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Thanks trope. Sometimes its good to have people that push things along, and other times you gotta tell people that don't believe "fuck you", because doing what others believe is impossible is already hard enough. And sometimes the people that disbelieve are themselves the spite-fuel for continuing.

ha, there is that.

There is the slim hope that they could all look at eachother's darkest organizational and national secrets, say "oh shit our nations are trapped in an iron-gripped self-reinforcing system of massive mutual bribery and blackmail leading to run-away political, social, military, and economic decay, and if this goes on we're all collectively going to crash and burn in world war three or end up in one of orwell's dystopias" and immediately about-face to fix their respective systems.

lol.

Nerd stuff

continuously disappointing a dozen or so people who are patiently waiting for it to release.

The goal is to break RSA. The rundown is that the algebraic set is generated by an algorithm that derives a whole bunch of variables purely from a public key. All these variables de facto leak information about variables in a parallel group called the unknown set (UKS). If any solution can be found between a known variable and a variable in the unknown set, then it leads to a O(1)-time exact solution to prime factorization, or a break of any public key cryptography method that relies on the difficulty of prime factorization.

I tried that for a long time, almost four years now, and wrote an entire suite of automation tools to search for solutions, but always landed on inexact solutions that didn't work for all numbers. I tried bundling those, genetic algorithms to refine them toward being universally general, but that failed as well.

It was like having all the answers (the unknown set), but all the answers were locked in impenetrable boxes (the known set)

So I figured out the algebraic set is probably indeterminate (no exact solution, or infinitely many solutions that are trivial, i.e. they don't give the private key from a public key).

From there I moved on to machine learning models, and figured out that I could take a known variable, lets say d4a, and d4u, which are products of three unknown variables [d4, a, u], and use those as boundaries for estimates.
But how? Sometimes you'd have unknowns that were below 1, meaning a boundary that might normally act as an upperbound, would act as a lower bound, and vice-versa.
Initially testing with a bag model of machine learning gave very promising results (predicting to within 95% of the unknowns value in some cases, and up to 98% in many others). Of course thats not good enough because of outliers.
But what if I didn't want to predict their values exactly? What if I just wanted to determine if some unknown that was part of a product or quotient in the known set, was inverted?

And from the testing that should be perfectly doable.

At some point I found an exact convergent solution to prime factorization, and hence a break of RSA, the caveat?

It was incredibly slow. For very large numbers? Effectively slower than bruteforce.

Unless......

Unless I knew the magnitude and leading digit or two of one of the public key's factors.

In which case I could strip off multiple inner and outer loops, massively reducing the search space to polynomial time, instead of NP or NP-intermediate.

In theory exact polynomial time equations aren't guaranteed to be really fast, because the polynomial could be some very large number, but in practice for most exact polynomial time equations, there is a non-deterministic polynomial time equation.

From what I've seen, starting with test keys where the private keys are known, convergent set converges very fast, even for very large keys in the 1024 bit range, which is what I've currently tested up to.

On a lark about a week ago, I tried something that had been in the back of my mind for a while, an implementation variation on an approach I'd turned to before, certain modular manipulations of n, which closely approximated N's (the public key's) factors, to what? To their magnitude and leading digits.

I realized pretty quickly, that all these different approaches, with the right training and architecture, could be combine into one larger algorithm, each giving a different piece of critical information that sped up the downstream steps massively.

And thats where the work is at now.

fwiw, inputting the code into 'chatAnything' is liable to tell you it is highly experimental and/or ill defined, and/or even 'impossible' because I'm working at the limit of mathematical tools and established understanding and techniques.

Just inputting the code for the algebraic set, and asking "is there a way to get from n to its factors, without bruteforcing, assuming xyz derived variables" and the answer will be a universal no, or the machine will hallucinate, or assume some variable must be zero (even if you tell it otherwise) in order to come up with a trivial (non-useful) solution.

All the individual pieces though work as intended. The algebraic set leaks information about the private keys and in training gives us boundaries for the threshold set. The convergent set does in fact converge in testing on training examples and validation data sets. The modular set always yields the magnitude and leading digit of at least one private key in testing, up to very long bitlengths, etc.

None of them by themselves solve factorization, but you can see, given the architecture diagram, how they would be combine, to mutually give an exact answer.

If I recall, the only component I haven't posted here at some time is the convergent set algorithm.

And while the basilisks, what I named the series, only go up to 301 currently, I've in fact tested thousands of variations over the last 4+ years, never thinking to combine any of the approaches in a major way until now.

Part of it was the fact that I lacked a precise approximation of any of the unknowns, let alone the factors of a public key, until just recently. That was the piece that made everything else click into place.

I'm currently racing to complete it, versus the various military research projects in quantum. Whichever nation builds a workable general-purpose quantum chip first, will very quickly pwn and dominate every other nation and organization the world over. If I beat all of them to a solution first, then I release it open source and in a short time every power on earth obtains it, and they all equally drag eachother down into the dustbin of history, every organization, every religion, every economic power, every business, every NGO, every nation.