How long does it take to crack RSA 1024 with a PC?

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?

• I think the standard estimate is $2^{40}$ work for 512-bit moduli and $2^{80}$ work for 1024-bit. A very optimistic guesstimate would probably be "1 day" for the 512-bit modulus, so $2^{40}$ (1 trillion) days for 1024-bit moduli. Of course I didn't use actual performance numbers (so no proper answer). – SEJPM May 26 '19 at 14:56
• Would you please tell me where or by which formula did you get 2^{80}? – R1w May 26 '19 at 19:26
• it's basically rounded from crypto.stackexchange.com/a/8692/24949 – Z.T. May 26 '19 at 19:38
• What CPU family? What clock speed? How much RAM? – forest May 26 '19 at 23:20
• @R1w Sure, but precise hardware information is necessary to make accurate estimates. However you should assume that RSA 1024 can be broken with sufficient computing power (whether a huge number of consumer PCs or a specialized ASIC). – forest May 27 '19 at 8:15

RSA-768 took 2000 years of 2.2Ghz single core Opteron from year 2009 [1].

DJB et al wrote in 2013 [2] 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 use up a lot of power and not get noticed for a year, is another matter entirely.

2 - https://www.hyperelliptic.org/tanja/vortraege/facthacks-29C3.pdf (see page 30 or slide 87 of 112 or about 10 minutes of this video https://youtu.be/95N2KXqH5cs?t=2100)

• So it makes Decryption-As-Service possible either for a legal issue or illegal. – R1w May 26 '19 at 16:00
• Yes, Nadia Heninger (co-author of that presentation I linked, cseweb.ucsd.edu/~nadiah) tried to run such a service on the public cloud. AFAIK this service doesn't exist, but anyone can create it using open source software (cado-nfs.gforge.inria.fr) and specialists can optimize the software for new hardware or to best use cloud spot instances, etc. – Z.T. May 26 '19 at 16:04