Re: [Full-Disclosure] Possibly a stupid question RPC over HTTP

From: Andrew Farmer (andfarm_at_teknovis.com)
Date: 10/22/04

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    To: "Airey, John" <John.Airey@rnib.org.uk>
Date: Fri, 22 Oct 2004 11:35:46 -0700

    On 22 Oct 2004, at 06:50, Airey, John wrote:
    >> On Thu, 21 Oct 2004 13:21:10 +0100, Airey, John
    >> <john.airey@rnib.org.uk> wrote:
    >>> This gives you two options. One, use brute force to break
    >>> the SSL encryption. Two (and it's entirely possible that the
    >>> security services have this already) come up with a
    >>> mathematical way to factor large primes rapidly.
    >>
    >> I think you may mean something slightly differently; given any large
    >> prime p, I can factor it completely extremely quickly:
    >>
    >> p = 1 * p
    >>
    >> There are no other factors; this *is* the prime factorization. :) Bill
    >> Gates made the same mistake in his book _The Road Ahead_. Factoring
    >> large primes is trivial; the prime factorization of large numbers is
    >> hard, and I guess that's what you meant.
    >
    > The whole security of encryption rests on the belief that prime
    > factorization isn't possible in a reasonable time, and it may well
    > have been solved.

    Need we tell you again?

    READ THE DEFINITION OF A PRIME NUMBER. Here's a site with a good
    definition:

            http://mathworld.wolfram.com/PrimeNumber.html

    A prime number, BY DEFINITION, cannot be factored. Factoring products
    of large primes - for example,

            8732977253934620914004266951938806186093326019599

    - is believed to be a Hard problem, and that's what RSA is based on.

    (The factorization is at the bottom of this message.)

    > Why would any government admit that it had cracked RSA security and
    > its derivates?

    It wouldn't. Partially because:

      - Governments use RSA too.

      - Businesses use RSA as well.

    Declaring RSA broken would kill e-commerce overnight.

    > I realise that we are getting into the realms of conspiracy theories
    > now, however history shows that the UK did not wish it to be made
    > public during the war that it had cracked the Enigma code. Why should
    > it be any different now?

    Because we aren't at war with Rivest, Shamir, and Adleman?

    > A prime is defined as being divisible by itself and 1 only, so for the
    > purpose of the definition, 1 is not a factor.

    Okay, so you do remember your elementary school math. So explain how
    "prime factorization" is possible, then.

    <snip half a sig>

    > Even if Embryonic Stem Cell Research yielded medical treatments, how
    > could enough eggs be obtained to make them viable? We can't even get
    > enough organs for transplant donation.

    Easily. Eggs are much easier to obtain than organs.

    Since you scrolled down to see it: Mathematica factors

            8732977253934620914004266951938806186093326019599

    to

            2925219829459042790944067 * 2985408879697632628675397

    in about 2 minutes.

    _______________________________________________
    Full-Disclosure - We believe in it.
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