factoring large numbers is hard. However, with the advances in number theory and computing power, it is getting easier. In 1977 Ron Rivest said that factoring a 125-digit number would take 40 quadrillion years. In 1994 RSA129 was factored using about 5000 MIPS-years of effort from idle CPU cycles on computers across the Internet for eight months. In 1995 the Blacknet key (116 digits) was factored using about 400 MIPS-years of effort (1 MIPS-year is a 1,000,000 instruction per second computer running for one year) from several dozen workstations and a MasPar for about three months. Given current trends the keysize that can be factored will only increase as time goes on. The table below estimates the effort required to factor some common PGP-based RSA public-key modulous lengths using the General Number Field Sieve:

KeySize MIPS-years required to factor

-----------------------------------------------------------------

512 30,000

768 200,000,000

1024 300,000,000,000

2048 300,000,000,000,000,000,000