Factorization of a 512-Bit RSA Modulus

On August we completed the factorization of the bit digit number RSA with the help of the Number Field Sieve factoring method NFS This is a new record for factoring general numbers Moreover bit RSA keys are frequently used for the protection of electronic commerce at least outside the USA so this factorization represents a breakthrough in research on RSA based systems The previous record factoring the digit number RSA was established on February also with the help of NFS by a subset of the team which factored RSA The amount of computing time spent on RSA was about MIPS years roughly four times that needed for RSA this is about half of what could be expected from a straightforward extrapolation of the computing time spent on factoring RSA and about a quarter of what would be expected from a straightforward extrapolation of the computing time spent on RSA The speed up is due to a new polynomial selection method for NFS of Murphy and Montgomery which was applied for the rst time to RSA and now with improvements to RSA Mathematics Subject Classi cation Primary Y Secondary A ACM Computing Classi cation System F