If you are trying to make a new cryptographic function for cryptocurrency technologies, you should first see if there is already a cryptographic function out there that suits your needs. If you can find one (you probably can), then that would be great. If you can't find one, then I hope that you are or can find a cryptographic professional to help design the cryptographic function for you. If you can't do that, then you will need to have a very good reason to put your cryptographic function in production code since there may be security risks.
Now with that caution notice out of the way, I must admit that I personally have developed my own cryptographic algorithm and put it into an actual cryptocurrency. I have a Ph.D. in Mathematics, but I did not specialize in cryptography during the Ph.D. program. I am not recommending for others to do what I have done. I am still doing mathematical research to test the cryptographic security of this mining algorithm, and I will like to share some techniques that I have developed for evaluating the security of mining algorithms.
My mining algorithm is actually based on an encryption function where the round function has a 32 bit long message size and a 1 bit long round key size. This means that my encryption function is extremely small and simple compared to most other cryptographic functions. On one hand, the simplicity of my mining algorithm may make it easier to attack. But then again, my mining algorithm only requires 16 bits of security. In other words, in order to break my algorithm, you will need to find a near fixed point for the encryption function faster than it takes to produce a near fixed point using a brute force approach. The problem is that it takes 65536 tries to find a near fixed point using a brute force approach, so since 65536 is not a terribly large number, it will be very difficult to do better than brute force. With that being said, it is still necessary to do mathematical research so that we have a good reason to believe that we cannot do any better than brute force.
I will give a good description of LSRDRs in my next post, but it is getting late here, so you will have to wait for it. But here is an article about this:
https://circcashcore.com/2022/08/08/measuring-block-cipher-round-function-security-using-spectral-radii/Joseph Van Name Ph.D.
-Creator of Circcash
