalysis, and symmetric. So it sounds like it is a method of symmetric encryption.
  2. Explain why other pre-existing solutions are unsatisfactory
    • e.g. they're slow, not provably secure, not well understood, etc
      • Make sure these points are actually true and supported by references
  3. Explain the algorithm and how it is an improvement or why it is a better solution than previously listed solutions

Explaining the algorithm may be lost on people who have no experience with cryptography, especially if they have no experience with math or algorithms in general. But the guts of what the algorithm does is not always as useful as what the algorithm accomplishes.

Note

I was going to leave this as a surprise to the user who asked the question, but it has been noted that the answer should state so explicitly:

Attempting to pursue this strategy with "chaotic cryptography" is going to fail at step 2 and step 3.

This is not because the strategy is insufficient, it is because there are no good reasons to pursue "chaotic cryptography".

Currently employed symmetric encryption algorithms are efficient, provide provable resistance to known attacks, are well understood, and importantly are standardized for public use.

To quote Geoffroy Couteau:

There have been almost no (if any) serious work on chaotic crypto providing any tool to base its security on clear and well-defined fundamental problems which resist cryptanalytic attempts. Today's chaotic crypto is at best a buzzword variant of the security-by-obscurity approach to crypto, which consists into thinking that "well, if we do many complicated stuff, that's probably hard to invert".

"Chaotic cryptography" is frequently coupled with "image encryption", and the latter demonstrates lack of understanding of basic principles of information theory and programming: There are no special requirements when encrypting images as opposed to any other types of information. Symmetric ciphers simply operate on bits.

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    $\begingroup$ Also, it might be worth mentioning at this stage that chaotic cryptography is not considered to be a better solution than state-of-the-art cryptography by any reasonable expert. There have been almost no (if any) serious work on chaotic crypto providing any tool to base its security on clear and well-defined fundamental problems which resist cryptanalytic attempts. Today's chaotic crypto is at best a buzzword variant of the security-by-obscurity approach to crypto, which consists into thinking that "well, if we do many complicated stuff, that's probably hard to invert". $\endgroup$
    – Geoffroy Couteau
    Commented Dec 10, 2018 at 10:11
  • $\begingroup$ @GeoffroyCouteau I was expecting OP to encounter figure that out when trying to go through the outlined process :) $\endgroup$
    – Ella Rose
    Commented Dec 10, 2018 at 17:48
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    $\begingroup$ That sounds like a good approach for teaching purpose, but it might be a bit optimistic in general to expect people without a lot of background in crypto to arrive at such opinions by themselves :) Often, observing that there exists a Wikipedia page on the subject (listing a few dozen papers), and that Google returns many results, will make people assume that this sounds like a serious line of work from at least the viewpoint of "some experts". Even cryptographers will usually make up their opinion mainly by observing that no work on chaos crypto was ever published in a serious conference. $\endgroup$
    – Geoffroy Couteau
    Commented Dec 10, 2018 at 17:56
  • $\begingroup$ @GeoffroyCouteau I suspect that lack of rigour so far is that the art is at a pre natal stage. A chaotic map (or Chua or fractal) is fundamentally no different to the chaotic intersections on an elliptic curve. It takes (IMHO) a ridiculous degree of shoehorning to quantize the EC analogue form into something remotely useful for crypto. It just needs development. There is certainly interest judging by the number of papers and the length of debate in Daniel's question. Don't understand the images thing though... $\endgroup$
    – Paul Uszak
    Commented Dec 10, 2018 at 21:47
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    $\begingroup$ @PaulUszak I do not intend to have a long debate on the subject; I'm simply formulating an educated opinion, as a cryptographer who saw (and sometimes reviewed) papers on the subject. Many exotic approaches to crypto are in more or less in their infancy, yet they still make up to good conferences if there is a proper cryptographic approach to their potential use for protecting data. This has until now never been the case for chaotic crypto. I'm not claiming it will never lead to anything secure, I'm claiming the current state of research does not provide any positive indication in this regard. $\endgroup$
    – Geoffroy Couteau
    Commented Dec 10, 2018 at 22:53

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