It’s coming. Monday Mathematics, a series of weekly papers addressing how to solve common difficult problems in mathematics, and the math behind those solutions.

Have a favorite math problem? Let me know.

I think I actually have a really good idea for a cryptography system. No more GRAWM-1 crap. I think this one actually works. I just need to work out the details, and then I think I have a solid hash function. A bit more work and I should be able to get some symmetric (and maybe even asymmetric!) cryptography going too.

In short, my idea is this: \sum_{i=0}^n Prime(i) x_i x_{n-i}. x_i is the (integer) value of each byte/word/dword/whatever in groups of n. (The primes would be pre-generated.) Diophantine equations are really tough to find solutions for in reverse, so collisions are hard to create. It’s second degree, so it already avalanches appreciably, and the primes prevent a single byte from masking another particular byte. I’d then collect a bunch of these sums, and run some other functions on them. I’m thinking some conditional modulo based on even/odd-ness, then another run through the Diophantine equation. The final sum would be the hash.

Anyone reading this who’s knowledgeable and interested in helping find vulnerabilities? I’m going to read up some more on group and ring theory first, because it might be relevant. Lemme know if you’re interested.