#77509 - juhees - Sat Apr 01, 2006 11:20 am
Hi,
i know, to crack a 1024 bit RSA key, we would have to check more numbers than atoms in the universe, BUT I was playing around with the key (the product of two big primes) and tried to find a solution for a*b = k (the known public key). I did not hope to find a solution, but to learn how to use the "bc" calculator, and guess what I found?
a =
105585499982697987150302742596036754462491173795986168307898
590572004889536263305147743017778828404557598884236595602855
38234849852189997276834260028430687
b =
105585499982697987150302742596036754462491173795986168307898
590572004889536263305415983697778830451357598886704619670924
56366414547309997276834273192471743
and a*b =
111482978065963166448159401053987664865250747451870159571865
610207644772561635570253159303861190826434252083206471998560
282985792642904433969730984843889689744431579849179209131364
493925652202239667375639502471788081466018568323285024036120
583023229016467698646091304701751747802730476179051116322834
881577441
== the key! whoo!
I have to get an unflashed DS or unflash mine to test it, but isn't that great news?
#77511 - lockwood - Sat Apr 01, 2006 11:50 am
roflmao I hate the 1st of april
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#77522 - Dan2552 - Sat Apr 01, 2006 2:40 pm
:'( you make me upset. i would've fallen for that
thank you lockwood
Last edited by Dan2552 on Sat Apr 01, 2006 3:27 pm; edited 1 time in total
#77525 - quadomatic - Sat Apr 01, 2006 2:49 pm
amazing how we always find out this stuff on april fools
#77530 - Critical_Impact - Sat Apr 01, 2006 3:37 pm
Ya mums an unsigned key
#77533 - juhees - Sat Apr 01, 2006 4:15 pm
I should have posted this a day later :-(
just look that number up in your firmware...
#77537 - Dan2552 - Sat Apr 01, 2006 4:33 pm
theres no point trying to continue it
#77602 - HyperHacker - Sat Apr 01, 2006 10:34 pm
| juhees wrote: |
I should have posted this a day later :-(
just look that number up in your firmware... |
But what byte order is it in??? :-p
#77613 - derula - Sat Apr 01, 2006 11:58 pm
| juhees wrote: |
Hi,
i know, to crack a 1024 bit RSA key, we would have to check more numbers than atoms in the universe, BUT I was playing around with the key (the product of two big primes) and tried to find a solution for a*b = k (the known public key). I did not hope to find a solution, but to learn how to use the "bc" calculator, and guess what I found?
a =
105585499982697987150302742596036754462491173795986168307898
590572004889536263305147743017778828404557598884236595602855
38234849852189997276834260028430687
b =
105585499982697987150302742596036754462491173795986168307898
590572004889536263305415983697778830451357598886704619670924
56366414547309997276834273192471743
and a*b =
111482978065963166448159401053987664865250747451870159571865
610207644772561635570253159303861190826434252083206471998560
282985792642904433969730984843889689744431579849179209131364
493925652202239667375639502471788081466018568323285024036120
583023229016467698646091304701751747802730476179051116322834
881577441
== the key! whoo!
I have to get an unflashed DS or unflash mine to test it, but isn't that great news? |
well, if the calculator source i found worked right, the two numbers you wrote are
325096266295131568936506258036059150029170437081654095710511
303451686845071524860787170427732217758189067857547641385705
760215155833286443142470915765760871788081466018568323285024
036120583023229016467698646091304701751747802730476179051116
322834881577441
when multiplicated.
I got the calculator source from here:
http://www.jonietz.de/jufo/1999a/node14.html#SECTION00060000000000000000
So 2 Possibilities:
1) Aprils fool.
2) The source is buggy.
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#77614 - swimgod - Sun Apr 02, 2006 12:03 am
worst day to release anything cool,
is today >.<;
so even if this was true...
to many people would hate you for talking about it today :P
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#77618 - caitsith2 - Sun Apr 02, 2006 12:16 am
About half of that large number will match the public key that resides in the firmware.
Additionally, he had chosen one number reletively close to the square root of that public key, that is a prime number, to make this somewhat believable.
integer sqrt of public key =
105585499982697987150302742596036754462491173795986168307898
590572004889536263305281863357778829427957598885470607636889
97800632199749997276834265312634192
#77619 - tepples - Sun Apr 02, 2006 12:19 am
| derula wrote: |
| juhees wrote: | a =
10558549998269798715[...]
b =
10558549998269798715[...]
and a*b =
11148297806596316644[...]
== the key! whoo! |
well, if the calculator source i found worked right, the two numbers you wrote are
32509626629513156893[...]
when multiplicated.
|
Use estimation. Try multiplying the first digits of each number and seeing if they are close to the purported result:
1055855 * 1055855 = 1114829781025 which agrees with the first 9 digits.
To verify every single solitary digit, I whip out the copy of Waterloo Maple that I got from school nearly seven years ago.
| Code: |
a := 1055854999826979871503027425960367544624\
911737959861683078985905720048895362633051477\
430177788284045575988842365956028553823484985\
2189997276834260028430687:
b := 10558549998269798715030274259603675446249\
1173795986168307898590572004889536263305415983\
6977788304513575988867046196709245636641454730\
9997276834273192471743:
ab := 1114829780659631664481594010539876648652\
5074745187015957186561020764477256163557025315\
9303861190826434252083206471998560282985792642\
9044339697309848438896897444315798491792091313\
6449392565220223966737563950247178808146601856\
8323285024036120583023229016467698646091304701\
751747802730476179051116322834881577441:
ab - a*b; |
Result: 0
Magic 8-ball says 2), or 3) you're using it wrong.
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#77639 - DS_XRAY - Sun Apr 02, 2006 3:25 am
at leased make something up that is like 1/10th believable. that was truly GAY , and not in the "hey im a guy who likes another guy" gay, I mean REALLY GAY as in "oh my god that was freaking GAY"
Happy 1st to you all.......
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#77640 - ultrablade - Sun Apr 02, 2006 3:27 am
OMG, I pissed in my pants!!! :(
j/k
ultrablADe
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#77674 - juhees - Sun Apr 02, 2006 10:08 am
| derula wrote: |
So 2 Possibilities:
1) Aprils fool.
2) The source is buggy. |
Ok, you've got me. But your source isn't correct too. The big number is realy the product of the two primes(?). I don't know if they are prime, but you can't divide them by a small number, so they look prime, Also, the real DS key start with the same digits (about half my number) and ends with the same 8 or so digits.
Happy 1. of April ;-)
#77679 - caitsith2 - Sun Apr 02, 2006 11:12 am
I had realized it was an April Fools joke, but the first thing I checked, was which of those two numbers were prime. A is prime, and B is not.
I also realized a few other things that might help with real cracking efforts. First off, one of the big numbers has to be larger than the integer square root of the Public Key, and the other number has to be smaller than the integer square root of the public key.
These are some of the numbers I have calculated related only to the NDS public Key of
111482978065963166448159401053987664865250747451870159571865
610207644772561635570253159303861190826434252083206471998560
293544342641174232684761231697361515939493559021955858591799
675033756462619574266417068557327049761687073845029179630942
911859660409475012129117554371096286193769012197625090764164
881577441.
| Code: |
Minimum Prime Number Possible for NDS Public Key:
831478036144872333037004465455783709208146380670042660400106
391771882090517282250173233505851720070199574737853375531500
1567006448839137929683878719575339
Prime Number before square root of NDS Public Key:
105585499982697987150302742596036754462491173795986168307898
590572004889536263305281863357778829427957598885470607636889
97800632199749997276834265312634103.
Prime Number after square root of NDS Public Key:
105585499982697987150302742596036754462491173795986168307898
590572004889536263305281863357778829427957598885470607636889
97800632199749997276834265312634249.
Maximum Prime Number Possible for NDS Public Key:
134078079299425970995740249982058461274793658205923933777235
614437217640300735469768018742981669034276900318581864860508
53753882811946569946433649006083527
Difference of Minimal Prime and Square Root Prime:
224376963682107538466022960504583835416765357289819022678879
513948166804845350802645400071936574209376414116852700837399
6233625750910859347150386593058764.
Difference of Square Root Prime and Maximal Prime:
284925793167279838454375073860217068123024844099377654693370
238652127507644721644861553852028396063193014331112572236185
5953250612196572669599383693449278. |
Or if you prefer these numbers in Hex,
Public Key:
9EC1CCC04A6BD0A06D62ED5F15678712
E6F4771FD85C81CE0CD02231F58908F5
BE04CBC14F63D95A98FFEB360F9C5DAD
15B999FBC6862C0A0CFCE6860360D487
28D566429CF704144E6F7320C33E3FF5
822E7818D6CDD5C2DCAA1D3491EC99C9
F7BFBFA00E1EF025F866175434282D28
A3AEF0A9FA3A7056D234A9C59E5DF5E1
| Code: |
Minimum Prime Number Possible for NDS Public Key:
9EC1CCC04A6BD0A06D62ED5F15678712
E6F4771FD85C81CE0CD02231F58908F5
BE04CBC14F63D95A98FFEB360F9C5DAD
15B999FBC6862C0A0CFCE6860360D52B
Prime Number before square root of NDS Public Key:
C9991E09C9FEC5A73F96233A80D79944
4B19C13826A76521DF152A98FB5E95E5
81C698D7D168A74CC25800B59850C10D
C05EE41F30282D90A35F00725731A4F7
Prime Number after square root of NDS Public Key:
C9991E09C9FEC5A73F96233A80D79944
4B19C13826A76521DF152A98FB5E95E5
81C698D7D168A74CC25800B59850C10D
C05EE41F30282D90A35F00725731A589
Maximum Prime Number Possible for NDS Public Key:
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7
Difference of Minimal Prime and Square Root Prime:
2AD751497F92F506D23335DB6B701231
64254A184E4AE353D245086705D58CEF
C3C1CD168204CDF22958157F88B46360
AAA54A2369A20186966219EC53D0CFCC
Difference of Square Root Prime and Maximal Prime:
3666E1F636013A58C069DCC57F2866BB
B4E63EC7D9589ADE20EAD56704A16A1A
7E3967282E9758B33DA7FF4A67AF3EF2
3FA11BE0CFD7D26F5CA0FF8DA8CE583E |
The first 50 and the last byte of the hex result of his A*B match the Hex public Key. In the case of the decimal public key, First 121 digits and last 10 digits match.
#77715 - shaz - Sun Apr 02, 2006 4:14 pm
I can't stand maths...
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#77725 - derula - Sun Apr 02, 2006 5:49 pm
| caitsith2 wrote: |
| Code: | Difference of Minimal Prime and Square Root Prime:
224376963682107538466022960504583835416765357289819022678879
513948166804845350802645400071936574209376414116852700837399
6233625750910859347150386593058764.
Difference of Square Root Prime and Maximal Prime:
284925793167279838454375073860217068123024844099377654693370
238652127507644721644861553852028396063193014331112572236185
5953250612196572669599383693449278. |
|
That means we "only" would have to check in a range of about 51*10^161 for prime numbers? The half of it is dividable by 2, so we have about 25*10^161 posibilities. A third of it is dividable by three. That would give a sequence like:
a(n)=a(n-1)(1-1/n); a(1)=51*10^161
a(n)=a(n-1)*(n-1)/n
analyzing (n-1)/n:
1/2 * 2/3 * ... * (n-1)/n = 1/n
So: a(n)=51*10^161/n
Maximum n would be the minimal prime. So we would only have to check
a(83*10^161)=51/83<1 Prime number! That's so easy.
(I know this is wrong, that's the purpose of it ^^)
Well @original post: I don't think Nintendo would be stupid enough to take 2 numbers that get so close to the square root (and to each other). Wouldn't that be TWO easy?
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#77752 - Dan2552 - Sun Apr 02, 2006 9:55 pm
Someone should setup a folding program so we can all donate idle CPU to cracking this...
#77755 - juhees - Sun Apr 02, 2006 10:04 pm
| derula wrote: |
| Well @original post: I don't think Nintendo would be stupid enough to take 2 numbers that get so close to the square root (and to each other). Wouldn't that be TWO easy? |
too easy? The square root of the (original) key is bigger than a, it's a differece of 1.34 * 10^67 ! I tested how long it takes to check 10^5 numbers on a 2.2 GHz Pentium: 63 sec. (bc)
We would only check every secound number, so that would take (on one PC): 11986301369863013698630136986301369863013698630136986 years
And that's with that "easy" number ;-)
Only to check the prime will not work too, because to if a number is prime would take too long...
The cheapest and fastest way to let everyone enjoy homebrew, without forcing them to buy extra hardware would be to buy a few million DSes, flash them and give them to everyone for free ;-)
#77756 - Dan2552 - Sun Apr 02, 2006 10:10 pm
| juhees wrote: |
| derula wrote: | | Well @original post: I don't think Nintendo would be stupid enough to take 2 numbers that get so close to the square root (and to each other). Wouldn't that be TWO easy? |
too easy? The square root of the (original) key is bigger than a, it's a differece of 1.34 * 10^67 ! I tested how long it takes to check 10^5 numbers on a 2.2 GHz Pentium: 63 sec. (bc)
We would only check every secound number, so that would take (on one PC): 11986301369863013698630136986301369863013698630136986 years
And that's with that "easy" number ;-)
Only to check the prime will not work too, because to if a number is prime would take too long...
The cheapest and fastest way to let everyone enjoy homebrew, without forcing them to buy extra hardware would be to buy a few million DSes, flash them and give them to everyone for free ;-) |
Do it!
#77763 - HyperHacker - Sun Apr 02, 2006 10:36 pm
| Dan2552 wrote: |
| Someone should setup a folding program so we can all donate idle CPU to cracking this... |
It's been discussed. We'd need practically every computer on the planet.
Hm, who's up for writing a worm? ;-)
#77848 - derula - Mon Apr 03, 2006 4:08 pm
Yes, seems that this was what I wanted to say lol...
| HyperHacker wrote: |
It's been discussed. We'd need practically every computer on the planet.
Hm, who's up for writing a worm? ;-) |
How many supercomputers are there on the planet? Assuming we caught all of them with that worm _and_ all other PCs (including PDAs and stuff, and *ix systems), how long would it take?
How long would it take if we managed all of the above plus using 100% system usage of every PC plus keeping them from shutting down? ;)
And, who is going to write the rootkit worm for *ix systems (and who assures all *ix developers are busy so they can't fix the bug in time?)
Argh, I guess it would be easier to build a quantum computer with enough power to crack the two primes in much less time.
Who is going to build the quantum computer? ;)
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#77850 - Lynx - Mon Apr 03, 2006 4:15 pm
Well, if nobody puts the program together (not a worm, just a cracker) it'll never happen. This is the ONLY Fact listed in any of these posts that can determine the time needed to crack the encryption. This is the same conversation we had over the DS cart encryption..
If nothing else, it'll be fun to see who can process the most amount of data. Just like the last "race".
#77852 - juhees - Mon Apr 03, 2006 4:27 pm
| Lynx wrote: |
Well, if nobody puts the program together (not a worm, just a cracker) it'll never happen. This is the ONLY Fact listed in any of these posts that can determine the time needed to crack the encryption. This is the same conversation we had over the DS cart encryption..
If nothing else, it'll be fun to see who can process the most amount of data. Just like the last "race". |
You can't compare this key problem with the DS cart encryption. We had both keys, one to encrypt the data and one to decrypt it for the card (they were somewhere in the DS/cart and the algorithsm was not known).
But here, we need one of those keys. It's a simple math equation and it is well known, that it's a hard problem.It isn't a problem that can be solved in a few thousand years (unless you find a better algorithm for that).
#77987 - loading - Tue Apr 04, 2006 11:46 am
well there are quite a few rsa factoring tools (google rsatool 2.14) it takes a few seconds to factor a lame 128 bit key with current pc, hours for a 256bit key and we are talking about a 2048bit (right?) key here. exponential growth is a bitch
| Quote: |
| Who is going to build the quantum computer? ;) |
working on that but so far i am only in phase 1 studing physics ;)
#77988 - Dan2552 - Tue Apr 04, 2006 12:01 pm
well if we do folding at least theres a small chance that one person's PC will randomly pick the correct one even in a few seconds :p i doubt thats got a high chance though, but still...
#78006 - caitsith2 - Tue Apr 04, 2006 2:36 pm
| loading wrote: |
| well there are quite a few rsa factoring tools (google rsatool 2.14) it takes a few seconds to factor a lame 128 bit key with current pc, hours for a 256bit key and we are talking about a 2048bit (right?) key here. exponential growth is a bitch |
Uhm, close, 1024 bit key, but yeah, exponential growth is a bitch.
#78038 - derula - Tue Apr 04, 2006 8:14 pm
| Dan2552 wrote: |
| well if we do folding at least theres a small chance that one person's PC will randomly pick the correct one even in a few seconds :p i doubt thats got a high chance though, but still... |
I think it would be easier if we all played lotto once. We would win billions and could be some super high speed multi processored computer that could solve it in a few hundred years. It think we had a higher chance to do so than to get the primes by chance... hadn't we?
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#78135 - Dan2552 - Wed Apr 05, 2006 10:18 am
| derula wrote: |
| Dan2552 wrote: | | well if we do folding at least theres a small chance that one person's PC will randomly pick the correct one even in a few seconds :p i doubt thats got a high chance though, but still... |
I think it would be easier if we all played lotto once. We would win billions and could be some super high speed multi processored computer that could solve it in a few hundred years. It think we had a higher chance to do so than to get the primes by chance... hadn't we? |
hmm. which do we have more chance, cracking this or winning the lottery? Cracking this seems a more cheaper method... If we had enough to buy all those lottery tickets we could just put our money together and make a super computer :/
#78148 - tepples - Wed Apr 05, 2006 1:32 pm
With the money for buying a really big supercomputer, you could buy a heck of a lot of Nintendo stock.
_________________
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-- Who?
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-- I think he moved to Tilwick.
#78199 - SeanMon - Wed Apr 05, 2006 10:16 pm
... or buy lots of official devkits.
#78275 - Frz - Thu Apr 06, 2006 11:33 am
| Quote: |
| Dan2552 wrote: |
I think it would be easier if we all played lotto once. We would win billions and could be some super high speed multi processored computer that could solve it in a few hundred years. It think we had a higher chance to do so than to get the primes by chance... hadn't we? |
hmm. which do we have more chance, cracking this or winning the lottery? Cracking this seems a more cheaper method... If we had enough to buy all those lottery tickets we could just put our money together and make a super computer :/ |
Solving this in a few hundered years doesn't sound that good o.o I mean it's 2048 and not 1024bit o.o" since you can crack 1024bit keys with a computer worth about a billion $ in one day you'd need to invest A LOT MORE to crack 2048bit keys in 100 hundred years o.o
#78278 - Dan2552 - Thu Apr 06, 2006 12:01 pm
| Frz wrote: |
| Quote: |
| Dan2552 wrote: |
I think it would be easier if we all played lotto once. We would win billions and could be some super high speed multi processored computer that could solve it in a few hundred years. It think we had a higher chance to do so than to get the primes by chance... hadn't we? |
hmm. which do we have more chance, cracking this or winning the lottery? Cracking this seems a more cheaper method... If we had enough to buy all those lottery tickets we could just put our money together and make a super computer :/ |
Solving this in a few hundered years doesn't sound that good o.o I mean it's 2048 and not 1024bit o.o" since you can crack 1024bit keys with a computer worth about a billion $ in one day you'd need to invest A LOT MORE to crack 2048bit keys in 100 hundred years o.o |
I think you screwed up a bit with those quotes btw :S
+ also, someone said it was 1024, not 2048
#78293 - Roc - Thu Apr 06, 2006 3:54 pm
Maybe Nintendo will be kind enough to release the key once the DS is end-of-life'ed :)
#78302 - derula - Thu Apr 06, 2006 4:26 pm
| Roc wrote: |
| Maybe Nintendo will be kind enough to release the key once the DS is end-of-life'ed :) |
I don't think so, really
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#78347 - tepples - Fri Apr 07, 2006 12:15 am
| Roc wrote: |
| Maybe Nintendo will be kind enough to release the key once the DS is end-of-life'ed :) |
The original Nintendo Entertainment System has been EOL'd for over a decade, but where's the source code for the 10NES program in the NES CIC lockout chip?
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#78520 - derula - Fri Apr 07, 2006 9:23 pm
You know what I'm wondering?
I coded an app that calculates all prime numbers between 2 and a given number (I didn't read anything about what algorythm should be used, I just did it my way). Then I expanded the app to calculate the time needed to calculate the primes, and to draw the results in a graph. from the resulting graph you could assume exponential growth, but when you let it calculate k (that k from f(x)=e^(k*x)), then it is not konstant, meaning it is not an exponential growth. That's somehow logical, because we all know, prime numbers get more and more rare the higher we get. That strikes me somewhat. I'll next let the app paint a graph of k, and look at that.
I know that it's senseless, but it is fun ^^
edit: the exponential growth constant seems to be exponentially falling lol.
edit: no that's not true. I should let it draw the derivation.
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#78748 - ricbit - Sun Apr 09, 2006 1:16 pm
The number of primes between 2 and n is more or less n/(ln n). Please see http://mathworld.wolfram.com/PrimeNumberTheorem.html
#78751 - zzo38computer - Sun Apr 09, 2006 2:35 pm
Maybe you could crack it if you had a quantum computer. Unfortunately, it is hard to isolate qubits in a quantum computer from being damaged by thermal energy around it
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#78768 - derula - Sun Apr 09, 2006 5:32 pm
so... the growth of the numbers of primes nears to a linear growth? so a good prime calculating algorythm should also have a linear growth of calculating time for high values of n? or am i wrong?
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#78805 - HyperHacker - Sun Apr 09, 2006 11:02 pm
You know, you might save a bit of time if you had a big list of prime numbers already. That'd save you having to calculate them.
#78832 - tepples - Mon Apr 10, 2006 2:30 am
Nobody has that list of all prime numbers between 2^400 and 2^624. I don't even know if such a list would be helpful.
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#78875 - juhees - Mon Apr 10, 2006 10:18 am
| tepples wrote: |
| Nobody has that list of all prime numbers between 2^400 and 2^624. I don't even know if such a list would be helpful. |
So, one number is 50-78 bytes.
(2^624)/ln(2^624) = 1.6096e+185
(2^400)/ln(2^400) = 9.3135e+117
So we would have to save 1.6096e+185 - 9.3135e+117 = 1.6096e+185 primes, each 50-78 bytes big. If we save each prime in 78 byte, that would be a list of 1.0385e+163 Yotabyte. If we only save the difference between two primes (say 1,1,2,2,4 instead of 2,3,5,7,11) in two bytes, that would still be 2.6629e+161 Yotabytes.
(btw, the list goes: giga, tera, peta, exa, zetta, yota)
If every atom(!) could save 2.6629e+83 yotabyte, we would need to use the whole universe as a harddrive...
So, brute force on a 1024bit RSA is not an option...
#78915 - derula - Mon Apr 10, 2006 4:11 pm
lol...
I like this thread.
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#78942 - Netix Riqua - Mon Apr 10, 2006 8:15 pm
yay im ina forum where geniuses are. thats a good thing i guess btw the byte transraction rate is 1024 bytes and we can brute force it by human brain as well (we'll go insane but... whatever) just think tha uhmm after checking thetopic review i found it stupid to ask for a human to calculate that.
#79138 - Lynx - Tue Apr 11, 2006 8:42 pm
It only takes 1 lucky guess.. :)
#79153 - juhees - Tue Apr 11, 2006 10:14 pm
| Lynx wrote: |
| It only takes 1 lucky guess.. :) |
give me a nondeterministic turing maschine and i'll do it in no time ;-)
#79157 - tepples - Tue Apr 11, 2006 10:27 pm
| Lynx wrote: |
| It only takes 1 lucky guess.. :) |
Winning Powerball, a big multi-state lottery in the United States, requires matching a 55 choose 5 and a 42 choose 1, for 27.12 bits of information. Imagine winning the lottery 38 times in a row.
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#79196 - Lynx - Wed Apr 12, 2006 2:05 am
Ok, I just imagined it.. now what?
#79224 - waruwaru - Wed Apr 12, 2006 6:37 am
| Lynx wrote: |
| Ok, I just imagined it.. now what? |
Go take a cold shower, and return all the stuff you just bought. ;)
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