Marco DI LEO quotes the "Free On-Line Dictionary Of Computing" at
http://wombat.doc.ic.ac.uk/foldoc/index.html:
> security of RSA is predicated on the assumption that factoring is
> difficult; an easy method for factoring large prime numbers would
> break RSA.

Actually, factoring primes is very easy.  It's factoring composites
that can be tricky.

Richard Nowak <nowak@EARTHLINK.NET> writes:
> I would like to get more data on this one.  Every so often someone claims to
> have cracked RSA but in every case I've heard of the claim was false.
>
> The problem is to show mathematically how to factor a *very* large pseudo
> prime number into its two prime factors.  This is the part I want to see.
>
> A billion computers working in parallel to do it once is not a crack.  If in
> fact it was accomplished it was either because the primes were
> insufficiently large or the guy was very lucky.

I think there may be differing definitions of "cracked" at work
here.  Richard seems to mean that a cracked code is one for which
an easy reversal algorithm exists.  Obviously an encryption scheme
becomes completely useless when "cracked"; I'm not aware of any of
the popular encryption schemes being "cracked" by this definition.

However, some people have worked on decoding single messages with
brute-force attacks.  RSA offers rewards for this, in fact, in
order to show that lesser encryption systems are inadequate.  One
such effort was at:

        http://www.frii.com/~rcv/deschall.htm

Where a DES-encoded message was decrypted by brute-force discovery
of the key.  They were a little lucky -- they found the key after
searching "only" 18 quadrillion of the 72 quadrillion keys.

This took place last summer.  Lehigh University computers contributed
to the effort, but they were #105 on the "keys checked" list.

Brian