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10

102-digit is two digits more than the first RSA challenge RSA-100 that has 330-bit. This can be easily achieved with existing libraries like; CADO-NFS ; http://cado-nfs.gforge.inria.fr/ NFS factoring: http://gilchrist.ca/jeff/factoring/nfs_beginners_guide.html Factoring as a service https://seclab.upenn.edu/projects/faas/ The Factoring as a Service ...


0

It is certainly possible to retrieve $N$ as this is directly written to the file. See msieve README II.2 The dat file is a record of the half way stage in the factoring process. It records “relations” that are expensive to find pairs of smooth numbers that encode information about $N$ in a linear equation in many variables. Given enough relations (which is ...


4

TL;DR There are no standards or RFCs that use this idea. There is a slightly improved number field sieve attack on your example number based on back of the envelope calculations (see below). Your proposed generator would be fine. The follow on proposal should not admit special polynomials for $\ell\ge 768$. The back-of-the-envelope generic attack To attack ...


1

A large issue with questions like this tends to be the technical details, so apologies if I come across as particularly nit-picky --- I just do not know how to answer questions like this without pointing out the nits that need to be picked. at least if the activation function is continuous, could carry up to even infinitely many links with just changes in ...


9

The Prime Number Theorem proves that there are approximately $\frac{x}{\ln x}$ primes less than any positive integer $x$. There are thus about $\frac{2^{2048}-1}{\ln (2^{2048}-1)}-\frac{2^{2047}}{\ln (2^{2047})}=22.8\times 10^{612} - 11.4\times 10^{612}=11\times 10^{612}$ 2048-bit primes. That's a rather large number, since there are only about $10^{80}$ ...


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