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I know this sounds too broad. But I noticed that there was a chapter on chaotic crypto in the recent Handbook of Information and Communication Security Editors: Stavroulakis, Peter, Stamp, Mark (Eds.) by Springer. Sorry about the paywall, the text has all the usual chapters you'd expect, in addition to chaotic encryption.

http://www.springer.com/gp/book/9783642041167

Here's a synopsis of the chapter actually entitled "chaos-based information security" authored by Jerzy Pejaś and Adrian Skrobek

  • 6.1 Chaos Versus Cryptography
  • 6.2 Paradigms to Design Chaos-Based Cryptosystems
  • 6.3 Analog Chaos-BasedCryptosystems
  • 6.3.1 Additive ChaosMasking
  • 6.3.2 Chaotic Switching
  • 6.3.3 ParameterModulation
  • 6.3.4 HybridMessage-Embedding
  • 6.4 DigitalChaos-BasedCryptosystems
  • 6.4.1 State of the Art
  • 6.4.2 Notes About the Key
  • 6.5 Introduction to ChaosTheory
  • 6.5.1 Basic Information for Dynamic Systems
  • 6.5.2 Some Examples of ChaoticMaps
  • 6.5.3 Applying Chaotic Systems to the Environment of Finite-Precision Computations
  • 6.6 Chaos-Based Stream Ciphers
  • 6.6.1 A Model of Chaos-Based Stream Cipher
  • 6.6.2 Analysis of Selected Chaos-Based Stream Ciphers
  • 6.7 Chaos-Based Block Ciphers
  • 6.7.1 A Model of a Chaos-Based Block Cipher
  • 6.7.2 Discretization of Chaotic Maps to Invertible Maps
  • 6.7.3 Analysis of Selected Chaos-Based Block Ciphers
  • 6.8 Conclusions and Further Reading

Does anyone here have any opinions on why/why not chaotic encryption is secure?

Why anyone would bother, given the hoops one seems forced to jump thrugh to get it working on finite precision systems, unlike finite field and number theory based classical cryptosystems?

FWIW, some of the other chapters are authored by recognised names in the traditional cryptography community.

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    $\begingroup$ Count me as fully open to the idea that a chaos-based cryptosystem can be made secure, but highly skeptical that it has any advantage over established cryptosystems. $\endgroup$
    – fgrieu-onstrike ♦
    Apr 17, 2015 at 22:29
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    $\begingroup$ The proof of the pudding is in the eating, and the proof of the cryptosystem is in the cryptanalysis. Until I see a chaos-based system undergo cryptanalysis by someone who knows what they're doing, I don't see any reason to trust it. $\endgroup$
    – poncho
    Apr 18, 2015 at 3:19
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    $\begingroup$ I located a review with a section about that chapter. It really is an overview, and totally non-committing. $\endgroup$
    – fgrieu-onstrike ♦
    Apr 18, 2015 at 5:59
  • $\begingroup$ @fgrieu,@poncho:thanks for the comments, it matches my intuitions about the topic. $\endgroup$
    – kodlu
    Apr 18, 2015 at 6:20

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