# Help in understanding how to apply nonlinear function in hashing

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 page 3 $S^t = (u^t + 2S^{t-1} + t) mod 256$ 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

• I can't tell what your question is. It seems to require a huge amount of background reading followed by a request for help with brainstorming. On this site, we're looking for clear questions with definite answers, not invitations to discussion. – David Richerby Jun 11 '16 at 10:43

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.

• Thank you for your reply. My primary Question was that how can I apply chaos as hash function in hashing for retrieving documents using nearest neighbor search? If chaos cryptography can use chaotic maps, then I was wondering how to apply it to other methods. Can you please suggest any idea that you may think can be some way? I can then check how good a hash function it is later but as of yet I cannot devise any way on applying chaos in hashing for similarity search. – SKM Jun 12 '16 at 17:20
• @SKM, I know that was your question, but I'm telling you that the answer is: you shouldn't. Chaotic maps yield inferior hash functions (slower, or mix less well), compared to the best existing schemes. So, don't use chaos. Use standard hash functions -- they're better than anything we know how to build using chaotic maps. You're asking "I have this sledgehammer; how can I use it to drive in this screw?" and I'm telling you "don't; use a screwdriver". – D.W. Jun 12 '16 at 23:40