RSA Weak?

Alexander W. Janssen yalla at
Fri Nov 2 21:29:13 CET 2007

On 11/2/07, Robert J. Hansen <rjh at> wrote:
> Alexander W. Janssen wrote:
> > How do you come to that figure? A keyspace of 1024 is the double
> > amount of 1023 bit, so I'm curious how you come to that figures.
> A keyspace of 1024 bits is double that of 1023 bits.  Prime numbers
> become more scarce as they go on.  For instance, there are two primes in
> a keyspace of two bits.  In a seven-bit keyspace--which, by your logic,
> there should be thirty-two times as many primes--there are only twelve
> and a half times as many.

I'm not too familiar with prime- or number-theory. Does that scale in
the same factor in all keyspaces?

> Read this:

Thanks for sharing that. Not sure if I'll understand it, but I'll
definetly have a look at it.

However, the fact that primes get more rare when the keyspace is
expanded isn't necessarily connected to that point that you still need
to check the whole keyspace - which stills grows linearly?

In cleartest: Even if primes get more rare, you still need to find
your whole way through *all* numbers as long as you don't find a
better algorithm.
Putting probalistic prime-tests aside.


"I am tired of all this sort of thing called science here... We have spent
millions in that sort of thing for the last few years, and it is time it
should be stopped."
 -- Simon Cameron, U.S. Senator, on the Smithsonian Institution, 1901.


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