Factorization of a 768-bit RSA modulus

[moebius]

Congratulations. So one can only hope that the computing power of the "Bundesamt für Sicherheit in der Informationstechnologie" is again available when it's required for the more important brute forcing of RSA 1024 - RSA 2048, and that the non-trivial modifications of the existing software is made quickly!

[chris2be8]

Originally Posted by FactorEyes

Then I'm lost.

Why even run 1 ECM curve on such a number?

To check if there's been a transcription error in the number? Such an error would usually result in a number with a small factor. A few seconds checking for 15 digit factors could save a lot of wasted time. Chris K

[Raman]

Originally Posted by R.D. Silverman

Applause!!!!!

Especially from someone who has not produced a single research result,
published a single paper, or implemented even a single relevant algorithm on
his own.

Do you know how keen I am in doing research and publishing papers? Just I do not
know the procedure. And what is the difference between those cranks that I see
regularly who frequently claim that they have discovered something without any proof?

My family is under severe financial crisis. If I go to USA to do research, who will pay
the flight expenses, who will manage my family since research is less paid, where will
I get money to live? The cost of living at USA is too high.

I am just at first year of MS in Computer Science and Engineering. Next year only are
the projects, and then only Ph.D. Then only I can have opportunity to do research...
Can you tell me at what age you published your first paper? I am just 22 years old.
This gives me more lifetime to do research.

For your information, I got Ph.D offer at Chennai Mathematical Institute. They offered
admission after 1 year of M.Sc? Couldn't I have joined it? They do research on Automata
Theory, Graph Theory, Probability, Computer Algorithms, Data Structures, etc. But I
am more focused towards Abstract Algebra, Topology, Group Theory, Modern Algebra,
Galois Theory, Number Theory, etc.

Remember that Number Theory is not the only area of mathematics. Studying regularly
about Integer Factorization and Primality Testing makes me feel inferior that I only know
about that topic, nothing else, just simply factoring an integer into its prime factors, a
simple concept... There are many more areas as well... Linear Programming, Linear
Algebra, Laplace and Fourier Transforms, Multi dimensional geometry, vector calculus,
advanced trigonometry... much more to be learnt about.

Regarding implementation of algorithms... I have already done atleast some work in the
past. The initial implementations will be very crude and slow... There are lots, lots and
lots of optimizations to be worked upon. And then I do not understand most of the
notations that are being given within the books. Implementing all these advanced
algorithms takes a lot of time. Were they all developed only within a day?

[S485122]

Originally Posted by Raman

Do you know how keen I am in doing research and publishing papers? Just I do not know the procedure. And what is the difference between those cranks that I see regularly who frequently claim that they have discovered something without any proof?

...

Raman,

R.D. Silverman commented about a comment about this post of yours :

Originally Posted by Raman

If the factors were available on that day itself (12 December 2009 to be exact) what were you all doing till now, why not report up the factors on that day itself Thus, waiting for only to prepare up and then publish that paper? Today is already (7 January 2010)

Since you have not yet published a paper you should have looked up what it implies before criticising people for the time it took them to publish one. The factors are not interesting as such, the way to find them is ! And that is in that "paper".

Jacob

[ixfd64]

Originally Posted by ixfd64

I wonder if RSA will mention this on its website despite having discontinued the contest in 2007. RSA did announce the factorization of RSA-200 from the old contest that was also cancelled, so I'm pretty curious how this will go.

No cash prize, but it's nice to get recognition from RSA!

http://www.rsa.com/blog/blog_entry.aspx?id=1569

[ixfd64]

http://www.schneier.com/blog/archive...it_number.html

[FactorEyes]

Originally Posted by 10metreh

Would RSA-1024 need a septic polynomial if it were ever done by GNFS?

The usual suspects likely started the polynomial search months ago. A few members of this forum likely know whether it's complete, or how much longer it will run before sieving begins.

In about a year and a half, it will start: a post here or there as to how quiet things have been, and that someone is likely up to something. Some of these remarks will come from those actually working on the code for filtering or linear algebra: "Nope. Haven't heard a peep; some big factorization might be in the works, but I'm damned if I know what it is."

Then, at some point in early 2015, one of the participants will post the results here.

[victor]

Congrats! :)

Great work indeed.

[ixfd64]

Another mention on the RSA website: http://www.rsa.com/rsalabs/node.asp?id=3723

[jasonp]

Discussion of tamper-resistant crypto hardware has been moved to the Hardware subforum (not directly related to how big an RSA key I need...)