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## RSA Factors, First Digits

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• Having verified the first digits of 576 and 640, I am posting the first digits of the factors of the remaining RSA Numbers RSA 704 804457 920341 RSA 768 305380
Message 1 of 5 , Apr 10, 2009
Having verified the first digits of 576 and 640,
I am posting the first digits of the factors
of the remaining RSA Numbers

RSA 704
804457
920341

RSA 768
305380
402838

RSA 896
494414
833357

RSA 1024
110530
122198

RSA 1536
114276
161687

RSA 2048
131123
192154

Milton L. Brown
miltbrown@...
• ... I hoped not to see more about these claims on this list after http://tech.groups.yahoo.com/group/primenumbers/message/14328 Your calculation of the first
Message 2 of 5 , Apr 15, 2009
Milton L. Brown wrote:
> Having verified the first digits of 576 and 640,
> I am posting the first digits of the factors
> of the remaining RSA Numbers

I hoped not to see more about these claims on this list after

Your "calculation" of the first digits of the factors of RSA-576
was made after the factors had been published.
you wrote:
> I calculate that the first
> digits of the factors of RSA 640 are
> 6 0 8 1 1
> and
> 5 1 0 9 8

How did that verification go?
RSA-640 = 163473... * 190087... was published in 2005:
http://www.crypto-world.com/announcements/rsa640.txt

After having seen the real factors, I guess you made a new "calculation"
and then "verified" that it matched those factors.
Calculating factors you don't already know tends to be a little harder.

> RSA 704
> 804457
> 920341

RSA-704 was generated to have two 352-bit factors. In that case their
first digits must be in the interval 458699 to 917399 and you fail.

> RSA 768
> 305380
> 402838

384-bit factors have first digits in 197010 to 394020. Failure.

> RSA 896
> 494414
> 833357

363419 to 726838. Failure.

> RSA 1024
> 110530
> 122198

670390 to 134078. This one is actually not impossible.

> RSA 1536
> 114276
> 161687

776259 to 155251. Failure.

> RSA 2048
> 131123
> 192154

898846 to 179769. Failure.

--
Jens Kruse Andersen
• ... As the mod who approved that post, it provided me with an only momentary problem. As per Ken s post to which you refer unless it contains an answer to the
Message 3 of 5 , Apr 16, 2009
--- On Wed, 4/15/09, Jens Kruse Andersen <jens.k.a@...> wrote:
> Milton L. Brown wrote:
> > Having verified the first digits of 576 and 640,
> > I am posting the first digits of the factors
> > of the remaining RSA Numbers
>
> I hoped not to see more about these claims on this list after
>
> Your "calculation" of the first digits of the factors of
> RSA-576
> was made after the factors had been published.

As the mod who approved that post, it provided me with an only momentary problem. As per Ken's post to which you refer
"unless it contains an answer to the challenge he has been issued"
Milton's post _did_ contain such answers. It's now approaching science, as it can be falsified.

> you wrote:
> > I calculate that the first
> > digits of the factors of RSA 640 are
> > 6 0 8 1 1
> > and
> > 5 1 0 9 8
>
> How did that verification go?
> RSA-640 = 163473... * 190087... was published in 2005:
> http://www.crypto-world.com/announcements/rsa640.txt
>
> After having seen the real factors, I guess you made a new
> "calculation"
> and then "verified" that it matched those factors.
> Calculating factors you don't already know tends to be a
> little harder.
>
> > RSA 704
> > 804457
> > 920341
>
> RSA-704 was generated to have two 352-bit factors. In that
> case their
> first digits must be in the interval 458699 to 917399 and
> you fail.
>
> > RSA 768
> > 305380
> > 402838
>
> 384-bit factors have first digits in 197010 to 394020.
> Failure.
>
> > RSA 896
> > 494414
> > 833357
>
> 363419 to 726838. Failure.
>
> > RSA 1024
> > 110530
> > 122198
>
> 670390 to 134078. This one is actually not impossible.
>
> > RSA 1536
> > 114276
> > 161687
>
> 776259 to 155251. Failure.
>
> > RSA 2048
> > 131123
> > 192154
>
> 898846 to 179769. Failure.

I'm curious why the ranges you've quoted (no doubt one end of which is correct, but I've not checked, probably the upper bound) are in ratio 1:2. Surely for correct (FIPS-stylee) RSA, the ratios would be 1:sqrt(2)? Of course, for the individual test numbers, the ranges could be shrunk even more. (Maybe this would push 1024 into the failure zone too?)

Not that it matters - it was put to the test, and it failed completely.

I consider the subject *now* completely closed. Thanks for having 5 well-sharpened stakes to hand!

Phil
• ... Note that sieving for RSA-768 has now finished. With luck, we should know the leading digits (indeed, all of them) of the prime factors within a few
Message 4 of 5 , Apr 16, 2009
On Thu, 2009-04-16 at 07:21 +0000, Phil Carmody wrote:

> As the mod who approved that post, it provided me with an only
> momentary problem. As per Ken's post to which you refer
> "unless it contains an answer to the challenge he has been issued"
> Milton's post _did_ contain such answers. It's now approaching
> science, as it can be falsified.

Note that sieving for RSA-768 has now finished. With luck, we should
know the leading digits (indeed, all of them) of the prime factors
within a few months.

Paul
• ... pon seeing Milton s post I thought of hammering a post or mail off to Bob S. or sci.crypt (irrespectively, probably) to enquire who, presuming someone,
Message 5 of 5 , Apr 16, 2009
--- On Thu, 4/16/09, Paul Leyland <paul@...> wrote:
> Phil Carmody wrote:
> > As the mod who approved that post, it provided me with an only
> > momentary problem. As per Ken's post to which you refer
> > "unless it contains an answer to the challenge he has been issued"
> > Milton's post _did_ contain such answers. It's now approaching
> > science, as it can be falsified.
>
> Note that sieving for RSA-768 has now finished. With luck, we should
> know the leading digits (indeed, all of them) of the prime factors
> within a few months.

'pon seeing Milton's post I thought of hammering a post or mail off to Bob S. or sci.crypt (irrespectively, probably) to enquire who, presuming someone, was attacking such a task. However, I've not had the time this last week to even contemplate actually following through with that.

Thanks for volunteering the information, and good luck finding some roots in your field. (Dare I say "That'll be a turnip for the books"? Nah, I probably shouldn't.) Do let us know each digit as you discover it, won't you?

Phil
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