Re: Reality check, surrogate factoring

From: Tim Smith (reply_in_group_at_mouse-potato.com)
Date: 01/26/05 

Date: Wed, 26 Jan 2005 07:01:12 GMT

In article <1106707007.031093.186480@z14g2000cwz.googlegroups.com>,
jstevh@msn.com wrote:
> But, you're factoring T, where T = M^2 - j^2, where M is your target, and
> j is picked. Like typically j is odd, as M is odd (though you may need to
> make it even, more later), and you can also pick j such that T is
> divisible by 3, or such that it is divisible by any number you wish it to
> be.
>
> You also get a partial factorization of T at the outset as
>
> T = (M-j)(M+j)
>
> so what I'm saying is that some people somewhere work really hard to pick
> p_1 and p_2 so that p_1 p_2 is hard to factor by known methods, and
> surrogate factoring allows you to blow all of that out of the water by
> shifting to another number, easy to factor.

You should give examples, using small integers. E.g., pick a couple of 2
digit primes, multiply them, and show how your methods would be used to
factor that product. 

-- 
--Tim Smith

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