July 31, 2015
Encryption development update
In order to continue with the development of my socialist millionaire protocol implementation that uses a 4096 bit key I need to find a generator for a Galois field of that size. This is no short term undertaking. Even using the access I have to a supercomputer it is going to take a while to find a generator.
The current level of mathematical understanding is that these generators must be brute-forced since there is no known pattern for what is and isn’t a Galois generator. So while my code is using the supercomputer to do a brute force search, I’m attacking the problem of finding a pattern. I’ve attempted to take a non-obvious approach and have already seen some interesting patterns. If what I’m seeing as patterns hold, I should be able to find a generator long before the brute force approach does. That would be nice since checking even one generator for 2^4096 values to see if the generator actually is a generator takes a long time, let alone multiple possible generators.
I’m eager to get the pattern found so I can share it with you and complete the SMP implementation.