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Is there any secure cryptographic hash function based on the logistic map?

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    $\begingroup$ Unlikely—there's very little, if anything, in cryptography that's inspired by chaotic behavior in continuous systems. $\endgroup$ – Squeamish Ossifrage May 17 at 1:43
  • $\begingroup$ I found some papers stating things like "Utilizing chaos to construct hash function is a promising direction which attracts more and more attention." Isn't that true? link.springer.com/chapter/10.1007/978-3-642-20542-2_5 pdfs.semanticscholar.org/94c2/… $\endgroup$ – LinusK May 17 at 13:10
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    $\begingroup$ It's not promising. It gets so much unwarranted attention and it is so bad that we joke about it. But we really wish it wasn't that way. It's a viral idea and it keeps getting reinvented. Academics (usually people who study something in a different field) that promote it likely haven't put significant effort into studying modern cryptography. To use an analogy: These are not chemists, they're members of a school alchemy club. And they don't even realize it because they're not humble enough to consider that there is a huge legitimate body of collective knowledge to base ideas off of. $\endgroup$ – Future Security May 17 at 14:02
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    $\begingroup$ @LinusK This is not a serious cryptography paper, and the journal is a paper mill publishing scam to harvest money from aspiring academics in developing countries. $\endgroup$ – Squeamish Ossifrage May 17 at 14:10
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A brief description of such functions can be found in chapter 9.3 of the paper “Cryptographic Hash Functions: Recent Design Trends and Security Notions” (eprint.iacr.org/2011/565). The following excerpt is taken from page 29 of the paper:

Hash functions based on chaos theory use chaotic maps, which are functions that exhibit particular chaotic behaviours; examples of these maps include: logistic map [source #75], tent map [source #120], and cat map [source #42]. Unfortunately, most chaos-based hash functions suffer from poor efficiency due to their inherent complex structure, which makes them unattractive as a practical approach for building hash functions.

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