Create key's over 4096 bit ????

[Ludwig Hügelschäfer]

Hi,

On 22.12.2005 17:06 Uhr, Atom Smasher wrote:
> On Thu, 22 Dec 2005, Ludwig Hügelschäfer wrote:
> 
>> That's true. Even considering a brute force attack, 1025 bits is in
>> average only sqrt(2) better as 1024 bits.
> ===============
> 
> so, does that mean that a 2048 bit asymmetric key is (only) this many
> times stronger than a 1024 bit key(?):
> 
> 13407807929942597099574024998205846127479365820592393377723561443721\
> 76403007354697680187429816690342769003185818648605085375388281194656\
> 9946433649006084096

This is something around 10^156. This doesn't match my result below.

> ???   sqrt((2^2048)/(2^1024))   ???

Exactly. This gives for me 1,84467440737e+146 - please correct me when
I'm wrong.

> i never studied higher math, so apologies for any confusion that i'm
> adding to things.

If an attacker wants to find the specific primes whose product make up
the secret key of the victim, then the the primes are usually around
sqrt(keylength).

Ludwig