If we then replace in the factorization of by for each -heavy prime , this increases (and does not decrease any of the factors of ), while eliminating all the -heavy primes. With a somewhat crude matching algorithm, I was able to do this using of the powers of dividing , leaving ...
Using a greedy algorithm, one can match a -heavy prime to each -heavy prime (counting multiplicity) in such a way that for a small (in most cases one can make , and often one also has ). If we then replace in the factorization of by for each -heavy prime , this increases (and ...
Some ZKP protocols use prime factorization as one-way (or trap door) functions along the lines of the Diffie-Hellman key exchange or the RSA encryption algorithm. With asymmetric encryption, the main goal is for both parties to arrive at a shared secret. In ZKP, the goal is to make ...
If you do not like my algorithm(s), please add a comment for the file/commit or open an issue, and I'll try to improve.I will link to each project that I complete. Some will be in this same repo, some bigger ones will have dedicated repos.To get started, fork this repo, delete...
et al. Wire-cell 3D pattern recognition techniques for neutrino event reconstruction in large LArTPCs: algorithm description and quantitative evaluation with MicroBooNE simulation. Preprint at arXiv https://arxiv.org/abs/2110.13961 (2021). Aiello, S. et al. Event reconstruction for KM3NeT/ORCA ...
Finally, we remark that it is possible to use the results above to find such an analytical bound which is quite good: compute the exact gradient (of f(x)2) at the constant vector and make one iteration in the gradient algorithm; let xˆ be the obtained unit vector, and compute the ...
Using a greedy algorithm, one can match a -heavy prime to each -heavy prime (counting multiplicity) in such a way that for a small (in most cases one can make , and often one also has ). If we then replace in the factorization of by for each -heavy prime , this increases (and ...
FactorizationLLL algorithmSimultaneous diophantine approximationsCoppersmith’s methodThis paper presents three new attacks on the RSA cryptosystem. The first two attacks work when k RSA public keys (N i ,e i ) are such that there exist k relations of the shape e i x y i φ(N i ) = z ...
Theorem 1 There does not exist any algorithm which, given a dimension , a periodic subset of , and a finite subset of , determines in finite time whether there is a translational tiling of by . The caveat is that we have to work with periodic subsets of , rather than all of ; we ...
so we did predictions with them: obtained a factorization algorithm that is completely new, with no similitude to any other factorization algorithm that we know of, and thoroughly checked the statistics of the solution against the prime number theorem. ...