Comments on: Got a prime number? This formula can tell you
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you/
Comments on MetaFilter post Got a prime number? This formula can tell youMon, 04 Nov 2002 12:41:30 -0800Mon, 04 Nov 2002 12:41:30 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Got a prime number? This formula can tell you
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you
<a href="http://www.cse.iitk.ac.in/news/primality.html">Got a prime number? This formula can tell you</a> . <a href="http://www.cse.iitk.ac.in/users/manindra/index.html" title="the professor's bio">Dr. Manindra Agrawal</a>, a professor of mathematics at the Indian Institute of Technology, and two doctoral students have solved a problem that has been puzzling mathematitians for literally centuries: testing with absolute certainty whether a number is prime. More inside.post:www.metafilter.com,2002:site.21352Mon, 04 Nov 2002 12:39:55 -0800me3diamathprimeBy: me3dia
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#380922
The formula works even on very large prime numbers. This has some application to the Internet, since current encryption algorithms take two large prime numbers and multiply them together; the formula <a href="http://news.com.com/2100-1001-949170.html" title="according to Cnet">could provide the basis</a> of even stronger encryption.
On the other hand, some enterprising (and mathematically talented) <a href="http://online.wsj.com/article/0,,SB1036367360105172588,00.html" title="according to WSJ's Boomtown column">criminals could use the formula</a> to develop a method of decryption, rendering current Internet security useless.
Download the paper <a href="http://www.cse.iitk.ac.in/news/primality.pdf">here</a>.comment:www.metafilter.com,2002:site.21352-380922Mon, 04 Nov 2002 12:41:30 -0800me3diaBy: cortex
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#380930
Before the imminent death of modern cryptography is predicted, I'd like to point out that the key to strong crypto is the difficulty of <b>factoring a large number</b>. Just knowing that a number is prime doesn't affect the situation, since your essential magic bullet would have to quickly tell you what the prime factors of some composite number is.
But this is pretty cool, regardless.comment:www.metafilter.com,2002:site.21352-380930Mon, 04 Nov 2002 12:48:17 -0800cortexBy: moz
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#380931
<a href="http://mathworld.wolfram.com/news/2002-08-07_primetest/">mathworld</a> has some more information on prime numbers as well as the work by agrawal et. al. in addition, you might be interested in the <a href="http://www.mersenne.org/prime.htm">GIMPS project</a>, a distributed computing effort that aims at proving a particular sort of prime numbers called mersenne primes.comment:www.metafilter.com,2002:site.21352-380931Mon, 04 Nov 2002 12:48:25 -0800mozBy: wanderingmind
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#380939
I'm not certain criminals could use the formula to decrypt anything; it doesn't tell you (AFAIK) how to factor a given number into primes. It just gives you a yes or no answer as to whether it's prime or not.
(on preview: what Cortex said.)comment:www.metafilter.com,2002:site.21352-380939Mon, 04 Nov 2002 12:52:47 -0800wanderingmindBy: ptermit
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#380952
Discussed <a href="http://www.metafilter.com/comments.mefi/19008">previously</a>, alas.comment:www.metafilter.com,2002:site.21352-380952Mon, 04 Nov 2002 12:59:49 -0800ptermitBy: kfury
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#380958
<i>On the other hand, some enterprising (and mathematically talented) criminals could use the formula to develop a method of decryption, rendering current Internet security useless.</i>
God damn the fucking DMCA. Before 4 years ago, trying to break encryption was a perfectly respectable thing to do. How better to make a solid algorithm than to have people other than the creator trying to break it? Criminalizing such efforts means we all get a security blanket to go along with the inevitably weaker encryption we get.
The amusing thing is that it isn't <i>that much</i> of a stretch to say that merely coming up with the algorithm that they did was in itself a criminal act, since it makes breaking existing encryption algorithms much easier, and this was a clear use of the formula before it was created.
The world is getting pretty fucked up.comment:www.metafilter.com,2002:site.21352-380958Mon, 04 Nov 2002 13:05:00 -0800kfuryBy: kfury
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#380963
<blockquote><i>On the other hand, some enterprising (and mathematically talented) criminals could use the formula to develop a method of decryption, rendering current Internet security useless.</i></blockquote>On the other hand, some enterprising (and mathematically talented) criminals could use the formula to develop a <i>stronger method of encryption</i>, rendering current government intelligence initiatives useless.comment:www.metafilter.com,2002:site.21352-380963Mon, 04 Nov 2002 13:07:56 -0800kfuryBy: namespan
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#380964
Note of course that people knew algorithms for determining if a number n was prime before -- like checking every whole number up to sqrt(n) to see if divided into n evenly. It just took a long, long time. This takes less time.comment:www.metafilter.com,2002:site.21352-380964Mon, 04 Nov 2002 13:08:45 -0800namespanBy: evinrude
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#380965
Right; I don't want to further rain on the parade here, but we already have 'algorithms' that deal with this, and generally in less time -- but these other 'algorithms' only provided a probabilistic proof that a number was prime, i.e., "with probability really super close to 100%, this number is prime." This paper is exciting because we now have a polynomial-time deterministic check instead of a probabilistic check; but for all intents and purposes, the probabilistic checks we have are sufficient. For CS folks, it's exciting since testing for primality is now definitely P and not NP. For other folks, your mileage, it may be varying. As those other folks said, I don't think we're entering a whole new world of cryptography here.comment:www.metafilter.com,2002:site.21352-380965Mon, 04 Nov 2002 13:08:50 -0800evinrudeBy: gleuschk
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#380966
<i>a problem that has been puzzling mathematitians for literally centuries: testing with absolute certainty whether a number is prime</i>
This misses the point completely. Doing what you said is completely trivial: you test all the numbers up to the square root of the one you've got, and see if they divide in evenly. Done.
What Agrawal et. al. did here is very different. They gave an algorithm whose complexity is polynomial in the number of bits of the input (rather than the brute-force method above).
<i>On the other hand, some enterprising (and mathematically talented) criminals could use the formula to develop a stronger method of encryption, rendering current government intelligence initiatives useless.</i>
No. There's nothing going on here that's mystical about numbers or primes or anything else. All this is is a <b>faster algorithm than we knew about before</b>.comment:www.metafilter.com,2002:site.21352-380966Mon, 04 Nov 2002 13:10:00 -0800gleuschkBy: gleuschk
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#380972
And one that was posted three months ago, to boot.comment:www.metafilter.com,2002:site.21352-380972Mon, 04 Nov 2002 13:12:30 -0800gleuschkBy: moz
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#380976
we'd be entering a whole new world of cryptography should quantum computing become practical for either the government or the mass-market to use. quantum computing would squash current cryptography methods with its fast factoring, but would also introduce new forms of cryptography that would be difficult to break. (once or twice i've heard that Q.cryptography could be "unbreakable," but i'm kind of wary...)comment:www.metafilter.com,2002:site.21352-380976Mon, 04 Nov 2002 13:16:04 -0800mozBy: me3dia
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#380983
Thanks, ptermit. You would have thought that a search for "prime numbers" would have turned that up, but it didn't.
Gleuschk, I was trying to give a layman's explanation of what the formula did -- I'm not a math person, and neither are most people here. My description is accurate, just not very deep. Assuming one read the links, the more nuanced explanation would be clear.
Sorry if my summary ruined it for you.comment:www.metafilter.com,2002:site.21352-380983Mon, 04 Nov 2002 13:20:19 -0800me3diaBy: kfury
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#380984
Quantum cryptography isn't so much unbreakable, even given current theory, as it is 'uneavesdroppable.' Since it relies on a heisenbergian principle of the detection of the data bit itself destroying that bit, it can only be 'listened to' once.
At least I think that was it. I've gotta re-read Singh's The Code Book, as that sounds suspiciously vulneralbe to a man-in-the-middle attack...comment:www.metafilter.com,2002:site.21352-380984Mon, 04 Nov 2002 13:20:29 -0800kfuryBy: gleuschk
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#381009
<i>I was trying to give a layman's explanation of what the formula did -- I'm not a math person, and neither are most people here. My description is accurate, just not very deep.</i>
I understand that my reaction seemed excessively harsh. I apologize for that. Still, I must say that your description is not accurate. The problem solved by this algorithm (not a formula) has not puzzled mathematicians for centuries. The problem that it solves is trivial.
The <i>way</i> that this algorithm solves the problem has indeed puzzled mathematicians for quite some time (the "centuries" part is debatable). But you made no reference to that, when it is in fact the whole point of their result, and of the page you linked.
The <a href="http://www.metafilter.com/comments.mefi/19008">previous thread</a> ran into these difficulties as well, and they were (mostly) eventually hashed out.comment:www.metafilter.com,2002:site.21352-381009Mon, 04 Nov 2002 13:36:05 -0800gleuschkBy: atom128
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#381013
"You are visitor N+1, where N is the number of visitors before you.
B0rken HTML courtesy of the web-authoring tool 'Pico' :-)
My girlfriend will refuse to proof-read my pages unless I cross-link to her: The Anna. "
Cute. On a related note, I just discovered the other day that my phone number is prime.comment:www.metafilter.com,2002:site.21352-381013Mon, 04 Nov 2002 13:38:32 -0800atom128By: hattifattener
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#381056
There are two different things commonly lumped under the heading of quantum cryptography. One is <a href="http://www.cs.berkeley.edu/%7Egottesma/QKD.html">quantum key distribution using entangled states</a>, which is <a href="http://physicsweb.org/article/news/6/10/5">nearly practical</a>. You still need an unspoofable channel in order to make sure you've agreed on the same key, but that channel can be low-bandwidth and eavesdroppable, as long as it's not spoofable.
The other technique is <a href="http://plato.stanford.edu/entries/qt-entangle/#5">quantum computation</a>, which might provide a way to solve NP problems quickly. This could weaken RSA and similar algorithms that depend on the difficulty of factoring large numbers. (I don't know if it also affects discrete-log or elliptic systems.) Quantum computation is much farther from being practical, although simple computations have been performed in the lab.comment:www.metafilter.com,2002:site.21352-381056Mon, 04 Nov 2002 14:10:15 -0800hattifattenerBy: Bonzai
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#381102
<i>Doing what you said is completely trivial: you test all <b>the numbers</b> up to the square root of the one you've got, and see if they divide in evenly.</i>
Actually, just the primes.comment:www.metafilter.com,2002:site.21352-381102Mon, 04 Nov 2002 14:45:10 -0800BonzaiBy: eddydamascene
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#381120
actually, primality checking belongs to a unique class of problems known as NP-<i>easy</i>; any instance of the primality checking problem can be turned into an NP-incomplete problem through a (Legendre) polynomial time reduction. <small><small>
[/disinformation]</small></small>comment:www.metafilter.com,2002:site.21352-381120Mon, 04 Nov 2002 15:08:50 -0800eddydamasceneBy: cortex
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#381180
<i>>>Doing what you said is completely trivial: you test all the numbers up to the square root of the one you've got, and see if they divide in evenly.
Actually, just the primes.
</i>
Well, that's a very slightly less trivial technique, though. You can do the other without any previous knowledge of the sequence of primes. :) Now, WHY you would want to do that is a different issue...comment:www.metafilter.com,2002:site.21352-381180Mon, 04 Nov 2002 16:39:19 -0800cortexBy: delmoi
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#381274
Actualy this can nither be used to create a stronger kind of encryption or break current encryption either.
Thanks for playing, though.comment:www.metafilter.com,2002:site.21352-381274Mon, 04 Nov 2002 20:16:18 -0800delmoiBy: delmoi
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#381282
<a href="http://www.metafilter.com/mefi/19008#318079">Here is my explanation from the last thread</a>
Anyway, as far as practical applications, there are none really. This only lets us be 100% sure if a number is prime rather then 99.9999999....% sure, and isn't all that much faster.
This will make encryption slightly better, in fact you can be 'sure' that the numbers you are using are prime rather then 99.99999999999..% sure.
beyond that, its pretty intresting for numbers freaks and CS nerds, but nothing that will have any impact whatsoever on anything in the real world.comment:www.metafilter.com,2002:site.21352-381282Mon, 04 Nov 2002 20:32:04 -0800delmoiBy: gleuschk
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#381287
Which is why that <a href="http://news.com.com/2100-1001-949170.html">Cnet article</a> is so infuriating. How can they miss the point so badly? And rustle up professional academic mathematicians to back up their nonsensical claims? Argh.comment:www.metafilter.com,2002:site.21352-381287Mon, 04 Nov 2002 20:43:15 -0800gleuschkBy: byort
http://www.metafilter.com/21352/Got-a-prime-number-This-formula-can-tell-you#381525
Just wanted you all to know that 2 made the cut...comment:www.metafilter.com,2002:site.21352-381525Tue, 05 Nov 2002 07:15:52 -0800byort