
Re: JSH: Upside down situation
Posted:
Mar 16, 2008 2:29 PM


On Mar 16, 10:32 am, rossum <rossu...@coldmail.com> wrote: > On Fri, 14 Mar 2008 17:06:50 0700 (PDT), JSH <jst...@gmail.com> > wrote: > > >I am currently working on my own practical implementation of what I > >call surrogate factoring that follows from the latest theory, and it > >is pleasingly fast, while I still have to work at getting it to factor > >really big numbers to my satisfaction. Oh, my stated goal is the > >ability to factor an RSA encryption sized number in under 10 minutes > >on a standard desktop. > > Have you actually calculated how fast your current method would be on > a 500 bit RSA number James? > > I posted some timings: > > Average timings over 200 numbers: > 20 bits: 2.265 mSec average per number. 0 misfactors. > 22 bits: 10.310 mSec average per number. 0 misfactors. > 24 bits: 12.345 mSec average per number. 0 misfactors. > 26 bits: 50.155 mSec average per number. 0 misfactors. > 28 bits: 294.765 mSec average per number. 0 misfactors. > > We can use those timings to do a rough backofanenvelope calculation > of how long it would take to factor a 500 bit RSA number.
Except your technique isn't the full surrogate factoring as I've explained repeatedly to you.
Here's output from my current program, and again I ask that you post YOUR timings for this particular number.
This time it is incumbent of you to do so as your posting could be taken as an attempt at convincing others against the theory.
And my research program still is not optimized as I continue to methodically work through issues, as it's still way too slow, but I'm still solving big problems in terms of practical implementation.
It took 10 seconds for this still relatively small number. Now what does your code do?
Example 20484149553887:
n=1 f_1.mod(p)=259 f_2.mod(p)=483 alpha*k mod(p)=182 alpha^{1}*(1+a^2)k mod(p)=235
k_0=196616 k=285340 alpha=23
maxPrime=619
k_0/p=317 steps=12
Total all combinations: 487652 Time: 4454 Time/combination: 0.009133562458474485
Surrogate: ( 3 )( 7 )( 619 )( 34033 )( 51239 ) Product: 22667875714113
Surrogate combinations checked: 5708 Initial Factorization:
f_1=214433 f_2=95527039 Now checking its factors... Success! Factors: ( 214433 )( 95527039 ) Product: 20484149553887
In coming is 20484149553887
Surrogate factorization data for target:
Surrogates factored : 430 Surrogates not factored : 9 Factored fuel percentage: 97%
Processing time: 10328 Number of digits: 14 bitLength=45
***************************************************
You posted timings rossum and made an extrapolation against an RSA number.
Now post timings with your code for 20484149553887.
Or concede that you're talking out of your ass.
James Harris

