1 Factorization of a 512 { bit RSA Modulus
نویسندگان
چکیده
On August 22, 1999, we completed the factorization of the 512{bit 155{digit number RSA{155 with the help of the Number Field Sieve factoring method (NFS). This is a new record for factoring general numbers. Moreover, 512{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 140{digit number RSA{140, was established on February 2, 1999, also with the help of NFS, by a subset of the team which factored RSA{155. The amount of computing time spent on RSA{155 was about 8400 MIPS years, roughly four times that needed for RSA{140; this is about half of what could be expected from a straightforward extrapolation of the computing time spent on factoring RSA{ 140 and about a quarter of what would be expected from a straightforward extrapolation of the computing time spent on RSA{130. 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{140 and now, with improvements, to RSA{155. 2000 Mathematics Subject Classi cation: Primary 11Y05. Secondary 11A51. 1999 ACM Computing Classi cation System: F.2.1.
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