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First, we need an equation that tell us how difficult it is, in # of operations, to factor a number of N bits. eg: N_ops(N) = # of operations it will take.
I think the fastest method that anyone admits to, by Odzyklo (spelling?), has an order of magnitude defined by: e^(sqrt(ln(x) ln(ln(x)))) I've been dusting off my Mathematica skills working on the crypto techniques Matt posts :-) so it looks like this in Mathematica: f[x_] := N[Exp[Sqrt[Log[x] Log[Log[x]]]]] x in bits difficulty 200 2.27 E11 384 5.54 E16 <- PGP casual 512 6.69 E19 <- PGP commercial 664 1.18 E23 1000 1.75 E29 1024 4.42 E29 <- PGP military 1500 8.11 E36 2000 3.11 E43 3000 5.49 E54 4000 2.44 E64 6000 7.06 E80 8000 8.99 E94 I don't know how many seconds until the end of the universe, but I think you'll be covered using an 8000 bit key :-) -----BEGIN PGP SIGNATURE----- Version: 2.3a iQCVAgUBLMbFXYOA7OpLWtYzAQEwrwP9G60hCktxcj7MwkOV2H7QPQ1+i+j5ceTK DEcj74ZFZdsp1vouMxtsN+zvqkdy1+DTzNUuXusWKhogDLFEPTuASZD3tcFgkoUT Uk0B805mJi/gfiBa7+CBWHgjF0T7NSZe1lTjqfru1u+XeU/7iAq+erU0ojydL/xi tqBAZZg3gEs= =wkBt -----END PGP SIGNATURE-----