<article>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#article10_01_07_1623249</id>
	<title>Factorization of a 768-Bit RSA Modulus</title>
	<author>CmdrTaco</author>
	<datestamp>1262884920000</datestamp>
	<htmltext>dtmos writes <i>"The 768-bit, 232-digit number RSA-768 <a href="http://eprint.iacr.org/2010/006.pdf">has been factored</a>. 'The number RSA-768 was taken from the now obsolete RSA Challenge list as a representative 768-bit RSA modulus. This result is a record for factoring general integers. Factoring a 1024-bit RSA modulus would be about a thousand times harder, and a 768-bit RSA modulus is several thousands times harder to factor than a 512-bit one.  Because the first factorization of a 512-bit RSA modulus was reported only a decade ago it is not unreasonable to expect that 1024-bit RSA moduli can be factored well within the next decade by an academic effort such as ours . . . . Thus, it would be prudent to phase out usage of 1024-bit RSA within the next three to four years.'"</i></htmltext>
<tokenext>dtmos writes " The 768-bit , 232-digit number RSA-768 has been factored .
'The number RSA-768 was taken from the now obsolete RSA Challenge list as a representative 768-bit RSA modulus .
This result is a record for factoring general integers .
Factoring a 1024-bit RSA modulus would be about a thousand times harder , and a 768-bit RSA modulus is several thousands times harder to factor than a 512-bit one .
Because the first factorization of a 512-bit RSA modulus was reported only a decade ago it is not unreasonable to expect that 1024-bit RSA moduli can be factored well within the next decade by an academic effort such as ours .
. .
. Thus , it would be prudent to phase out usage of 1024-bit RSA within the next three to four years .
' "</tokentext>
<sentencetext>dtmos writes "The 768-bit, 232-digit number RSA-768 has been factored.
'The number RSA-768 was taken from the now obsolete RSA Challenge list as a representative 768-bit RSA modulus.
This result is a record for factoring general integers.
Factoring a 1024-bit RSA modulus would be about a thousand times harder, and a 768-bit RSA modulus is several thousands times harder to factor than a 512-bit one.
Because the first factorization of a 512-bit RSA modulus was reported only a decade ago it is not unreasonable to expect that 1024-bit RSA moduli can be factored well within the next decade by an academic effort such as ours .
. .
. Thus, it would be prudent to phase out usage of 1024-bit RSA within the next three to four years.
'"</sentencetext>
</article>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685700</id>
	<title>Re:Bad math...</title>
	<author>SoVeryTired</author>
	<datestamp>1262893260000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>You need to brush up on your exponents.</p><p>If a is some constant, then a^(n/b) = (a^(1/b))^n.<br>Define c = a^(1/b)<br>then<br>a^(n/b) = c^n</p><p>You can't just say "where a is constant". You need to specify a.</p></htmltext>
<tokenext>You need to brush up on your exponents.If a is some constant , then a ^ ( n/b ) = ( a ^ ( 1/b ) ) ^ n.Define c = a ^ ( 1/b ) thena ^ ( n/b ) = c ^ nYou ca n't just say " where a is constant " .
You need to specify a .</tokentext>
<sentencetext>You need to brush up on your exponents.If a is some constant, then a^(n/b) = (a^(1/b))^n.Define c = a^(1/b)thena^(n/b) = c^nYou can't just say "where a is constant".
You need to specify a.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684784</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685394</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Anonymous</author>
	<datestamp>1262891820000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>RSA uses semiprimes - numbers with only two prime factors. If you know the factors p and q, you can derive the private key from the public key through multiplication mod (p-1)(q-1).

There are much faster ways to factorize numbers than brute force - the best is the general number field sieve.

It is Diffie-Hellman which uses discrete logs. There are better attacks against discrete logs than brute force, too.

Once we have sufficiently powerful quantum computers, both the factorization problem and the discrete log problem will be made trivial by Schor's algorithm.</htmltext>
<tokenext>RSA uses semiprimes - numbers with only two prime factors .
If you know the factors p and q , you can derive the private key from the public key through multiplication mod ( p-1 ) ( q-1 ) .
There are much faster ways to factorize numbers than brute force - the best is the general number field sieve .
It is Diffie-Hellman which uses discrete logs .
There are better attacks against discrete logs than brute force , too .
Once we have sufficiently powerful quantum computers , both the factorization problem and the discrete log problem will be made trivial by Schor 's algorithm .</tokentext>
<sentencetext>RSA uses semiprimes - numbers with only two prime factors.
If you know the factors p and q, you can derive the private key from the public key through multiplication mod (p-1)(q-1).
There are much faster ways to factorize numbers than brute force - the best is the general number field sieve.
It is Diffie-Hellman which uses discrete logs.
There are better attacks against discrete logs than brute force, too.
Once we have sufficiently powerful quantum computers, both the factorization problem and the discrete log problem will be made trivial by Schor's algorithm.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684988</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684954</id>
	<title>Re:Bad math...</title>
	<author>jasonwc</author>
	<datestamp>1262889960000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>4</modscore>
	<htmltext><p>They're comparing the relative strength of a 768 bit RSA key to a 1024 bit RSA key. Because of the mathematical correlation between the public and private keys, the strength is nowhere near 2^768 or 2^1024. RSA has created a comparison table for RSA -&gt; symetric cipher strength.</p><p>1024 bit ----&gt; 80 bit<br>2048 bit  ----&gt; 112 bit<br>3072 bit ----&gt; 128 bit</p><p>However, "1000 times stronger" seems far too small, in any case.</p><p>Source: <a href="http://www.rsa.com/RSALABS/node.asp?id=2004" title="rsa.com">http://www.rsa.com/RSALABS/node.asp?id=2004</a> [rsa.com]</p></htmltext>
<tokenext>They 're comparing the relative strength of a 768 bit RSA key to a 1024 bit RSA key .
Because of the mathematical correlation between the public and private keys , the strength is nowhere near 2 ^ 768 or 2 ^ 1024 .
RSA has created a comparison table for RSA - &gt; symetric cipher strength.1024 bit ---- &gt; 80 bit2048 bit ---- &gt; 112 bit3072 bit ---- &gt; 128 bitHowever , " 1000 times stronger " seems far too small , in any case.Source : http : //www.rsa.com/RSALABS/node.asp ? id = 2004 [ rsa.com ]</tokentext>
<sentencetext>They're comparing the relative strength of a 768 bit RSA key to a 1024 bit RSA key.
Because of the mathematical correlation between the public and private keys, the strength is nowhere near 2^768 or 2^1024.
RSA has created a comparison table for RSA -&gt; symetric cipher strength.1024 bit ----&gt; 80 bit2048 bit  ----&gt; 112 bit3072 bit ----&gt; 128 bitHowever, "1000 times stronger" seems far too small, in any case.Source: http://www.rsa.com/RSALABS/node.asp?id=2004 [rsa.com]</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684708</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685998</id>
	<title>Re:Meanwhile in Canada...</title>
	<author>Anonymous</author>
	<datestamp>1262894460000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>You're so wrong I'm not bothering to provide a correction. If your laziness and opinionated ignorance is that great, it's probably a waste of time. Google is your friend.</p></htmltext>
<tokenext>You 're so wrong I 'm not bothering to provide a correction .
If your laziness and opinionated ignorance is that great , it 's probably a waste of time .
Google is your friend .</tokentext>
<sentencetext>You're so wrong I'm not bothering to provide a correction.
If your laziness and opinionated ignorance is that great, it's probably a waste of time.
Google is your friend.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685316</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30688382</id>
	<title>Re:Can someone explain this to me?</title>
	<author>tlhIngan</author>
	<datestamp>1262862900000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>What about how does this RSA-768 refer to the common RSA-128 "strong encryption" used in SSL/HTTPS?</p><p>Does the 128-bit mean a 128-bit key that can be trivially factored? Or is it something different?</p></htmltext>
<tokenext>What about how does this RSA-768 refer to the common RSA-128 " strong encryption " used in SSL/HTTPS ? Does the 128-bit mean a 128-bit key that can be trivially factored ?
Or is it something different ?</tokentext>
<sentencetext>What about how does this RSA-768 refer to the common RSA-128 "strong encryption" used in SSL/HTTPS?Does the 128-bit mean a 128-bit key that can be trivially factored?
Or is it something different?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30688014</id>
	<title>The Meaning of Factorization</title>
	<author>gratuitous\_arp</author>
	<datestamp>1262861340000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>RSA Labs explains the meaning of factorization in the old Challenge FAQ:</p><p><a href="http://www.rsa.com/rsalabs/node.asp?id=2094" title="rsa.com" rel="nofollow">http://www.rsa.com/rsalabs/node.asp?id=2094</a> [rsa.com]</p><p>Look at the section, "What does it mean when a Challenge Number is factored?"</p><p>It is interesting to note that this section of the FAQ makes an example of RSA-768 being cracked in 2010 -- turns out they were very close, whether they tried to be or not (the article states that the number was actually factored in Dec 2009).</p></htmltext>
<tokenext>RSA Labs explains the meaning of factorization in the old Challenge FAQ : http : //www.rsa.com/rsalabs/node.asp ? id = 2094 [ rsa.com ] Look at the section , " What does it mean when a Challenge Number is factored ?
" It is interesting to note that this section of the FAQ makes an example of RSA-768 being cracked in 2010 -- turns out they were very close , whether they tried to be or not ( the article states that the number was actually factored in Dec 2009 ) .</tokentext>
<sentencetext>RSA Labs explains the meaning of factorization in the old Challenge FAQ:http://www.rsa.com/rsalabs/node.asp?id=2094 [rsa.com]Look at the section, "What does it mean when a Challenge Number is factored?
"It is interesting to note that this section of the FAQ makes an example of RSA-768 being cracked in 2010 -- turns out they were very close, whether they tried to be or not (the article states that the number was actually factored in Dec 2009).</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685722</id>
	<title>Re:Meanwhile in Canada...</title>
	<author>canajin56</author>
	<datestamp>1262893380000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>That would be RBC<nobr> <wbr></nobr>;)  BMO uses 3DES-196, TD also uses AES-256, but with a 2048 cert.  Scotia Bank and CIBC use RC4-128 though.  I guess the OP uses one of those two, and figured "if my bank does this, they all must!"</htmltext>
<tokenext>That would be RBC ; ) BMO uses 3DES-196 , TD also uses AES-256 , but with a 2048 cert .
Scotia Bank and CIBC use RC4-128 though .
I guess the OP uses one of those two , and figured " if my bank does this , they all must !
"</tokentext>
<sentencetext>That would be RBC ;)  BMO uses 3DES-196, TD also uses AES-256, but with a 2048 cert.
Scotia Bank and CIBC use RC4-128 though.
I guess the OP uses one of those two, and figured "if my bank does this, they all must!
"</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684956</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30690024</id>
	<title>Re:Can someone explain this to me?</title>
	<author>selven</author>
	<datestamp>1262875080000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>2^84 atoms? That's only 32 moles! Did you mean 10^84 atoms?</p></htmltext>
<tokenext>2 ^ 84 atoms ?
That 's only 32 moles !
Did you mean 10 ^ 84 atoms ?</tokentext>
<sentencetext>2^84 atoms?
That's only 32 moles!
Did you mean 10^84 atoms?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685432</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30686066</id>
	<title>Re:The real scary part is 3 years to obsolecence</title>
	<author>EndlessNameless</author>
	<datestamp>1262894820000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Your sig makes your post exceptionally ironic.</p></htmltext>
<tokenext>Your sig makes your post exceptionally ironic .</tokentext>
<sentencetext>Your sig makes your post exceptionally ironic.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685224</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30687096</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Maladius</author>
	<datestamp>1262856660000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>In the observable universe, there are about 2^84 atoms</p></div><p>

Approximations of the number of atoms in the universe are around 10^80 minimum.<br>

<a href="http://en.wikipedia.org/wiki/Observable\_universe" title="wikipedia.org" rel="nofollow">http://en.wikipedia.org/wiki/Observable\_universe</a> [wikipedia.org] <br> <br>

That's still far less than 2^768 though.  So your original point still stands.<br>
That's a crazy realization though, that there literally wouldn't be enough atoms in the universe to store every number from 1 to 2^768.</p></div>
	</htmltext>
<tokenext>In the observable universe , there are about 2 ^ 84 atoms Approximations of the number of atoms in the universe are around 10 ^ 80 minimum .
http : //en.wikipedia.org/wiki/Observable \ _universe [ wikipedia.org ] That 's still far less than 2 ^ 768 though .
So your original point still stands .
That 's a crazy realization though , that there literally would n't be enough atoms in the universe to store every number from 1 to 2 ^ 768 .</tokentext>
<sentencetext>In the observable universe, there are about 2^84 atoms

Approximations of the number of atoms in the universe are around 10^80 minimum.
http://en.wikipedia.org/wiki/Observable\_universe [wikipedia.org]  

That's still far less than 2^768 though.
So your original point still stands.
That's a crazy realization though, that there literally wouldn't be enough atoms in the universe to store every number from 1 to 2^768.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685432</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684708</id>
	<title>Bad math...</title>
	<author>Anonymous</author>
	<datestamp>1262889000000</datestamp>
	<modclass>Funny</modclass>
	<modscore>1</modscore>
	<htmltext><p>WTF?  2^1024 != 2^768*1000</p><p>Screw you slashdot for making me type more than my perfectly concise statement above that gets the effing point across just fine.</p></htmltext>
<tokenext>WTF ?
2 ^ 1024 ! = 2 ^ 768 * 1000Screw you slashdot for making me type more than my perfectly concise statement above that gets the effing point across just fine .</tokentext>
<sentencetext>WTF?
2^1024 != 2^768*1000Screw you slashdot for making me type more than my perfectly concise statement above that gets the effing point across just fine.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30687362</id>
	<title>Re:Meanwhile in Canada...</title>
	<author>bytesex</author>
	<datestamp>1262857980000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Eh, the one doesn't really have anything to do with the other.  What you're talking about is 128 bit AES, which is symmetric encryption, which is shifting, xoring, and otherwise the making of chaotic of a block of data (16 bytes, in this case).  RSA asymmetric encryption/decryption is more like a calculation that you miss certain parts of and therefore can really only be performed one way.  To put it another way: symmetric encryption sees a block of data as a bits to be pushed around, while asymmetric encryption sees a block of data as a number to perform a calculation on.  A really big number.  Strengths of keys in amount of bits are useless in a comparison of both algorithms.</p></htmltext>
<tokenext>Eh , the one does n't really have anything to do with the other .
What you 're talking about is 128 bit AES , which is symmetric encryption , which is shifting , xoring , and otherwise the making of chaotic of a block of data ( 16 bytes , in this case ) .
RSA asymmetric encryption/decryption is more like a calculation that you miss certain parts of and therefore can really only be performed one way .
To put it another way : symmetric encryption sees a block of data as a bits to be pushed around , while asymmetric encryption sees a block of data as a number to perform a calculation on .
A really big number .
Strengths of keys in amount of bits are useless in a comparison of both algorithms .</tokentext>
<sentencetext>Eh, the one doesn't really have anything to do with the other.
What you're talking about is 128 bit AES, which is symmetric encryption, which is shifting, xoring, and otherwise the making of chaotic of a block of data (16 bytes, in this case).
RSA asymmetric encryption/decryption is more like a calculation that you miss certain parts of and therefore can really only be performed one way.
To put it another way: symmetric encryption sees a block of data as a bits to be pushed around, while asymmetric encryption sees a block of data as a number to perform a calculation on.
A really big number.
Strengths of keys in amount of bits are useless in a comparison of both algorithms.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684616</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685060</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Anonymous</author>
	<datestamp>1262890380000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>No. Factorization means that they split the product of two prime numbers into the constituent factors.<br>As you know now, the premise of RSA public key crypto lies in that it's hard to factorize "long" numbers<br>(768 bit long, in this case). They have shown that it's doable to factor a 768 bit long non-prime<br>number.</p><p>Keep in mind that proving non-primality and finding a factor are two separate issues. There are very<br>good primality tests that work in reasonable time on numbers tens of millions bit long (see GIMPS,<br>for example), yet (some/any) factors of those non-prime numbers are yet to be found, in most cases.</p></htmltext>
<tokenext>No .
Factorization means that they split the product of two prime numbers into the constituent factors.As you know now , the premise of RSA public key crypto lies in that it 's hard to factorize " long " numbers ( 768 bit long , in this case ) .
They have shown that it 's doable to factor a 768 bit long non-primenumber.Keep in mind that proving non-primality and finding a factor are two separate issues .
There are verygood primality tests that work in reasonable time on numbers tens of millions bit long ( see GIMPS,for example ) , yet ( some/any ) factors of those non-prime numbers are yet to be found , in most cases .</tokentext>
<sentencetext>No.
Factorization means that they split the product of two prime numbers into the constituent factors.As you know now, the premise of RSA public key crypto lies in that it's hard to factorize "long" numbers(768 bit long, in this case).
They have shown that it's doable to factor a 768 bit long non-primenumber.Keep in mind that proving non-primality and finding a factor are two separate issues.
There are verygood primality tests that work in reasonable time on numbers tens of millions bit long (see GIMPS,for example), yet (some/any) factors of those non-prime numbers are yet to be found, in most cases.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685196</id>
	<title>Re:Can someone explain this to me?</title>
	<author>shadow\_slicer</author>
	<datestamp>1262890980000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>No, 768-bit RSA is not broken. they just found the factors for a single number. It only took them 2.5 years, and over 5 terabytes of data too. I don't consider this making 768-bit RSA "broken" any more than 56bit DES is "broken", because they didn't find a way to solve it faster than brute force. The point is that it is now possible to solve this kind of problem. And if they can do it in 2.5 years with 3 supercomputers, a dedicated adversary could probably do it in a few months with a couple dozen.</p><p>Factorization is simply finding the prime factors of a number:<br>For example, the factors of n=21 are p=3 and q=7.</p><p>In RSA, I would take these factors and use them to calculate some other things:<br>I choose e=11 to be my public key exponent (since it is less than and shares no common factors with (7-1)*(3-1)). Then I would calculate my private key exponent "d" such that d*e=1 mod n: for example, d=2 would work.</p><p>So you announce n and e publicly. Someone can break your key if they can find d, which is equivalent to finding the two factors of n: p and q. So if I were to tell you 21, you have basically broken my private key once you know 3 and 7 are p and q.<br>In the article, it's not much different. Basically they found p and q for a 768-bit n.</p></htmltext>
<tokenext>No , 768-bit RSA is not broken .
they just found the factors for a single number .
It only took them 2.5 years , and over 5 terabytes of data too .
I do n't consider this making 768-bit RSA " broken " any more than 56bit DES is " broken " , because they did n't find a way to solve it faster than brute force .
The point is that it is now possible to solve this kind of problem .
And if they can do it in 2.5 years with 3 supercomputers , a dedicated adversary could probably do it in a few months with a couple dozen.Factorization is simply finding the prime factors of a number : For example , the factors of n = 21 are p = 3 and q = 7.In RSA , I would take these factors and use them to calculate some other things : I choose e = 11 to be my public key exponent ( since it is less than and shares no common factors with ( 7-1 ) * ( 3-1 ) ) .
Then I would calculate my private key exponent " d " such that d * e = 1 mod n : for example , d = 2 would work.So you announce n and e publicly .
Someone can break your key if they can find d , which is equivalent to finding the two factors of n : p and q. So if I were to tell you 21 , you have basically broken my private key once you know 3 and 7 are p and q.In the article , it 's not much different .
Basically they found p and q for a 768-bit n .</tokentext>
<sentencetext>No, 768-bit RSA is not broken.
they just found the factors for a single number.
It only took them 2.5 years, and over 5 terabytes of data too.
I don't consider this making 768-bit RSA "broken" any more than 56bit DES is "broken", because they didn't find a way to solve it faster than brute force.
The point is that it is now possible to solve this kind of problem.
And if they can do it in 2.5 years with 3 supercomputers, a dedicated adversary could probably do it in a few months with a couple dozen.Factorization is simply finding the prime factors of a number:For example, the factors of n=21 are p=3 and q=7.In RSA, I would take these factors and use them to calculate some other things:I choose e=11 to be my public key exponent (since it is less than and shares no common factors with (7-1)*(3-1)).
Then I would calculate my private key exponent "d" such that d*e=1 mod n: for example, d=2 would work.So you announce n and e publicly.
Someone can break your key if they can find d, which is equivalent to finding the two factors of n: p and q. So if I were to tell you 21, you have basically broken my private key once you know 3 and 7 are p and q.In the article, it's not much different.
Basically they found p and q for a 768-bit n.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685500</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Anonymous</author>
	<datestamp>1262892240000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>What they did is considerably more involved than "testing all the possible values". I've got a PhD in maths (wrong sort for what they're doing), and it will still take me a couple of hours (at least) to understand what they did and why it works. Its all tied into number field theory and other such fun. The basics seem to be finding solutions of u^2 = v^2 mod n over some smoothed approximation to the integers. u and v then have a beter than even chance of being factors of n. The tricky part is how you find trial values for u and v...</p><p>So, the short answer to "can someone explain this to me?" is "not without a course in number theory first".</p></htmltext>
<tokenext>What they did is considerably more involved than " testing all the possible values " .
I 've got a PhD in maths ( wrong sort for what they 're doing ) , and it will still take me a couple of hours ( at least ) to understand what they did and why it works .
Its all tied into number field theory and other such fun .
The basics seem to be finding solutions of u ^ 2 = v ^ 2 mod n over some smoothed approximation to the integers .
u and v then have a beter than even chance of being factors of n. The tricky part is how you find trial values for u and v...So , the short answer to " can someone explain this to me ?
" is " not without a course in number theory first " .</tokentext>
<sentencetext>What they did is considerably more involved than "testing all the possible values".
I've got a PhD in maths (wrong sort for what they're doing), and it will still take me a couple of hours (at least) to understand what they did and why it works.
Its all tied into number field theory and other such fun.
The basics seem to be finding solutions of u^2 = v^2 mod n over some smoothed approximation to the integers.
u and v then have a beter than even chance of being factors of n. The tricky part is how you find trial values for u and v...So, the short answer to "can someone explain this to me?
" is "not without a course in number theory first".</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684666</id>
	<title>Re:Meanwhile in Canada...</title>
	<author>jasonwc</author>
	<datestamp>1262888880000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>5</modscore>
	<htmltext><p>I hope this is a joke. If not, you are confusing the strength of symmetric key encryption and public key encryption. The latter requires larger key sizes because the public and private key pair are mathetmically related whereas in symmetric encryption, there is a single key, and it ought to be randomly generated, and have no mathematical relation to any other value.</p><p>The key sizes are given for RSA/DSA encryption. Elliptical curve crypto can use much smaller key sizes while maintaining equivalent security levels. Unfortunately, most ECC is patent encumbered.</p></htmltext>
<tokenext>I hope this is a joke .
If not , you are confusing the strength of symmetric key encryption and public key encryption .
The latter requires larger key sizes because the public and private key pair are mathetmically related whereas in symmetric encryption , there is a single key , and it ought to be randomly generated , and have no mathematical relation to any other value.The key sizes are given for RSA/DSA encryption .
Elliptical curve crypto can use much smaller key sizes while maintaining equivalent security levels .
Unfortunately , most ECC is patent encumbered .</tokentext>
<sentencetext>I hope this is a joke.
If not, you are confusing the strength of symmetric key encryption and public key encryption.
The latter requires larger key sizes because the public and private key pair are mathetmically related whereas in symmetric encryption, there is a single key, and it ought to be randomly generated, and have no mathematical relation to any other value.The key sizes are given for RSA/DSA encryption.
Elliptical curve crypto can use much smaller key sizes while maintaining equivalent security levels.
Unfortunately, most ECC is patent encumbered.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684616</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30687084</id>
	<title>Re:Can someone explain this to me?</title>
	<author>immakiku</author>
	<datestamp>1262856660000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Not exactly true, though the conclusion is almost correct. The problem is that the domain is not 2^768 large. Not all numbers 768 bits long are products of two primes.</htmltext>
<tokenext>Not exactly true , though the conclusion is almost correct .
The problem is that the domain is not 2 ^ 768 large .
Not all numbers 768 bits long are products of two primes .</tokentext>
<sentencetext>Not exactly true, though the conclusion is almost correct.
The problem is that the domain is not 2^768 large.
Not all numbers 768 bits long are products of two primes.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685432</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30686852</id>
	<title>Re:Bad math...</title>
	<author>pow(b,2)</author>
	<datestamp>1262855520000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>4</modscore>
	<htmltext>Cryptographic strength, as applied to RSA keys, is measured by the time needed to factor the public modulus.  The fastest way to do this is today is using the general number field sieve.  The run time of the general number field sieve can be estimated as T(b) = exp(1.923 * ln(2^b)^(1/3) * (ln( ln(2^b)))^(2/3)), where b is the size of the input in bits.  See Aoki's paper on a kilobit SNFS factorization for details.  Chug through this estimate for b = 1024 and b = 768, and you'll find that the ratio is approximately 1000 (I got 1221.15).  That's why 1024 bit RSA keys are approximately 1000 times stronger.</htmltext>
<tokenext>Cryptographic strength , as applied to RSA keys , is measured by the time needed to factor the public modulus .
The fastest way to do this is today is using the general number field sieve .
The run time of the general number field sieve can be estimated as T ( b ) = exp ( 1.923 * ln ( 2 ^ b ) ^ ( 1/3 ) * ( ln ( ln ( 2 ^ b ) ) ) ^ ( 2/3 ) ) , where b is the size of the input in bits .
See Aoki 's paper on a kilobit SNFS factorization for details .
Chug through this estimate for b = 1024 and b = 768 , and you 'll find that the ratio is approximately 1000 ( I got 1221.15 ) .
That 's why 1024 bit RSA keys are approximately 1000 times stronger .</tokentext>
<sentencetext>Cryptographic strength, as applied to RSA keys, is measured by the time needed to factor the public modulus.
The fastest way to do this is today is using the general number field sieve.
The run time of the general number field sieve can be estimated as T(b) = exp(1.923 * ln(2^b)^(1/3) * (ln( ln(2^b)))^(2/3)), where b is the size of the input in bits.
See Aoki's paper on a kilobit SNFS factorization for details.
Chug through this estimate for b = 1024 and b = 768, and you'll find that the ratio is approximately 1000 (I got 1221.15).
That's why 1024 bit RSA keys are approximately 1000 times stronger.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684708</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685672</id>
	<title>Re:Can someone explain this to me?</title>
	<author>morgan\_greywolf</author>
	<datestamp>1262893140000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Exactly.  They found p and q for <em>one</em> 768-bit n, and it took them 2.5 years, 3 supercomputers and 5 terabytes of data.  If your data is important enough for someone to spend these kind of resources, you simply choose a 1024-bit n, or, even better, a 2048-bit n.</p><p>If your data is <em>not</em> important enough for someone to spend those kind of resources, then you can continue with 768-bit RSA and suffer no ill effects.  If Moore's law holds true, you may want to consider upgrading to 1024-bit.  The truly paranoid will want to use 2048-bit n or larger.</p><p>To put it very briefly: nothing to see here, move along.</p></htmltext>
<tokenext>Exactly .
They found p and q for one 768-bit n , and it took them 2.5 years , 3 supercomputers and 5 terabytes of data .
If your data is important enough for someone to spend these kind of resources , you simply choose a 1024-bit n , or , even better , a 2048-bit n.If your data is not important enough for someone to spend those kind of resources , then you can continue with 768-bit RSA and suffer no ill effects .
If Moore 's law holds true , you may want to consider upgrading to 1024-bit .
The truly paranoid will want to use 2048-bit n or larger.To put it very briefly : nothing to see here , move along .</tokentext>
<sentencetext>Exactly.
They found p and q for one 768-bit n, and it took them 2.5 years, 3 supercomputers and 5 terabytes of data.
If your data is important enough for someone to spend these kind of resources, you simply choose a 1024-bit n, or, even better, a 2048-bit n.If your data is not important enough for someone to spend those kind of resources, then you can continue with 768-bit RSA and suffer no ill effects.
If Moore's law holds true, you may want to consider upgrading to 1024-bit.
The truly paranoid will want to use 2048-bit n or larger.To put it very briefly: nothing to see here, move along.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685196</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30696136</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Anonymous</author>
	<datestamp>1262972400000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>being pedantic I suppose, but you'd only need to store numbers up to sqrt(2^768)<br>(2^384) - within that if my math is right 3.4e113 is expected to be prime.</p><p>so more like a universe 1.7e88 times the size of ours =)</p></htmltext>
<tokenext>being pedantic I suppose , but you 'd only need to store numbers up to sqrt ( 2 ^ 768 ) ( 2 ^ 384 ) - within that if my math is right 3.4e113 is expected to be prime.so more like a universe 1.7e88 times the size of ours = )</tokentext>
<sentencetext>being pedantic I suppose, but you'd only need to store numbers up to sqrt(2^768)(2^384) - within that if my math is right 3.4e113 is expected to be prime.so more like a universe 1.7e88 times the size of ours =)</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685432</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684662</id>
	<title>Re:Meanwhile in Canada...</title>
	<author>Anonymous</author>
	<datestamp>1262888820000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I don't believe you. Post your account credentials so I can check for myself.</p></htmltext>
<tokenext>I do n't believe you .
Post your account credentials so I can check for myself .</tokentext>
<sentencetext>I don't believe you.
Post your account credentials so I can check for myself.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684616</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30686974</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Hawke</author>
	<datestamp>1262856180000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>It means they broke a 768-bit RSA key in 6 months.  As a practical matter, everyone has to have the information they had, so the decryption can be done offline.  They only used 80 computers, so assuming the task is linearly parallelizable (which I don't know), anyone who cares (and can afford 1000 high-end computers) can break a 768-bit RSA key in about 2 days or so.
</p><p>
Which means that a 1024-bit key is only safe for about 3 years.  (But 3 years of 1000 high-end computers dedicated to the task of breaking your key is still really expensive.  So that's probably pretty safe.  Stealing the computer with the private key is still cheaper).  But given the pace of technology and factoring techniques, that will likely come down.
</p><p>
4096-bit keys seem to be sufficiently safe for the foreseeable future.  (Didn't gpg used to mock you if you told it to create a key that large?)</p></htmltext>
<tokenext>It means they broke a 768-bit RSA key in 6 months .
As a practical matter , everyone has to have the information they had , so the decryption can be done offline .
They only used 80 computers , so assuming the task is linearly parallelizable ( which I do n't know ) , anyone who cares ( and can afford 1000 high-end computers ) can break a 768-bit RSA key in about 2 days or so .
Which means that a 1024-bit key is only safe for about 3 years .
( But 3 years of 1000 high-end computers dedicated to the task of breaking your key is still really expensive .
So that 's probably pretty safe .
Stealing the computer with the private key is still cheaper ) .
But given the pace of technology and factoring techniques , that will likely come down .
4096-bit keys seem to be sufficiently safe for the foreseeable future .
( Did n't gpg used to mock you if you told it to create a key that large ?
)</tokentext>
<sentencetext>It means they broke a 768-bit RSA key in 6 months.
As a practical matter, everyone has to have the information they had, so the decryption can be done offline.
They only used 80 computers, so assuming the task is linearly parallelizable (which I don't know), anyone who cares (and can afford 1000 high-end computers) can break a 768-bit RSA key in about 2 days or so.
Which means that a 1024-bit key is only safe for about 3 years.
(But 3 years of 1000 high-end computers dedicated to the task of breaking your key is still really expensive.
So that's probably pretty safe.
Stealing the computer with the private key is still cheaper).
But given the pace of technology and factoring techniques, that will likely come down.
4096-bit keys seem to be sufficiently safe for the foreseeable future.
(Didn't gpg used to mock you if you told it to create a key that large?
)</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685560</id>
	<title>Re:Can someone explain this to me?</title>
	<author>u38cg</author>
	<datestamp>1262892540000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Factorisation is just the process of splitting a number - say, 21 - into the numbers that multiply to produce it: 3*7=21.  It is cryptographically useful because it doesn't have a short way of doing it: you have to simply try dividing by 2, 3, 4, 5, etc, till you get an answer.  When you have a number that's several hundred digits long and only has two relatively large factors, this takes a very long time.  There are some tricks you can use to speed it up, but that's essentially it.</htmltext>
<tokenext>Factorisation is just the process of splitting a number - say , 21 - into the numbers that multiply to produce it : 3 * 7 = 21 .
It is cryptographically useful because it does n't have a short way of doing it : you have to simply try dividing by 2 , 3 , 4 , 5 , etc , till you get an answer .
When you have a number that 's several hundred digits long and only has two relatively large factors , this takes a very long time .
There are some tricks you can use to speed it up , but that 's essentially it .</tokentext>
<sentencetext>Factorisation is just the process of splitting a number - say, 21 - into the numbers that multiply to produce it: 3*7=21.
It is cryptographically useful because it doesn't have a short way of doing it: you have to simply try dividing by 2, 3, 4, 5, etc, till you get an answer.
When you have a number that's several hundred digits long and only has two relatively large factors, this takes a very long time.
There are some tricks you can use to speed it up, but that's essentially it.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685082</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Anonymous</author>
	<datestamp>1262890500000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>They factored a particular number named "RSA-768". They did this using a large but obtainable amount of computing power, meaning that RSA-768 probably shouldn't be used to protect secrets that are more valuable than the amount of computing power they expended (and given how easy it is to use bigger keys, they recommend doing that for everything).</p></htmltext>
<tokenext>They factored a particular number named " RSA-768 " .
They did this using a large but obtainable amount of computing power , meaning that RSA-768 probably should n't be used to protect secrets that are more valuable than the amount of computing power they expended ( and given how easy it is to use bigger keys , they recommend doing that for everything ) .</tokentext>
<sentencetext>They factored a particular number named "RSA-768".
They did this using a large but obtainable amount of computing power, meaning that RSA-768 probably shouldn't be used to protect secrets that are more valuable than the amount of computing power they expended (and given how easy it is to use bigger keys, they recommend doing that for everything).</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</id>
	<title>Can someone explain this to me?</title>
	<author>Monkeedude1212</author>
	<datestamp>1262889420000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>2</modscore>
	<htmltext><p>So I just did a Wikipedia Crash course on RSA (I knew it was for public/private key encryption) and how it all works mathematically.</p><p>But I still don't know what they mean by Factorization, or what that exactly means.</p><p>I'm guessing they found all and compiled and tested the possible values and now have a nice big chart? Is 768-bit RSA now considered "broken"?</p></htmltext>
<tokenext>So I just did a Wikipedia Crash course on RSA ( I knew it was for public/private key encryption ) and how it all works mathematically.But I still do n't know what they mean by Factorization , or what that exactly means.I 'm guessing they found all and compiled and tested the possible values and now have a nice big chart ?
Is 768-bit RSA now considered " broken " ?</tokentext>
<sentencetext>So I just did a Wikipedia Crash course on RSA (I knew it was for public/private key encryption) and how it all works mathematically.But I still don't know what they mean by Factorization, or what that exactly means.I'm guessing they found all and compiled and tested the possible values and now have a nice big chart?
Is 768-bit RSA now considered "broken"?</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30686086</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Anonymous</author>
	<datestamp>1262894940000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I don't really want to know how RSA and other encryption systems work as much as I want a simple table of settings/key sizes that will make me immune to advances in technology making them crackable without my having to learn the details of each cryptosystem.
</p><p>What is the minimum key length for each style of encryption that will mean that cracking the key with a Beowulf cluster of today's best technology would take longer than the age of the universe?
</p><p>I want to be able to encrypt my signed confession to assassinating President Oprah Winfrey, post it on usenet for posterity and be able to rest easy that not even the concerted effort of nations could uncover by secret by decrypting the file.
</p><p>Often the author of an encryption package will put a 'recommended value' in the documentation, but it's always with respect to the day's current technology.  I want confession goddamnit proof against anything short of discovering P=NP.  Speed is nice, slow is OK.  Absolutely reliable encryption from now and into the future for at least 100 years is a must.</p></htmltext>
<tokenext>I do n't really want to know how RSA and other encryption systems work as much as I want a simple table of settings/key sizes that will make me immune to advances in technology making them crackable without my having to learn the details of each cryptosystem .
What is the minimum key length for each style of encryption that will mean that cracking the key with a Beowulf cluster of today 's best technology would take longer than the age of the universe ?
I want to be able to encrypt my signed confession to assassinating President Oprah Winfrey , post it on usenet for posterity and be able to rest easy that not even the concerted effort of nations could uncover by secret by decrypting the file .
Often the author of an encryption package will put a 'recommended value ' in the documentation , but it 's always with respect to the day 's current technology .
I want confession goddamnit proof against anything short of discovering P = NP .
Speed is nice , slow is OK. Absolutely reliable encryption from now and into the future for at least 100 years is a must .</tokentext>
<sentencetext>I don't really want to know how RSA and other encryption systems work as much as I want a simple table of settings/key sizes that will make me immune to advances in technology making them crackable without my having to learn the details of each cryptosystem.
What is the minimum key length for each style of encryption that will mean that cracking the key with a Beowulf cluster of today's best technology would take longer than the age of the universe?
I want to be able to encrypt my signed confession to assassinating President Oprah Winfrey, post it on usenet for posterity and be able to rest easy that not even the concerted effort of nations could uncover by secret by decrypting the file.
Often the author of an encryption package will put a 'recommended value' in the documentation, but it's always with respect to the day's current technology.
I want confession goddamnit proof against anything short of discovering P=NP.
Speed is nice, slow is OK.  Absolutely reliable encryption from now and into the future for at least 100 years is a must.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684988</id>
	<title>Re:Can someone explain this to me?</title>
	<author>bytethese</author>
	<datestamp>1262890080000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Don't worry, I'm puzzled by this too.  My profs in school taught us that RSA can't be broken unless you know how to solve discrete logarithms so I am unsure what factoring has to do with it?  Although I suppose if I know all the factors of a certain number, I could try to test all possible relatively prime inverses...</htmltext>
<tokenext>Do n't worry , I 'm puzzled by this too .
My profs in school taught us that RSA ca n't be broken unless you know how to solve discrete logarithms so I am unsure what factoring has to do with it ?
Although I suppose if I know all the factors of a certain number , I could try to test all possible relatively prime inverses.. .</tokentext>
<sentencetext>Don't worry, I'm puzzled by this too.
My profs in school taught us that RSA can't be broken unless you know how to solve discrete logarithms so I am unsure what factoring has to do with it?
Although I suppose if I know all the factors of a certain number, I could try to test all possible relatively prime inverses...</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685030</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Mini-Geek</author>
	<datestamp>1262890320000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>4</modscore>
	<htmltext><p>What they did was factor a 768-bit number, like one that could be used as a 768-bit RSA public key.  e.g. to factor 15, you need to find that it is equal to 3*5, which can be easily done by dividing the first few primes and finding that 3 divides 15.  To factor a very large number, like a 768-bit number that is semiprime with the two factors both about the same size, (as is the case with RSA public keys) is a very difficult task.  It is currently best done by the General Number Field Sieve (GNFS).  For more info on any of these concepts, use Wikipedia.<br>This demonstrates the possibility of breaking any given 768-bit RSA key by factoring the public modulus, and shows how much work that takes.  Note, however, that it is still very difficult, and in this case took multiple years of calendar time and hundreds of years of CPU time to crack.<br>This does not mean that every 768-bit RSA key can be cracked any more easily than it could before, it just demonstrates that we have the ability to crack any 768-bit RSA key (given the time and resources).</p></htmltext>
<tokenext>What they did was factor a 768-bit number , like one that could be used as a 768-bit RSA public key .
e.g. to factor 15 , you need to find that it is equal to 3 * 5 , which can be easily done by dividing the first few primes and finding that 3 divides 15 .
To factor a very large number , like a 768-bit number that is semiprime with the two factors both about the same size , ( as is the case with RSA public keys ) is a very difficult task .
It is currently best done by the General Number Field Sieve ( GNFS ) .
For more info on any of these concepts , use Wikipedia.This demonstrates the possibility of breaking any given 768-bit RSA key by factoring the public modulus , and shows how much work that takes .
Note , however , that it is still very difficult , and in this case took multiple years of calendar time and hundreds of years of CPU time to crack.This does not mean that every 768-bit RSA key can be cracked any more easily than it could before , it just demonstrates that we have the ability to crack any 768-bit RSA key ( given the time and resources ) .</tokentext>
<sentencetext>What they did was factor a 768-bit number, like one that could be used as a 768-bit RSA public key.
e.g. to factor 15, you need to find that it is equal to 3*5, which can be easily done by dividing the first few primes and finding that 3 divides 15.
To factor a very large number, like a 768-bit number that is semiprime with the two factors both about the same size, (as is the case with RSA public keys) is a very difficult task.
It is currently best done by the General Number Field Sieve (GNFS).
For more info on any of these concepts, use Wikipedia.This demonstrates the possibility of breaking any given 768-bit RSA key by factoring the public modulus, and shows how much work that takes.
Note, however, that it is still very difficult, and in this case took multiple years of calendar time and hundreds of years of CPU time to crack.This does not mean that every 768-bit RSA key can be cracked any more easily than it could before, it just demonstrates that we have the ability to crack any 768-bit RSA key (given the time and resources).</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30687346</id>
	<title>Very large numbers are awesome.</title>
	<author>Anonymous</author>
	<datestamp>1262857860000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Whenever something comes up involving work with very large numbers, I have to try to explain this seemingly simple concept to people and usually they look at me like I'm either insane or an idiot. The people that have a decent grasp of math and some common sense, though, get their minds blown and have a new respect for encryption, which is rewarding.</p></htmltext>
<tokenext>Whenever something comes up involving work with very large numbers , I have to try to explain this seemingly simple concept to people and usually they look at me like I 'm either insane or an idiot .
The people that have a decent grasp of math and some common sense , though , get their minds blown and have a new respect for encryption , which is rewarding .</tokentext>
<sentencetext>Whenever something comes up involving work with very large numbers, I have to try to explain this seemingly simple concept to people and usually they look at me like I'm either insane or an idiot.
The people that have a decent grasp of math and some common sense, though, get their minds blown and have a new respect for encryption, which is rewarding.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685432</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684744</id>
	<title>Re:Meanwhile in Canada...</title>
	<author>Anonymous</author>
	<datestamp>1262889120000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Don't worry, your money will be safe in my offshore account.</p></htmltext>
<tokenext>Do n't worry , your money will be safe in my offshore account .</tokentext>
<sentencetext>Don't worry, your money will be safe in my offshore account.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684616</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30686486</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Anonymous</author>
	<datestamp>1262897160000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><i>But I still don't know what they mean by Factorization, or what that exactly means.</i> <br>
<br>
I don't necessarily mean to pick on you, but this post is mostly in response to a number of the other posts below yours that seem to be confused on the subject, too. There seem to be a lot of other people posting here that clearly have some sort of CS and programming backgrounds that don't seem to understand factorization either. And yet somehow this is something that I learned about in high school (and it was covered in a few math classes in college, too). I've never taken a CS class in my life, but I am able to follow the general ideas of what the article is talking about. Why is it that people that specifically work in the field that this applies to don't seem to understand these concepts very well?</htmltext>
<tokenext>But I still do n't know what they mean by Factorization , or what that exactly means .
I do n't necessarily mean to pick on you , but this post is mostly in response to a number of the other posts below yours that seem to be confused on the subject , too .
There seem to be a lot of other people posting here that clearly have some sort of CS and programming backgrounds that do n't seem to understand factorization either .
And yet somehow this is something that I learned about in high school ( and it was covered in a few math classes in college , too ) .
I 've never taken a CS class in my life , but I am able to follow the general ideas of what the article is talking about .
Why is it that people that specifically work in the field that this applies to do n't seem to understand these concepts very well ?</tokentext>
<sentencetext>But I still don't know what they mean by Factorization, or what that exactly means.
I don't necessarily mean to pick on you, but this post is mostly in response to a number of the other posts below yours that seem to be confused on the subject, too.
There seem to be a lot of other people posting here that clearly have some sort of CS and programming backgrounds that don't seem to understand factorization either.
And yet somehow this is something that I learned about in high school (and it was covered in a few math classes in college, too).
I've never taken a CS class in my life, but I am able to follow the general ideas of what the article is talking about.
Why is it that people that specifically work in the field that this applies to don't seem to understand these concepts very well?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685448</id>
	<title>Re:Meanwhile in Canada...</title>
	<author>morgan\_greywolf</author>
	<datestamp>1262892120000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>3</modscore>
	<htmltext><blockquote><div><p>Unfortunately, most ECC is patent encumbered.</p></div></blockquote><p>Well, djb wrote a particular algorithm, <a href="http://cr.yp.to/ecdh.html" title="cr.yp.to" rel="nofollow">Curve25519</a> [cr.yp.to], that's in the public domain.</p><p>(Yeah, yeah, save your comments about djb's personality.  Like it or not, the guy's a crypto and security genius.)</p></div>
	</htmltext>
<tokenext>Unfortunately , most ECC is patent encumbered.Well , djb wrote a particular algorithm , Curve25519 [ cr.yp.to ] , that 's in the public domain .
( Yeah , yeah , save your comments about djb 's personality .
Like it or not , the guy 's a crypto and security genius .
)</tokentext>
<sentencetext>Unfortunately, most ECC is patent encumbered.Well, djb wrote a particular algorithm, Curve25519 [cr.yp.to], that's in the public domain.
(Yeah, yeah, save your comments about djb's personality.
Like it or not, the guy's a crypto and security genius.
)
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684666</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684860</id>
	<title>Re:Bad math...</title>
	<author>Anonymous</author>
	<datestamp>1262889540000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>They just took the line from the abstract in the paper.</p></htmltext>
<tokenext>They just took the line from the abstract in the paper .</tokentext>
<sentencetext>They just took the line from the abstract in the paper.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684708</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30686542</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Anonymous</author>
	<datestamp>1262897400000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>In college I wrote a Python program capable of factoring primes up to 1024 bits long.  It ran fairly quickly. I should dig out that program, and post it here for peer review.  I think you'll find some cleverness in the algorithm used.</p><p>Oh here it is.</p><p><tt><br># Title:   Circular Imaginary Number Prime Factorization Program.<br># Released under the GPL<br>#<br># Uses imaginary numbers, ratio of circumference to diameter in<br># the calculation of the factors of a prime number.<br>#<br># Able to factor prime numbers as large as 1024 bits and up<br>#<br># Key in your input in either decimal or binary</tt></p><p><tt># Runs in O() time.</tt></p><p><tt>import math</tt></p><p><tt>def exponentiate(num, exponent):<br>
&nbsp; &nbsp; &nbsp; &nbsp; """exponentiate function, starts at 1, and multiplies by num<br>
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; as many times as exponent tells you to.<br>
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Needed as a function, since ^ operator doesn't work on<br>
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; complex numbers."""<br>
&nbsp; &nbsp; &nbsp; &nbsp; result = 1<br>
&nbsp; &nbsp; &nbsp; &nbsp; for x in range(exponent.real):<br>
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; result = result * num<br>
&nbsp; &nbsp; &nbsp; &nbsp; return result</tt></p><p><tt>primenum = int(raw\_input("Please enter a really big prime number: "))<br>factors = []<br>i = complex(0,1)</tt></p><p><tt>for factor\_candidate in range ((exponentiate(math.e,math.pi*i)),2):<br>
&nbsp; &nbsp; &nbsp; &nbsp; if primenum \% factor\_candidate == 0:<br>
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; factors.extend([factor\_candidate, primenum/factor\_candidate])<br>print factors<br></tt></p></htmltext>
<tokenext>In college I wrote a Python program capable of factoring primes up to 1024 bits long .
It ran fairly quickly .
I should dig out that program , and post it here for peer review .
I think you 'll find some cleverness in the algorithm used.Oh here it is. # Title : Circular Imaginary Number Prime Factorization Program. # Released under the GPL # # Uses imaginary numbers , ratio of circumference to diameter in # the calculation of the factors of a prime number. # # Able to factor prime numbers as large as 1024 bits and up # # Key in your input in either decimal or binary # Runs in O ( ) time.import mathdef exponentiate ( num , exponent ) :         " " " exponentiate function , starts at 1 , and multiplies by num               as many times as exponent tells you to .
              Needed as a function , since ^ operator does n't work on               complex numbers .
" " "         result = 1         for x in range ( exponent.real ) :                 result = result * num         return resultprimenum = int ( raw \ _input ( " Please enter a really big prime number : " ) ) factors = [ ] i = complex ( 0,1 ) for factor \ _candidate in range ( ( exponentiate ( math.e,math.pi * i ) ) ,2 ) :         if primenum \ % factor \ _candidate = = 0 :                 factors.extend ( [ factor \ _candidate , primenum/factor \ _candidate ] ) print factors</tokentext>
<sentencetext>In college I wrote a Python program capable of factoring primes up to 1024 bits long.
It ran fairly quickly.
I should dig out that program, and post it here for peer review.
I think you'll find some cleverness in the algorithm used.Oh here it is.# Title:   Circular Imaginary Number Prime Factorization Program.# Released under the GPL## Uses imaginary numbers, ratio of circumference to diameter in# the calculation of the factors of a prime number.## Able to factor prime numbers as large as 1024 bits and up## Key in your input in either decimal or binary# Runs in O() time.import mathdef exponentiate(num, exponent):
        """exponentiate function, starts at 1, and multiplies by num
              as many times as exponent tells you to.
              Needed as a function, since ^ operator doesn't work on
              complex numbers.
"""
        result = 1
        for x in range(exponent.real):
                result = result * num
        return resultprimenum = int(raw\_input("Please enter a really big prime number: "))factors = []i = complex(0,1)for factor\_candidate in range ((exponentiate(math.e,math.pi*i)),2):
        if primenum \% factor\_candidate == 0:
                factors.extend([factor\_candidate, primenum/factor\_candidate])print factors</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685316</id>
	<title>Re:Meanwhile in Canada...</title>
	<author>xZgf6xHx2uhoAj9D</author>
	<datestamp>1262891520000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Keep in mind that AES-256 only uses a 128-bit key and has recently been broken (down to 118 bits of security or something like that?). AES-256 is currently less secure than AES-128.</htmltext>
<tokenext>Keep in mind that AES-256 only uses a 128-bit key and has recently been broken ( down to 118 bits of security or something like that ? ) .
AES-256 is currently less secure than AES-128 .</tokentext>
<sentencetext>Keep in mind that AES-256 only uses a 128-bit key and has recently been broken (down to 118 bits of security or something like that?).
AES-256 is currently less secure than AES-128.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684956</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685188</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Anonymous</author>
	<datestamp>1262890980000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>1</modscore>
	<htmltext><p>No, solving discrete logarithms allows you to break the El Gamal public key encryption system.  Like prime factorization, the discrete logarithm problem is considered "hard".</p></htmltext>
<tokenext>No , solving discrete logarithms allows you to break the El Gamal public key encryption system .
Like prime factorization , the discrete logarithm problem is considered " hard " .</tokentext>
<sentencetext>No, solving discrete logarithms allows you to break the El Gamal public key encryption system.
Like prime factorization, the discrete logarithm problem is considered "hard".</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684988</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30690064</id>
	<title>Re:The real scary part is 3 years to obsolecence</title>
	<author>Eil</author>
	<datestamp>1262875680000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>My take on it has been this: If a larger key length doesn't incur a significant performance or storage penalty, use it. There's always the outward chance that a weakness in the algorithm (or more likely, the implementation that you're using) will contain a flaw that reduces the effective key length. For example, it is believed that brute-forcing AES 128-bit symmetric encryption would take more energy than exists in the known universe. Yet, almost all implementations offer a 256-bit key length. If a shortcut is found that reduces the effective key length of AES by 128 bits, then anyone using a 256-bit key is still fully protected. On modern hardware, the performance difference between the two is completely negligible so there's not really a good argument against using a 256-bit key except that it's probably overkill from a theoretical standpoint.</p><p>(Disclaimer to the greater Slashdot audience: I'm an amateur at encryption but I'm always willing to learn more, so if I've got something wrong please correct me rather than insulting me.)</p></htmltext>
<tokenext>My take on it has been this : If a larger key length does n't incur a significant performance or storage penalty , use it .
There 's always the outward chance that a weakness in the algorithm ( or more likely , the implementation that you 're using ) will contain a flaw that reduces the effective key length .
For example , it is believed that brute-forcing AES 128-bit symmetric encryption would take more energy than exists in the known universe .
Yet , almost all implementations offer a 256-bit key length .
If a shortcut is found that reduces the effective key length of AES by 128 bits , then anyone using a 256-bit key is still fully protected .
On modern hardware , the performance difference between the two is completely negligible so there 's not really a good argument against using a 256-bit key except that it 's probably overkill from a theoretical standpoint .
( Disclaimer to the greater Slashdot audience : I 'm an amateur at encryption but I 'm always willing to learn more , so if I 've got something wrong please correct me rather than insulting me .
)</tokentext>
<sentencetext>My take on it has been this: If a larger key length doesn't incur a significant performance or storage penalty, use it.
There's always the outward chance that a weakness in the algorithm (or more likely, the implementation that you're using) will contain a flaw that reduces the effective key length.
For example, it is believed that brute-forcing AES 128-bit symmetric encryption would take more energy than exists in the known universe.
Yet, almost all implementations offer a 256-bit key length.
If a shortcut is found that reduces the effective key length of AES by 128 bits, then anyone using a 256-bit key is still fully protected.
On modern hardware, the performance difference between the two is completely negligible so there's not really a good argument against using a 256-bit key except that it's probably overkill from a theoretical standpoint.
(Disclaimer to the greater Slashdot audience: I'm an amateur at encryption but I'm always willing to learn more, so if I've got something wrong please correct me rather than insulting me.
)</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685224</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30686794</id>
	<title>Re:The real scary part is 3 years to obsolecence</title>
	<author>JDeane</author>
	<datestamp>1262855280000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Your post gave me a great idea...</p><p>Sure your account may be empty and cracking the encryption not worth it.</p><p>but I am sure that there would be more then 10 million dollars worth of accounts in the banking computer.</p><p>So why not try to crack them all at one time? What I mean is that if a key does not work for say your encrypted account or what ever try the same key on all the accounts. Probably faster that way then then to try all the keys on one account.</p><p>Of course this all assumes unfettered access to a banks computer, and at that point it may just be easier to rob the local Quicky Mart.</p><p>Now for downloaded<nobr> <wbr></nobr>.gov files thats a whole different mess. Pretty much the more secret something is they should encrypt the hell out of it pick some number of bits that makes it so hard to crack that by the time they do the information will be 50 years old.</p><p>I think for something to remain that secret the encryption should be measured in MB's not bits. I like the idea of a random location in a Mandelbrot sequence used as key but that might be too easy to crack (I am not a math person when it comes to stuff like this the hardest encryption I ever cracked in my entire life was the Captain Crunch hidden letter crap.. lol) So yeah it could be way too easy for all I know.  but I think cracking it would look awesome lol</p></htmltext>
<tokenext>Your post gave me a great idea...Sure your account may be empty and cracking the encryption not worth it.but I am sure that there would be more then 10 million dollars worth of accounts in the banking computer.So why not try to crack them all at one time ?
What I mean is that if a key does not work for say your encrypted account or what ever try the same key on all the accounts .
Probably faster that way then then to try all the keys on one account.Of course this all assumes unfettered access to a banks computer , and at that point it may just be easier to rob the local Quicky Mart.Now for downloaded .gov files thats a whole different mess .
Pretty much the more secret something is they should encrypt the hell out of it pick some number of bits that makes it so hard to crack that by the time they do the information will be 50 years old.I think for something to remain that secret the encryption should be measured in MB 's not bits .
I like the idea of a random location in a Mandelbrot sequence used as key but that might be too easy to crack ( I am not a math person when it comes to stuff like this the hardest encryption I ever cracked in my entire life was the Captain Crunch hidden letter crap.. lol ) So yeah it could be way too easy for all I know .
but I think cracking it would look awesome lol</tokentext>
<sentencetext>Your post gave me a great idea...Sure your account may be empty and cracking the encryption not worth it.but I am sure that there would be more then 10 million dollars worth of accounts in the banking computer.So why not try to crack them all at one time?
What I mean is that if a key does not work for say your encrypted account or what ever try the same key on all the accounts.
Probably faster that way then then to try all the keys on one account.Of course this all assumes unfettered access to a banks computer, and at that point it may just be easier to rob the local Quicky Mart.Now for downloaded .gov files thats a whole different mess.
Pretty much the more secret something is they should encrypt the hell out of it pick some number of bits that makes it so hard to crack that by the time they do the information will be 50 years old.I think for something to remain that secret the encryption should be measured in MB's not bits.
I like the idea of a random location in a Mandelbrot sequence used as key but that might be too easy to crack (I am not a math person when it comes to stuff like this the hardest encryption I ever cracked in my entire life was the Captain Crunch hidden letter crap.. lol) So yeah it could be way too easy for all I know.
but I think cracking it would look awesome lol</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685810</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684948</id>
	<title>New algorithms?</title>
	<author>Jonas Buyl</author>
	<datestamp>1262889900000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>3</modscore>
	<htmltext>1024 bit RSA keys are already considered insecure due to the possibility of finding more efficient algorithms.
2048 is considered secure enough.</htmltext>
<tokenext>1024 bit RSA keys are already considered insecure due to the possibility of finding more efficient algorithms .
2048 is considered secure enough .</tokentext>
<sentencetext>1024 bit RSA keys are already considered insecure due to the possibility of finding more efficient algorithms.
2048 is considered secure enough.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30687358</id>
	<title>Re:The real scary part is 3 years to obsolecence</title>
	<author>sp3d2orbit</author>
	<datestamp>1262857980000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>At my bank $47.32 + overdraft fees ~= $10 M</p></htmltext>
<tokenext>At my bank $ 47.32 + overdraft fees ~ = $ 10 M</tokentext>
<sentencetext>At my bank $47.32 + overdraft fees ~= $10 M</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685810</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685810</id>
	<title>Re:The real scary part is 3 years to obsolecence</title>
	<author>FrankSchwab</author>
	<datestamp>1262893680000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>4</modscore>
	<htmltext><p>In the security world, there's always a tradeoff between the cost of the security, the cost to an attacker to break the security, and the value of the thing being protected.</p><p>In the military world, there are many secrets which need to be (are seen as needing to be) kept for many years.  For these, an encryption that takes a year and $10M to break may not be good enough, because after a year and $10M, an enemy might have information worth more than that.  For my bank account, encryption that takes a year and $10M to break is more than sufficient, because the value to an attacker is approximately $47.32, plus the overdraft fees that they can stick me with.</p><p>There is no current concern for the average person, unless you're dealing in nuclear secrets or are protecting a politicians date book.  Given a choice in the future, moving to a larger RSA key size is prudent change, but that's about it.</p><p><nobr> <wbr></nobr>/frank</p></htmltext>
<tokenext>In the security world , there 's always a tradeoff between the cost of the security , the cost to an attacker to break the security , and the value of the thing being protected.In the military world , there are many secrets which need to be ( are seen as needing to be ) kept for many years .
For these , an encryption that takes a year and $ 10M to break may not be good enough , because after a year and $ 10M , an enemy might have information worth more than that .
For my bank account , encryption that takes a year and $ 10M to break is more than sufficient , because the value to an attacker is approximately $ 47.32 , plus the overdraft fees that they can stick me with.There is no current concern for the average person , unless you 're dealing in nuclear secrets or are protecting a politicians date book .
Given a choice in the future , moving to a larger RSA key size is prudent change , but that 's about it .
/frank</tokentext>
<sentencetext>In the security world, there's always a tradeoff between the cost of the security, the cost to an attacker to break the security, and the value of the thing being protected.In the military world, there are many secrets which need to be (are seen as needing to be) kept for many years.
For these, an encryption that takes a year and $10M to break may not be good enough, because after a year and $10M, an enemy might have information worth more than that.
For my bank account, encryption that takes a year and $10M to break is more than sufficient, because the value to an attacker is approximately $47.32, plus the overdraft fees that they can stick me with.There is no current concern for the average person, unless you're dealing in nuclear secrets or are protecting a politicians date book.
Given a choice in the future, moving to a larger RSA key size is prudent change, but that's about it.
/frank</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685224</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30686626</id>
	<title>Re:Can someone explain this to me?</title>
	<author>vxice</author>
	<datestamp>1262897700000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Breaking RSA encryption will become much easier once quantum computing becomes realistic.  When factoring large numbers the bottleneck is in data transfer if using multiple computers which is almost required due to processing requirements.  Quantum computing allows for better data transfer rates and there are already algorithms that take advantage of this and have been proven in theory but until we get our hands on quantum computing rsa will remain secure.</htmltext>
<tokenext>Breaking RSA encryption will become much easier once quantum computing becomes realistic .
When factoring large numbers the bottleneck is in data transfer if using multiple computers which is almost required due to processing requirements .
Quantum computing allows for better data transfer rates and there are already algorithms that take advantage of this and have been proven in theory but until we get our hands on quantum computing rsa will remain secure .</tokentext>
<sentencetext>Breaking RSA encryption will become much easier once quantum computing becomes realistic.
When factoring large numbers the bottleneck is in data transfer if using multiple computers which is almost required due to processing requirements.
Quantum computing allows for better data transfer rates and there are already algorithms that take advantage of this and have been proven in theory but until we get our hands on quantum computing rsa will remain secure.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685432</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Digital\_Quartz</author>
	<datestamp>1262892000000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>4</modscore>
	<htmltext><p>Other people have explained factorization in this thread (finding the prime factors that make up a composite number), but I just wanted to point out why making a "nice big chart" won't work.</p><p>The "nice big chart" would have to be very big.  If you wanted to factor all the numbers from 1 to 2^768, you'd need a chart with 2^768 entries on it.  This chart would need to be made of something, or stored on a disk that was made of something.  Made of something means it needs to be made of matter, which means it needs to be made of atoms.  In the observable universe, there are about 2^84 atoms, so you'd need a universe around 8x10^205 times larger than ours to store the chart in.</p></htmltext>
<tokenext>Other people have explained factorization in this thread ( finding the prime factors that make up a composite number ) , but I just wanted to point out why making a " nice big chart " wo n't work.The " nice big chart " would have to be very big .
If you wanted to factor all the numbers from 1 to 2 ^ 768 , you 'd need a chart with 2 ^ 768 entries on it .
This chart would need to be made of something , or stored on a disk that was made of something .
Made of something means it needs to be made of matter , which means it needs to be made of atoms .
In the observable universe , there are about 2 ^ 84 atoms , so you 'd need a universe around 8x10 ^ 205 times larger than ours to store the chart in .</tokentext>
<sentencetext>Other people have explained factorization in this thread (finding the prime factors that make up a composite number), but I just wanted to point out why making a "nice big chart" won't work.The "nice big chart" would have to be very big.
If you wanted to factor all the numbers from 1 to 2^768, you'd need a chart with 2^768 entries on it.
This chart would need to be made of something, or stored on a disk that was made of something.
Made of something means it needs to be made of matter, which means it needs to be made of atoms.
In the observable universe, there are about 2^84 atoms, so you'd need a universe around 8x10^205 times larger than ours to store the chart in.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685580</id>
	<title>Re:The real scary part is 3 years to obsolecence</title>
	<author>Anonymous</author>
	<datestamp>1262892660000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p><div class="quote"><p>I'd agree with that for government and it's true that the military should phase out 1024, but does the general public need to worry?</p></div><p>Yes, what could the general public possibly fear from ubiquitous monitoring by the government or military?</p></div>
	</htmltext>
<tokenext>I 'd agree with that for government and it 's true that the military should phase out 1024 , but does the general public need to worry ? Yes , what could the general public possibly fear from ubiquitous monitoring by the government or military ?</tokentext>
<sentencetext>I'd agree with that for government and it's true that the military should phase out 1024, but does the general public need to worry?Yes, what could the general public possibly fear from ubiquitous monitoring by the government or military?
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685224</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684784</id>
	<title>Re:Bad math...</title>
	<author>marcosdumay</author>
	<datestamp>1262889300000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Yep, but factoration also isn't O(a^n) where a is constant. It is more like O(a^(n/b)) where b is quite bigger than 1.</p></htmltext>
<tokenext>Yep , but factoration also is n't O ( a ^ n ) where a is constant .
It is more like O ( a ^ ( n/b ) ) where b is quite bigger than 1 .</tokentext>
<sentencetext>Yep, but factoration also isn't O(a^n) where a is constant.
It is more like O(a^(n/b)) where b is quite bigger than 1.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684708</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684616</id>
	<title>Meanwhile in Canada...</title>
	<author>Anonymous</author>
	<datestamp>1262888640000</datestamp>
	<modclass>Troll</modclass>
	<modscore>-1</modscore>
	<htmltext><p>We are forced to use 128-bit encryption for online banking!</p></htmltext>
<tokenext>We are forced to use 128-bit encryption for online banking !</tokentext>
<sentencetext>We are forced to use 128-bit encryption for online banking!</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30686586</id>
	<title>Re:Can someone explain this to me?</title>
	<author>marcosdumay</author>
	<datestamp>1262897520000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Well, 768 was never a standard length for RSA. Everything smaler than 1024 bits was considered broken long ago (512 was broken a few years ago). What this really means is that we should stop using 1024 bits already, and standardize on 2048. By the way, 2048 bits RSA is expected to never be broken on Earth (if we ever go to space and start gathering the majority of the power released by a star, things change), but nobody is really certain.</htmltext>
<tokenext>Well , 768 was never a standard length for RSA .
Everything smaler than 1024 bits was considered broken long ago ( 512 was broken a few years ago ) .
What this really means is that we should stop using 1024 bits already , and standardize on 2048 .
By the way , 2048 bits RSA is expected to never be broken on Earth ( if we ever go to space and start gathering the majority of the power released by a star , things change ) , but nobody is really certain .</tokentext>
<sentencetext>Well, 768 was never a standard length for RSA.
Everything smaler than 1024 bits was considered broken long ago (512 was broken a few years ago).
What this really means is that we should stop using 1024 bits already, and standardize on 2048.
By the way, 2048 bits RSA is expected to never be broken on Earth (if we ever go to space and start gathering the majority of the power released by a star, things change), but nobody is really certain.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684956</id>
	<title>Re:Meanwhile in Canada...</title>
	<author>havock</author>
	<datestamp>1262889960000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>We are forced to use 128-bit encryption for online banking!</p></div><p>Maybe you need to get a better bank!  I just logged into a top 5 Canadian bank and they are using AES-256 with a 1024-bit RSA cert.</p></div>
	</htmltext>
<tokenext>We are forced to use 128-bit encryption for online banking ! Maybe you need to get a better bank !
I just logged into a top 5 Canadian bank and they are using AES-256 with a 1024-bit RSA cert .</tokentext>
<sentencetext>We are forced to use 128-bit encryption for online banking!Maybe you need to get a better bank!
I just logged into a top 5 Canadian bank and they are using AES-256 with a 1024-bit RSA cert.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684616</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685064</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Sir\_Lewk</author>
	<datestamp>1262890440000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>The very short version of it is that a private key is a set of two very large prime numbers.  The public key is these two prime numbers multiplied together.  If you have the public key, and are able to factor it, you can determine the private key.</p><p>The security of RSA relies on the assumption that integer factorization is hard.  So far that assumption, at least publically, has not been shown false (unless you have a quantum computer).</p></htmltext>
<tokenext>The very short version of it is that a private key is a set of two very large prime numbers .
The public key is these two prime numbers multiplied together .
If you have the public key , and are able to factor it , you can determine the private key.The security of RSA relies on the assumption that integer factorization is hard .
So far that assumption , at least publically , has not been shown false ( unless you have a quantum computer ) .</tokentext>
<sentencetext>The very short version of it is that a private key is a set of two very large prime numbers.
The public key is these two prime numbers multiplied together.
If you have the public key, and are able to factor it, you can determine the private key.The security of RSA relies on the assumption that integer factorization is hard.
So far that assumption, at least publically, has not been shown false (unless you have a quantum computer).</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685004</id>
	<title>Re:Can someone explain this to me?</title>
	<author>jonbryce</author>
	<datestamp>1262890200000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I think it means you can find the private key for a given public key.</p></htmltext>
<tokenext>I think it means you can find the private key for a given public key .</tokentext>
<sentencetext>I think it means you can find the private key for a given public key.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684814</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30687426</id>
	<title>Re:Can someone explain this to me?</title>
	<author>hivebrain</author>
	<datestamp>1262858280000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Or you could just store it on the Amazon cloud. Their 5 gazillabyte plan will run you about $40/month.</htmltext>
<tokenext>Or you could just store it on the Amazon cloud .
Their 5 gazillabyte plan will run you about $ 40/month .</tokentext>
<sentencetext>Or you could just store it on the Amazon cloud.
Their 5 gazillabyte plan will run you about $40/month.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685432</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30689146</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Anonymous</author>
	<datestamp>1262867280000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Then gzip it. Duh.</p><p>(Kidding!)</p></htmltext>
<tokenext>Then gzip it .
Duh. ( Kidding ! )</tokentext>
<sentencetext>Then gzip it.
Duh.(Kidding!)</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685432</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30689914</id>
	<title>Re:Can someone explain this to me?</title>
	<author>TubeSteak</author>
	<datestamp>1262874120000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>The "nice big chart" would have to be very big. If you wanted to factor all the numbers from 1 to 2^768, you'd need a chart with 2^768 entries on it.</p></div><p>Why would you need a chart that big?<br>Can't you ignore everything that ends in a 0, 2, 4, 5, 6, 8?</p><p>I mean, we're only trying to factor prime numbers.</p></div>
	</htmltext>
<tokenext>The " nice big chart " would have to be very big .
If you wanted to factor all the numbers from 1 to 2 ^ 768 , you 'd need a chart with 2 ^ 768 entries on it.Why would you need a chart that big ? Ca n't you ignore everything that ends in a 0 , 2 , 4 , 5 , 6 , 8 ? I mean , we 're only trying to factor prime numbers .</tokentext>
<sentencetext>The "nice big chart" would have to be very big.
If you wanted to factor all the numbers from 1 to 2^768, you'd need a chart with 2^768 entries on it.Why would you need a chart that big?Can't you ignore everything that ends in a 0, 2, 4, 5, 6, 8?I mean, we're only trying to factor prime numbers.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685432</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685668</id>
	<title>Re:New algorithms?</title>
	<author>Dc0der</author>
	<datestamp>1262893140000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Due to the possibility of finding more efficient algorithms? Wouldn't that rule out RSA-any size?

1024 bit RSA keys are considered mildly secure because they are breakable with a large budget.</htmltext>
<tokenext>Due to the possibility of finding more efficient algorithms ?
Would n't that rule out RSA-any size ?
1024 bit RSA keys are considered mildly secure because they are breakable with a large budget .</tokentext>
<sentencetext>Due to the possibility of finding more efficient algorithms?
Wouldn't that rule out RSA-any size?
1024 bit RSA keys are considered mildly secure because they are breakable with a large budget.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684948</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685630</id>
	<title>Re:Meanwhile in Canada...</title>
	<author>FrankSchwab</author>
	<datestamp>1262892960000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>uhh, no.</p><p>AES-256 uses a 256 bit key.  It may have a weaker than expected key schedule for using that key, as Schneier has opined (do I know what that means?  Not a chance), but it's certainly 256 bits long.</p></htmltext>
<tokenext>uhh , no.AES-256 uses a 256 bit key .
It may have a weaker than expected key schedule for using that key , as Schneier has opined ( do I know what that means ?
Not a chance ) , but it 's certainly 256 bits long .</tokentext>
<sentencetext>uhh, no.AES-256 uses a 256 bit key.
It may have a weaker than expected key schedule for using that key, as Schneier has opined (do I know what that means?
Not a chance), but it's certainly 256 bits long.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685316</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30691122</id>
	<title>Re:Can someone explain this to me?</title>
	<author>Anonymous</author>
	<datestamp>1262889360000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p><div class="quote"><p>In the observable universe, there are about 2^84 atoms</p></div><p>Fyi: It's actually about <a href="http://en.wikipedia.org/wiki/Observable\_universe" title="wikipedia.org" rel="nofollow">10^80 atoms in the observable universe</a> [wikipedia.org] (or about 2^265).</p></div>
	</htmltext>
<tokenext>In the observable universe , there are about 2 ^ 84 atomsFyi : It 's actually about 10 ^ 80 atoms in the observable universe [ wikipedia.org ] ( or about 2 ^ 265 ) .</tokentext>
<sentencetext>In the observable universe, there are about 2^84 atomsFyi: It's actually about 10^80 atoms in the observable universe [wikipedia.org] (or about 2^265).
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685432</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685444</id>
	<title>Re:Meanwhile in Canada...</title>
	<author>FrozenGeek</author>
	<datestamp>1262892120000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>128-bit keys for symmetric ciphers, such as we use for banking equate to much large key sizes for asymmetric ciphers such as RSA.  You are comparing apples and volkswagens.</htmltext>
<tokenext>128-bit keys for symmetric ciphers , such as we use for banking equate to much large key sizes for asymmetric ciphers such as RSA .
You are comparing apples and volkswagens .</tokentext>
<sentencetext>128-bit keys for symmetric ciphers, such as we use for banking equate to much large key sizes for asymmetric ciphers such as RSA.
You are comparing apples and volkswagens.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684616</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30687136</id>
	<title>Oblig. Futurama reference</title>
	<author>TeethWhitener</author>
	<datestamp>1262856900000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Or you could just use tiny atoms...but have you priced those lately?  I'm not made of money!</htmltext>
<tokenext>Or you could just use tiny atoms...but have you priced those lately ?
I 'm not made of money !</tokentext>
<sentencetext>Or you could just use tiny atoms...but have you priced those lately?
I'm not made of money!</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685432</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30685224</id>
	<title>The real scary part is 3 years to obsolecence</title>
	<author>DRAGONWEEZEL</author>
	<datestamp>1262891160000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>2</modscore>
	<htmltext><p>I'd agree with that for government and it's true that the military should phase out 1024, but does the general public need to worry?</p></htmltext>
<tokenext>I 'd agree with that for government and it 's true that the military should phase out 1024 , but does the general public need to worry ?</tokentext>
<sentencetext>I'd agree with that for government and it's true that the military should phase out 1024, but does the general public need to worry?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_01_07_1623249.30684948</parent>
</comment>
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