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In my earlier Question asked here Help in understanding how to apply nonlinear function in hashing about chaos cryptography, since then I have come across several research papers that apply atleat theoretically chaos based cryptography. It is still an active area of research with advantages and disadvantages.

How can I prove that the has collision is minimum or collision resistance for any chaos function used for chaos based cryptography, where the chaos map is the hash function?

An algorithm to achieve cryptography hashing is the chaos based cryptographic hash function which indexes all items in hash tables and searches for near items via hash table lookup. The hash

table is a data structure that is composed of buckets, each of which is indexed by a hash code.

Two hash codes for two different messages can collide if they have the same hash code. This is often called the Birthday paradox.

The properties of a good hash function is that there should be no hash collision. This property also holds for Locality sensitive hashing where a hash function is used to search for the approximate nearest neighbor.

How can I proof this statement for chaos based hashing in cryptography? If the hashing function is a chaotic map, $f()$, then how to show the expression of collision probability? Please help.

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  • $\begingroup$ Cryptography specific questions are often a better fit for crypto.stackexchange.com. $\endgroup$ – orlp Mar 29 '17 at 15:37
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Chaos-based encryption ain't an active area of research among the best crypto researchers; it's looking like a dead end. You might find papers published on the topic, but they're generally in lower-reputation conferences. Why is it a dead end? Because it doesn't seem to work. The schemes typically end up being either insecure, or worse than existing algorithms (e.g., slower). Basically, it initially sounded like an intriguing idea, but at this point I would advise you that studying chaos-based cryptography appears to be a waste of your time, if you want to accomplish something useful or practical. (See also https://security.stackexchange.com/q/31000/971, though it doesn't really address this point.)

You can't prove collision-resistance. Even the state-of-the-art hash functions don't come with a mathematical proof of collision-resistance. See https://crypto.stackexchange.com/q/18730/351 and https://crypto.stackexchange.com/q/26094/351 and https://security.stackexchange.com/q/5101/971.

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  • $\begingroup$ I had asked here math.stackexchange.com/questions/2206095/… on how to calculate the hash collision probability. Is the formula applicable to any hash function, be it chaotic or non-chaotic? How would the expression change for chaos hash function. For educational purposes, this is important to understand how the sensitivity to initial condition plays a role in hash collision resistance.\ $\endgroup$ – SKM Mar 29 '17 at 17:19
  • $\begingroup$ @SKM, cryptographic hashes (e.g., SHA256) aren't a function family; they are a single function, so those kinds of calculations aren't relevant for cryptographic hash functions. I suspect you might enjoy some self-study with a few good cryptography textbooks or lecture notes! $\endgroup$ – D.W. Mar 29 '17 at 17:20

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