----- Forwarded Message -----
From: Jules Gilbert <repeatable_compress...@yahoo.com>
To: Paul
Sent: Monday, November 7, 2016 9:43 AM
Subject: a factoring program I've decided to give away
Hello Paul.
I should mention, consistent with my purpose in writing (to effect simultaneous
distribution of a program I wrote,) several friends of mine are BCC'ed.
I would like to give away, using your website forum as a base, a program I
wrote maybe five years ago. The program is a fast-factoring engine. See the
attachment, I'm giving you a copy. I seek to give it to thousands of
cryptologic programmers and analyst's as simultaneously as possible, it's
written in C, does not make use of methods based on primes, but instead employs
what I believe is a completely different method to factor numbers, presumably
the product of two large primes.
My purpose is to encourage further research in this area and also to cause the
people who make the big decisions to consider moving away from privacy tools
based on factoring and public/private keys. Why?, this simple program
localizes the smaller of the two primes used to setup an instance of
encryption. And look how simple it is!, it's really just the junior program,
the 'senior' program does much better. (As you will see it's based on
functions like the 'ratio' tool included here.)
About the size of the numbers, today I use a tool that converts bignum
references to 'BSD bignum code, but when I wrote this I used MAPM.
Probably the most important thing I can say to describe it, is that it isn't
the kind of tool one might use to, say, break down the security of a bank's
files. Yes it can factor any pair of large integers, but it's not written to
be the tool of a criminal, rather a tool to aid number research, particularly
with regard to factoring related research.
Given:
c = a*b, where a,b,c, are large positive integers.
And, given only 'c', it finds 'a'. By convention (my convention,) 'a' is the
smaller factor.
The program proves the method by building a thousand example pairs of (a,b) and
then, using only the 'c' value, locates 'a'. It takes, depending the speed of
one's computer, from a few hours to maybe just half an hour to do all thousand
problems. The thousand pairs of large numbers are assembled using random
numbers. Looking at the code you'll see all this, it's pretty obvious.
But read this next section!
If we use c = a*b, then 'a' must be within the range of 3 .. sqrt(c), it can
not be outside this range -- not if we're talking about positive integers.
My program divides this range into 1,024 sub-sections and identifies which 32
sections the 'a' value is closest too. Assuming we're using the values 'lo'
and 'hi' which represent the total range, then knowing the approximate location
of 'a', the program be used to respecify 'lo' and 'hi', reflecting this smaller
space and re-applied to further localize the exact value of 'a'.
Though I'd like to say my program is doing a true binary decomposition --
something that many researchers have been attempting, no -- my program isn't
quite that.
When the number of sub-sections is 1,024 and the program resolves 'a' to one of
32 sub-sections, that's a five bit gain. True, five bits isn't much when
compared to the thousands of bits that is typical for 'c'. Which is why
re-application is so important.
Originally I wrote code to do backup when necessary; When the program makes a
wrong choice the process quickly fails, and the program backs up several steps
(originally the default back-step value was set to five,) and then retry making
the alternative choice five steps back. Because I'm trying to avoid empowering
criminals and similar types, I've cut that logic out from what I'm giving away.
And second, also deter bad guys, I include only one "left-right deciding"
method. These are the lowest level routines that are the basis of program
operation. Originally I used GAC, one of Spear's genetic tools (which btw,
are pretty cool, and very easy to use!, too.) The method provided works but
isn't the best one. (eg., I don't think a "best" one exists, this is a
probabilistic problem.) What's really best is to use several and vote the
answers, to go left or right. The 'ratio' model I supply is simple and
sufficient for others to learn from.
The program core makes use of a very simple left-right decider, which takes
advantage of the differing limits of two sums, each sum derived by summing the
results of modulus taking arithmetic. I don't know if this property is known
to others, (as I discuss above,) I discovered it using mechanical search
techniques.
So why am I publishing this at all, and why now? First, my work relating to
prediction has taken a turn that I want to pursue. (And ah, my health isn't so
good -- I do what I'm supposed to, but I'm still declining.)
But second, the more I learn about number theory and some related topics, the
more I fear the NSA made a mistake forty years ago by focusing most American
cryptography on factoring and public-key methods. Why was this such an awful
mistake?, because science always moves forward, and what was impossibly hard
forty years ago is today is today millions of times easier. (eg., more
feasible.)
The NSA website encourages researchers to publish, to bring forward their
ideas, to tell others. I contacted them privately two years ago, and then
again, perhaps a year ago, at the time American police stations were getting
hit by the Russian mob and I wanted to help the NSA to stop this. Each time I
offered my consulting service, each time no one thought enough of my offer to
reply. Okay -- though when I had my career and applied for work I always,
without fail, always, either got the work or at least a nice letter in reply.
Apparently the NSA has different standards... (From what the news reports are
saying they prefer people such as Snowden and now, Martin.)
Anyway, I have something else I'm working on but since my health isn't so good
and since I fear we (our nation,) is headed into worse problems, maybe I can at
least improve our cryptologic health by encouraging America's IT manager's to
move away from methods that more and more seem to be weak and suspect. Yes I
mean methods based on factoring.
For me to post the program you will need to give me my account name and
password, I've forgotten them. Sorry.
The program is attached.
_______________________________________________
freebsd-security@freebsd.org mailing list
https://lists.freebsd.org/mailman/listinfo/freebsd-security
To unsubscribe, send any mail to "freebsd-security-unsubscr...@freebsd.org"
