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Old 2014-12-29, 08:07   #1
clowns789
 
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Default Back after 8½ years plus 9½ weeks

I logged on just now for the first time since 21 June 2006 to a forum that looks largely the same (you haven't updated vBulletin?). I have come back a few times since then to look around, and it seems like the Operation Billion Digits project I started had a good run for a number of years.

I wanted to come back on to ask a couple questions. The first was what made me think of GIMPS and the community here: the search for a RSA factor that would break asymmetric encryption used in many information security applications. In particular, the 1024 bit RSA key is believed by some to have already been broken by the NSA, although the highest publicly known crack is for the 768 bit key. Perhaps there could be a project that could utilize GPU power to achieve this and be able to work on the 2048 key after (although this would be considerably more difficult). I see there's a computational number theory subforum now, so perhaps I could take this idea there. I thought I'd mention it here as I'm just getting back after so long.

The second is more personal - since my last visit, I've gone from having completed one year of high school to being a year and a half out of college with a BA. Admittedly, I took basic math and am now yearning to return to a more academic focus. I'm looking at entering a Ph.D. program in Economics and need to take math at a community college and apply sometime next year for admission in August 2016. I'm planning on doing Calculus I starting in the spring, then Calculus II in the summer, and some combination of Calculus III, linear algebra and differential equations afterwards. According to most of the university websites, I won't need Calc III and the linear and differential aren't explicitly required, although I've been informed that macroeconomics uses differential equations and matrix algebra. I also feel like I might as well finish the sequence and do Calculus III. Perhaps the sequence is done differently depending on the college, but that's how I see it, especially since all three (at least at the program I looked at) used the same book and completed each third in separate four credit hour classes. I want to ask if there are any opinions as to how I should approach the order of these classes or any study advice as I go along, considering the fact that I haven't taken a formal math class in almost five years.

Hopefully that wasn't too long winded, but I wanted to say hello to everyone again and solicit any opinions on these two points.
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Old 2014-12-29, 09:58   #2
xilman
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Quote:
Originally Posted by clowns789 View Post
I logged on just now for the first time since 21 June 2006 to a forum that looks largely the same (you haven't updated vBulletin?).
I thought I hadn't seen you around recently...
Quote:
Originally Posted by clowns789 View Post
I wanted to come back on to ask a couple questions. The first was what made me think of GIMPS and the community here: the search for a RSA factor that would break asymmetric encryption used in many information security applications. In particular, the 1024 bit RSA key is believed by some to have already been broken by the NSA, although the highest publicly known crack is for the 768 bit key.
Not a hope in hell of doing the 2048-bit challenge number. (Note that none of the RSA challenges are RSA keys per se as they were created and then the factors destroyed immediately. At least that's what Bob Silverman, their creator, states and I've no reason to doubt him).

The kilobit number is now feasible, IMAO, but extremely arduous. If we started very soon it could be finished by the end of the decade. Some people here have been giving serious thought but not, as yet, serious computation.
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Old 2014-12-29, 10:25   #3
Nick
 
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Happy Birthday for 10 days ago!

The dilemma (as I understand it) for economics researchers is not what sort of mathematics to use but whether to toe the pre-2008 line in order to get your research accepted by the big journals or not.
http://www.post-crasheconomics.com/
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Old 2014-12-29, 17:43   #4
clowns789
 
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Quote:
Originally Posted by xilman View Post
The kilobit number is now feasible, IMAO, but extremely arduous. If we started very soon it could be finished by the end of the decade. Some people here have been giving serious thought but not, as yet, serious computation.
Perhaps so, but it might be worth a shot, especially with GPUs getting so much faster.

Quote:
Originally Posted by Nick View Post
Happy Birthday for 10 days ago!
The dilemma (as I understand it) for economics researchers is not what sort of mathematics to use but whether to toe the pre-2008 line in order to get your research accepted by the big journals or not.
http://www.post-crasheconomics.com/
Thanks for the birthday wishes! That website is interesting too; I looked at their report and I agree that there is too much of an emphasis on neoclassical economics in most intro classes. The faculty where I studied were known to have come from a variety of heterodox schools of thought, but the one class I took in high school was definitely neoclassical through and through. (Incidentally, I took that high school class in the spring of 2009 in the depth of the recession.)
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Old 2014-12-29, 18:22   #5
R.D. Silverman
 
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Quote:
Originally Posted by clowns789 View Post
I wanted to come back on to ask a couple questions. The first was what made me think of GIMPS and the community here: the search for a RSA factor that would break asymmetric encryption used in many information security applications.
Huh? What have you been smoking?? Specify exactly which "RSA factor" would break asymmetric encryption. What
is this key that is "used in many.... applications". Are you so deluded to believe that any of the RSA challenge numbers
are actually used? If so, please tell us how the users manage to construct the private key.


Quote:
In particular, the 1024 bit RSA key is believed by some to have already been broken by the NSA
Oh? Where did you get this myth from? Some people believe in the tooth fairy.
Unless you have some actual evidence, please refrain from
promoting baseless rumors.

Quote:
, although the highest publicly known crack is for the 768 bit key. Perhaps there could be a project that could utilize GPU power to achieve this
You have been gone and have missed many discussions. GPU's are not suited to running NFS.


Quote:
and be able to work on the 2048 key after (although this would be considerably more difficult).
I suggest that you do the arithmetic and determine for yourself how much time it would take
and what the space requirements would be. Until then, please refrain from such "speculation".

Quote:
I'm planning on doing Calculus I starting in the spring, then Calculus II in the summer, and some combination of Calculus III, linear algebra and differential equations afterwards. According to most of the university websites, I won't need Calc III and the linear and differential aren't explicitly required, although .....

<snip>
Take lots of statistics.
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Old 2014-12-29, 18:37   #6
xilman
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Quote:
Originally Posted by R.D. Silverman View Post
You have been gone and have missed many discussions. GPU's are not suited to running NFS.
Not suitable for NFS sieving, certainly. AFAIK they're not suitable for the post-sieving phases either though I'd be delighted to be proven wrong (though I'm not hopeful).

Where they are eminently suitable, perhaps a hundred times more efficient than cpus on either a cash or energy basis, is finding polynomials. It's sad that polynomial searching is such a small part of the overall computation.
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Old 2014-12-29, 18:42   #7
xilman
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Quote:
Originally Posted by R.D. Silverman View Post
Huh? What have you been smoking?? Specify exactly which "RSA factor" would break asymmetric encryption. What is this key that is "used in many.... applications".
An example might be either factor of the MSFT-owned key used to sign binaries released by that corporation. Note: it would not break all asymmetric encryption but it would certainly break asymmetric encryption used in many applications and, for that matter, by many people.

A dose of pedantry is useful in this thread, I believe.

Last fiddled with by xilman on 2014-12-29 at 18:43 Reason: Fix tag
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Old 2014-12-30, 00:45   #8
retina
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Quote:
Originally Posted by R.D. Silverman View Post
Huh? What have you been smoking?? Specify exactly which "RSA factor" would break asymmetric encryption.
I think that having the factors for RSA4096 would say a lot about the state of security of RSA in general. If someone factored that then all asymmetric encryption using RSA would have to be considered broken also. RSA is not the only asymmetric encryption scheme but it is very widely used so I think that could qualify as "breaking asymmetric encryption".
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Old 2014-12-30, 02:58   #9
R.D. Silverman
 
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Quote:
Originally Posted by retina View Post
I think that having the factors for RSA4096 would say a lot about the state of security of RSA in general. If someone factored that then all asymmetric encryption using RSA would have to be considered broken also. RSA is not the only asymmetric encryption scheme but it is very widely used so I think that could qualify as "breaking asymmetric encryption".
You are totally misstating what was said.
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Old 2014-12-30, 04:23   #10
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Quote:
Originally Posted by R.D. Silverman View Post
Quote:
In particular, the 1024 bit RSA key is believed by some to have already been broken by the NSA
Oh? Where did you get this myth from? Some people believe in the tooth fairy.
Unless you have some actual evidence, please refrain from
promoting baseless rumors.
I think it's quite likely that the NSA can crack 1024-bit semiprimes -- not that they'd often want to do this, with its expense, but they should have far more practical experience with NFS than anyone 'outside', and we've reduced 1024-bit factoring with NFS to an engineering problem rather than a mathematical one per se.

Do you think that the NSA hasn't factored any (hard) 1024-bit semiprimes, Bob? (I think you're an expert here, and I'd update my beliefs with that knowledge if so.)
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Old 2014-12-30, 06:42   #11
VBCurtis
 
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OP-
I'm a community college instructor, and regularly teach the courses you plan to work through. Once you have Calc I and II complete, it doesn't much matter which of differentials, calc III, and linear you tackle in which order; but note that the JC linear curriculum, as a lower-division course (by def'n since it's at a community college), is usually not rigorous enough to prepare you for the applications used in graduate economics. So, I'd put that one off the longest; however, at the JC level calculus is hardly required for it, so you could take it alongside any of calc II, III, diffeq.

You could also take Calc III and Differentials at the same time; in fact, this would be a pretty good plan.

As for what to do after 5 yrs outside a math classroom before starting Calc I, that is a very individual question. If you don't think you could get 2/3rds of a precalc final exam correct, I suggest a self-study online system such as ALEKS or MyMathLab. Aleks is an online-HW system developed by UC Irvine, quite useful though intensive to refresh forgotten skills. Quite a few universities use it as a remedial self-study course for students who aren't ready for precalc when they enter the university. MyMathLab is Pearson publishing online HW/study system, but is usually attached to a specific textbook or college course. I could add you manually to my college algebra course for winter quarter (starting 6 jan for 10 weeks), but then you'd be subject to my duedates/etc. A code for MyMathLab is good for 6 months, and there are other texts you could join than mine (but I don't have details, it's not really intended for independent study).

If you did well in precalc in college, and feel like you could just review your notes and be okay for calculus, you're not crazy and this is possible. A review of some trig maniuplations online/free might be all you need tinker with before JC coursework.

Good luck!
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