First, apologies. I'm decent at math, but i don't have a degree in it. Please excuse any ignorance on my part. And if any of my math is wrong, please correct me!
So, for anyone not familiar with the diffie-hellman problem it is:
given the following:
- g = can be any number (but usually 2, and known before hand)
- p = an absurdly large, known prime
- X = (ga % p)
- Y = (gb % p)
where only a and b are unknown, find K = (g^ab) % p
Using simple math, I notice that all of the following are equal:
- XY % p
- (ga % p)gb % p % p
- (gabg % p)
- (gab % p)g % p
- Kg % p
As long as all that math is correct, and the knowledge that Diffie-Hellman is still unsolved, that means this is the furthest you can get. the real question: when both g and p are known, what makes solving for K in (Kg % p) so difficult?