1993-10-21 - MATH: factoring, # of bits

Header Data

From: Karl Lui Barrus <klbarrus@owlnet.rice.edu>
To: cypherpunks@toad.com
Message Hash: fc0ab586ba2a206e85f35bcdd8d1fcea0f9e7291af2cad3c39639e99efa52cc1
Message ID: <9310211724.AA10107@arcadien.owlnet.rice.edu>
Reply To: N/A
UTC Datetime: 1993-10-21 17:27:56 UTC
Raw Date: Thu, 21 Oct 93 10:27:56 PDT

Raw message

From: Karl Lui Barrus <klbarrus@owlnet.rice.edu>
Date: Thu, 21 Oct 93 10:27:56 PDT
To: cypherpunks@toad.com
Subject: MATH: factoring, # of bits
Message-ID: <9310211724.AA10107@arcadien.owlnet.rice.edu>
MIME-Version: 1.0
Content-Type: text/plain


-----BEGIN PGP SIGNED MESSAGE-----

>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-----





Thread