Can somebody help in brainstorming how to apply the map as a hashing function?I am aware that chaos is used in cryptography but I fail to understand how to apply it. Most popular hashing techniques is the modulo hash function Why is it best to use a prime number as a mod in a hashing function?A modulo chaotic function that comes to my mind  is the Dyadic map $\theta = 2 \theta mod 1$.  Not getting into the details of collision resolution and other technicalities, it shall be of immense help if the application of chaos map is shown in generating hash codes. Chaos based cryptography link to paper shows that the equation on page3 $S^t = (u^t + 2S^{t-1} + t) mod 256$ is the hashing function for cryptography. $t$ are the number of sub-blocks of the message (plaintext) and $u_0$ is the decimal value of the first block of the message.  Please help! Thank you
Help in understanding how to apply nonlinear function in hashing
mathematical foundations;hashing
Cryptographers have studied various schemes for using chaos theory to try to construct cryptographic primitives (hash functions, encryption algorithms, etc.).  None of them have been successful.  Chaos simply does not seem useful for designing cryptographic algorithms.First, many of the chaos-based schemes have been broken.  They didn't have as much nonlinearity as the designers anticiapted.Second, the chaos-based schemes are slower than the state of the art.  You need to iterate many times to get reasonable mixing/nonlinearity.  By the time you do that, you end up with something quite slow.  In comparison, we know of alternative schemes for hashing and encryption that are very fast and appear to be very secure.  So, chaos-based schemes are simply not competitive.In my opinion, chaotic maps do not appear to be a promising angle for hashing or other cryptographic algorithms.