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I have been reading about chaos-based cryptosystems. Every designer claims that his design is a secure system without much cryptographic analysis; however, it turns out that this is a false claim in many cases. I do not know if all these systems are weak or inefficient. I do not have the time to perform cryptanalysis on them all.

For the examples of the chaos-based cipher, almost every designer has his style without real proof of why he does this. They take the word "complex" as a synonym for "secure".

For guidelines that rarely is followed (if any, assuming that it is applicable or even sufficient, I can not judge): Some basic cryptographic requirements for chaos-based cryptosystems. Some Hints for the Design of Digital Chaos-Based Cryptosystems: Lessons Learned from Cryptanalysis. Lessons Learnt from the Cryptanalysis of Chaos-Based Ciphers. Framework for the analysis and design of encryption strategies based on discrete-time chaotic dynamical systems.

My question is:

How can I analyze these systems cryptographically? And what subjects in mathematics or computer science do I need?

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    $\begingroup$ Welcome to SE Crypto! Could you please provide the references that you have been reading? $\endgroup$
    – Patriot
    Aug 3 at 8:05
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    $\begingroup$ Not quite all chaos-based cipher are susceptible to cryptanalysis. And I don't think a single cryptanalytic strategy can work. There is too wide a spectrum of chaos-based constructions, starting with a dichotomy between (at least roughly) continuous (e.g. logisitic map) and discrete (e.g. rule 30). Plus not everyone will agree on what counts as a success in cryptanalysis: ciphertext-only ? known plaintext ? chosen plaintext ? side channel ? Perhaps, restrict the question... $\endgroup$
    – fgrieu
    Aug 3 at 8:35
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    $\begingroup$ @Theprince: Not susceptible to (known) cryptanalysis is not a sufficient criteria for mainstream cryptography. Symmetric ciphers are of interest to mainstream cryptography only when they have an advantage over established constructions, on the tune of: better performance on some common hardware, while having some level of demonstrable/arguable security. I don't know a chaos-based cipher that's efficient and not susceptible to cryptanalysis, much less one that's efficient and comes with some sound security argument. $\endgroup$
    – fgrieu
    Aug 3 at 9:28
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    $\begingroup$ The closest to practical use chaos-based crypto gets is in Physically Unclonable Functions (PUFs) which use the sensitive dependence on initial conditions of some parts of semiconductor manufacturing to produce chips that are impractical to duplicate or emulate. $\endgroup$ Aug 3 at 11:46
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    $\begingroup$ If I would do an educated guess: it's a "chaotic mathematical system" that is mainly useful in hardware to prevent cloning. The hardware is likely part of a finite precision computer. So no, I don't think you get that right. $\endgroup$
    – Maarten Bodewes
    Aug 3 at 23:07

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