The security of RSA public key algorithm is based on a mathematical problem: factorization of large integers. At present, the decomposition scale of RSA number is 768 bits.
The decomposition of RSA numbers above 1024 bit is a huge engineering problem at present, which can only be carried out with large-scale computing power.
Limited by financial resources, small-scale teams can only decompose RSA-768 in the order of 768 bits, using hundreds of CPU cores and running for about 2 years.
The decomposition of RSA-5 12 is relatively simple for individual users. With GNFS, the main screening time is 3000 cpu- hours, and 30 CPU cores can be completed in one week.
According to the papers published by Wiki, the following RSA number decomposition of symbols has been completed:
Historically, if the computing power can be increased by 1 year; Almost every 10 year, the computing power of traditional computers is expanded by 1000 times (2 10 = 1024), which can be advanced by about 256 bits (80 bits). It can be estimated that RSA 2048 will take 40-50 years to decompose with the current gnfs algorithm and with sufficient human and financial support.
However, explosive breakthroughs in science and technology can often go beyond convention. There is also a variable here, that is, when the practical quantum computer will have a breakthrough.
1994, Peter Shor proposed a factorization algorithm for quantum computers, called Shor algorithm. At that time, people were not optimistic about making practical quantum computers.
At present, the quantum computer in the laboratory can only decompose very simple two-digit integer factors, such as 2 1 = 3*7.
Practical quantum computers, according to the most optimistic estimate, will not appear for at least ten years. So RSA-2048 can't be cracked at present.