Collision resistant Hash function in chaos cryptography

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.

• Cryptography specific questions are often a better fit for crypto.stackexchange.com.
– orlp
Mar 29 '17 at 15:37