I wonder how difficult would it be to brute force the private key for an RSA 760 bit public key from 1998. Does anyone know?
Later, in 2019, a 795 bit key was factored with CPU time that "amounted to approximately 900 core-years on a 2.1 GHz Intel Xeon Gold 6130 CPU. Compared to the factorization of RSA-768, the authors estimate that better algorithms sped their calculations by a factor of 3–4 and faster computers sped their calculation by a factor of 1.25–1.67."
So assuming the better algorithms transfer to smaller numbers, someone who knows how to use them (factoring big numbers seems significantly harder than just running CADO-NFS and pointing it at a number and a cluster) could probably do it in a couple months on a couple dozen modern machines.
For example, using the "795-bit computations should be 2.25 times harder than 768-bit computations" from the publication accompanying the second factorization, we could assume 900/2.25 = 400 Core-years of the Xeon reference CPU (which is 6 years old by now) would be needed to break the smaller key with the modern software. Two dozen servers with 64 equivalently strong cores each would need slightly over 3 months. Not something a hobbyist would want to afford just for fun, but something that even a company with a moderate financial interest in doing could easily do, provided they had people capable of understanding and replicating this work.
Edit: Okay, I see it now. 64 bits of cipher of which 24 bits of that cipher are set to a value derived from a 760 bit pubkey.