Re: Bug in Sun compiler WS6U2? - Crashes during compile phase with-fast.

From: iON (ion_at_operamail.com)
Date: 03/24/05 

Date: 24 Mar 2005 06:24:02 -0800

> Dave wrote:
> >> However, you can factor large
> >> numbers that are the product of two primes, and if you did that, it'd
> >> be a bad thing for cryptography as we know it.

It would be "bad" for crytosystems that is based on the ASSUMPTION
that factoring is hard*. (RSA for example)

> Logan Shaw wrote:
> As far as I know, the only way to do this is to just brute force it
> by dividing by numbers from 2 .. floor(sqrt(7621615238978741781241003))
> until you get one that comes out evenly.

There are a lot of different algorithms for factoring numbers. (Number
Field Sieve, Eliptic curve, Quadric sieve just to mention a few).
Brute force is not used, other than on very very small numbers.
Matematica (and other math software) has of course the regular
algorithms implemented.

BR
Jon

*=By hard one usually mean "impossible to do in a reasonable time"
when talking cryptography.

Relevant Pages

  • Re: Revisions to the FAQ
    ... The most important observation about factoring is that all known ... Cryptgraphic algorithms built on the ... number field sieve for small n, ... Certain properties make composites easier to factor. ...
    (sci.crypt)
  • Re: SF: Generalized SFTs
    ... I don't know if I can describe the feeling, ... He knows darned well too that his previous rounds of "proven correct" factoring algorithms were proved wrong by trying examples, ...
    (sci.math)
  • SF: Back to theory
    ... I see a lot of negative postings about my ideas, ... factoring is getting a lot of bashing, but hey, it's just an idea. ... Basically with the latest surrogate factoring I've been analyzing the ... algorithms, which I'll get to later, require that both j and T be ...
    (sci.math)
  • SF: Back to theory
    ... I see a lot of negative postings about my ideas, ... factoring is getting a lot of bashing, but hey, it's just an idea. ... Basically with the latest surrogate factoring I've been analyzing the ... algorithms, which I'll get to later, require that both j and T be ...
    (sci.crypt)
  • Re: JSH: Contradictory behavior, issue of math fraud
    ... In order for your algorithm to be pertinent, it needs to bring something that other factoring algorithms don't have, like the most efficient when the two numbers are same order of magnitude, are be most efficient over all. ... can't just downplay or lie about, and in so doing prove that you DID ... What punishment fits the crime? ...
    (sci.math)