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What factor is preventing cryptography based on chaos theory from being of practical use? Is it because of the unpredictability of the system?

Fathima Abdur Rahman
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  • Pretty much all blockciphers are chaotic. – CodesInChaos Jun 06 '18 at 20:11
  • Confusion and diffusion? – Fathima Abdur Rahman Jun 06 '18 at 20:12
  • https://stackoverflow.com/questions/1216002/fractal-encryption – Paul Uszak Jun 06 '18 at 20:45
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    What would ‘cryptography based on chaos theory’ be, if all cryptography in widespread use does not qualify? – Squeamish Ossifrage Jun 06 '18 at 21:20
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    What makes it practical to use? What makes it secure? What makes it better than alternatives? What are we even talking about? – Future Security Jun 06 '18 at 21:31
  • @forest Well if you say so - crypto isn't my strong suite. But. I look at something like a Lorenz system and see similarities with traverses around an elliptic curve. I look at the computational effort in getting from the left hand side to the right hand side of a Julia set and I see a hard problem. Might these be put to use? There was a recent answer about a Lorenz based CSPRNG, and these make good TRNGs. Remember ECC was just invented out of the blue and needs huge mathematical shoehorning to get it to even work. Perhaps I've just had too much coffee/gin. – Paul Uszak Jun 07 '18 at 11:41
  • I don't understand why data encrypted using Mandlebrot set drawings is quantum-safe. (Just curious) – Fathima Abdur Rahman Jun 07 '18 at 11:49

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All chaotic crypto papers I have seen lack rigorous security analysis, their main shortcoming being that there is no understood mathematical machinery of the type used in non-chaotic crypto such as:

  • low differential probability
  • low linear bias
  • guaranteed period, window, nonlinearity properties

Also, most chaotic systems are continuous, need infinite precision real numbers to represent, so since sampling/quantization will be needed, some of the properties of chaos may be lost.

Most chaotic crypto papers appear in the general physics/engineering literature, and are not even seen by most crypto researchers.

So, why would anyone use them when there are well understood techniques with long history of resisting cryptanalysis. The chaotic crypto authors display computational evidence (equidistribution only, in most cases) and quit.

If they dont properly cryptanalyze their designs no one else will. However, typical chaotic systems are almost impossible to analyze theoretically, their state trajectories are uncontrollable, by definition.

kodlu
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Kodlu's answer succinctly addresses the practical challenge with digital systems, but a form of chaotic cryptography is used in analog. Chaotic oscillators are used to encrypt analog video streams, ie: http://www.dtic.mil/get-tr-doc/pdf?AD=ADA503411 Unfortunately, most of the papers are paywalled; however, the fundamental mathematics are based on reductions of Chua's Circuit.

I've seen the results and the pictures are grainy, but the brain can figure it out. Also, I know that these techniques have been used to retrofit old analog modems, but I've never seen one in practice.

b degnan
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