Using an Intel Core i5 CPU, how long does it take to crack RSA using a key size of 1024 bit (generated using a secure key pair generation function)?
Suppose for instance that we have thousands of zombies or a big network of computers. To calculate all the combinations or possibilities, can we distribute the process through a big network of computers?
RSA-768 took 2000 years of 2.2Ghz single-core Opteron from the year 2009.
DJB et al wrote in 2013 (see page 30) (see also: 29C3: FactHacks (EN); slide 87/112; about 10 minutes) that RSA-1024 would take $2^{70}$ differences with $2^{24}$ per machine per second in 2009, so 2 million years. Hardware improved since then, and GNFS can use GPUs, so maybe better, but about a million years I guess.
Absolutely the computation can be parallelized to use many devices, for example to use a botnet, which is what DJB recommends. Whether one can have a botnet with a million devices with strong CPU/GPU that uses up a lot of power and not get noticed for a year, is another matter entirely.
