r/crypto • u/AbbreviationsGreen90 • 2d ago

A new possible method of factorization for arbitrary semiprimes? Weil pairing factorization

I was noticing something: unlike on semiprimes, it s quite easy to generate a point of known small order on a curve defined on a semiprime without knowing it s factorization. The idea is to transfer this small order to the underlying semiprime using a pairing method derived from the Weil pairing. Knowing if a given specific small order exists can be derived using congruences modulo N.

As you know, the problem is then to avoid a degenerate output from the Miller s algorithm. The problem is the only method I know to avoid this without using the factorization is to use a distortion map that works only with supersingular elliptic curves. But using a supersingular curve caps the order to gcd(p+1,q+1) which is unknown most of the time or just equal to 2. Taking order 2 result in generating outputs equal to 1 or -1. Useless for gcd factoring.

So, any idea of a pairing mechanism that would works over ordinary elliptic curves using embedding degree 1? Possibly using a distortion map that works over ordinary elliptic curves in such a case? Or a pairing that works with simple final exponentiation such as cubing or squaring?

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u/NohatCoder 1d ago

Uh, you just AIed this shit up right? Just like your other stuff.

I know that there are people who have gotten some mathematical results using AI, but it is really not that simple. It takes expert steering, and even then you generally have to hook the whole thing up to an automated proof verifier in order to sort out all the nonsense that the AI will generate regardless of how well you prompted it. The AI claiming that it has a result really has nothing to do with the AI actually having a result. Asking the rest of us to verify what your AI spat out is just a waste of everyone's time.

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u/AbbreviationsGreen90 22h ago

the idea to use pairings to get elments of low order in the ring comes from me. I used llm just for getting a point of known order. You can also notice I started coding about elliptic curves before llm mananged to be able to do it so I can check their results.