# 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). May 26, 2019 at 14:56
• Would you please tell me where or by which formula did you get 2^{80}?
– R1w
May 26, 2019 at 19:26
• it's basically rounded from crypto.stackexchange.com/a/8692/24949
– Z.T.
May 26, 2019 at 19:38
• What CPU family? What clock speed? How much RAM?
– forest
May 26, 2019 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, 2019 at 8:15

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.