Topic: Why Can't We Get A Digital Signature? (Read 752 times)

modthebox.tk · « **Reply #30 on:** December 06, 2005, 07:04:00 PM »

I have a question.

Would they be decimals or real numbers?

with Decimals there are (I think) and infinite number of possibilites. If there are real numbers involved all you need is a couple of mathematicians together at a table for a couple of days; I mean, with real numebrs there are only so many combinations.

and if we don't know, we go with real numbers first than try the obvious decimals (square roots) and stuff like that.

it is hard to crack, but whoever made it be it Bill Gates or somebody else is a human and humans have limits to thinking.

lordvader129 · « **Reply #31 on:** December 06, 2005, 07:06:00 PM »

QUOTE(modthebox.tk @ Dec 6 2005, 08:08 PM)

I have a question.

Would they be decimals or real numbers?

with Decimals there are (I think) and infinite number of possibilites. If there are real numbers involved all you need is a couple of mathematicians together at a table for a couple of days; I mean, with real numebrs there are only so many combinations.

you mean the factors? they ar eprime numbers (whole numbers) but i dont think you realize the scale of it, a computer cant crack it in a couple of millennia, how can a few people crack it in days? it would take weeks if not months for a few people to come up with and test just 1 possible prime factor

QUOTE

it is hard to crack, but whoever made it be it Bill Gates or somebody else is a human and humans have limits to thinking.

its not so much that its hard to crack, its that it takes a long time to crack due to sheer size of the numbers involved

im thinking of a number between 1 and 20740119327258723760276023509063017138455993606274883526731955113241109007354362
37412899609629104635357230674211030545694682486220386711504236987872970347576511
22801674981890464377946029661688124194233651969796694319295889511268046487430293
87833666031765734337165949634731375592471670294246180877815104812674626967450097
04500511754665706870054526306410502488876911803205991784586765304041940400368455
98825091953986309228240504053796205135896999939802056942669732360957721534763882
67418476533663512746243310317853861946430053072890502949319703765023792161144942
611323629444409600173894963797156859916567288947565058003, can you guess what it is?

lordvader129 · « **Reply #32 on:** December 06, 2005, 09:09:00 PM »

QUOTE

Nah, not really. Here you go, the first one's free:

90744758568471273891824362793417296786383470630768325777379673958980107083484583
12920297595915579822647903851739418727374745237510765748925595602805156100237680
00462368525803390238669274724897040728977546396982769628694962048172534622989091
90488374257959082939518841187313558210841447668297015369654192506593

That's a 1,024-bit prime number. Like I said in another post, coming up with primes is easy. Testing whether a given prime number divides a given composite number is also easy. It's the sheer number of possible candidates that makes it hard.

but did you come up with that on your own or with a a computer? lol remember modthebox wants a couple guys sitting at a table to crack this, lol

joshf · « **Reply #33 on:** December 06, 2005, 11:29:00 PM »

QUOTE(VoiceOfReason @ Dec 7 2005, 04:07 AM)

In the first place, there is an infinite number of rationals (decimals, to you.) There is also an infinite number of reals. But the number of reals is actually greater than the number of rationals. (See: Cantor's diagonalization proof.)

Okay, I just looked up Cantor's diag proof, and YOU HAVE IT BACKWARDS!!!

quote from Cantor:
...the infinity of decimal numbers is greater than the infinity of counting numbers...

VoiceOfReason · « **Reply #34 on:** December 07, 2005, 09:47:00 AM »

QUOTE(joshf @ Dec 6 2005, 10:36 PM)

Okay, I just looked up Cantor's diag proof, and YOU HAVE IT BACKWARDS!!!

Do not.

QUOTE

quote from Cantor:
...the infinity of decimal numbers is greater than the infinity of counting numbers...

That's not a quote from Cantor, it's a quote from a page about Cantor. When it says decimal numbers, it means real numbers. Few if any mathematicians would call the reals decimals (they're symbolized by a block boldface R for crying out loud.) Since modthebox.tk talked about decimals as being different from reals, I assumed that me was talking about the rationals.

"Counting numbers" means the natural numbers; the integers from 1 on up. The number of natural numbers is equal to the number of rational numbers, that is, numbers that can be expressed as a ratio... everything except for the nonrepeating transcendental numbers, like pi.

Modthebox.tk said that there were more "decimals" than reals. Whatever he meant by "decimals", he's wrong. The set of reals has the largest cardinality of any set of numbers.

lordvader129 · « **Reply #35 on:** December 07, 2005, 09:52:00 AM »

QUOTE(joshf @ Dec 7 2005, 12:36 AM)

Okay, I just looked up Cantor's diag proof, and YOU HAVE IT BACKWARDS!!!

quote from Cantor:
...the infinity of decimal numbers is greater than the infinity of counting numbers...

hes talking about reals vs rationals, your talking about decimals vs counting numbers, theres a difference

although i guess then shouldnt have used cantors proof as an argument, lol

fluffhead · « **Reply #36 on:** December 08, 2005, 02:35:00 PM »

ok let me backup for just a minute.

I've also always had a lot of questions about how signing works. the response in this thread is basically, well if you know the two magic numbers that when multipled equals this number than you can sign software.... but how does this work??? where did you get that big number??? is that number pulled from xbox disks, or xbox executable file or what??
why do I need to know the original 2 prime numbers?? why cant I just write that big number to the disk?? If i make a bit for bit copy of an xbox disk, why doesn't the signature get copied along with it??

sorry for being a newb when it comes to encryption, but i just need a more satisfying explanation.

lordvader129 · « **Reply #37 on:** December 08, 2005, 02:45:00 PM »

QUOTE

but how does this work???

http://www.muppetlab.../txt/rsa.html#0

QUOTE

where did you get that big number???

i believe it was extracted from the kernel of the xbox

QUOTE

why do I need to know the original 2 prime numbers??

see link above

QUOTE

why cant I just write that big number to the disk??

because the big number is the public key, the xbes (discs) need to be signed with the private key (the orginal primes)

QUOTE

If i make a bit for bit copy of an xbox disk, why doesn't the signature get copied along with it??

well first off you cant make a bit by bit copy of any dvd, the dvd spec prevents this

however, the signature DOES stay on the xbe of a backup, however that is not the only level of security, there is also a media check which prevents the xbe from running off anything but a retail pressed dvd-rom

if you patch the media check the signature is invalid the xbe wont run then either

the idea is if we had the private key we could patch the media check, then re-sign the patched xbe

s0ftm0d · « **Reply #38 on:** December 08, 2005, 07:53:00 PM »

I just don't understand why all this talk about the signature has came up. For the majority of people, the only reason they want the sig is to sign their pirated games, since the 360 isn't modded.

Just give it a rest, and give this thing some time, also stop worring about cracking the damn keys, IT'S NOT GOING TO HAPPEN

CattyKid · « **Reply #39 on:** December 08, 2005, 08:00:00 PM »

QUOTE(lordvader129 @ Dec 6 2005, 11:16 PM)

but did you come up with that on your own or with a a computer? lol remember modthebox wants a couple guys sitting at a table to crack this, lol

Yes, but they have laptops with Inyel Celeron Technology!

Mad_Gouki · « **Reply #40 on:** December 11, 2005, 01:13:00 AM »

QUOTE

its not so much that its hard to crack, its that it takes a long time to crack due to sheer size of the numbers involved

im thinking of a number between 1 and 20740119327258723760276023509063017138455993606274883526731955113241109007354362

37412899609629104635357230674211030545694682486220386711504236987872970347576511

22801674981890464377946029661688124194233651969796694319295889511268046487430293

87833666031765734337165949634731375592471670294246180877815104812674626967450097

04500511754665706870054526306410502488876911803205991784586765304041940400368455

98825091953986309228240504053796205135896999939802056942669732360957721534763882

67418476533663512746243310317853861946430053072890502949319703765023792161144942

611323629444409600173894963797156859916567288947565058003, can you guess what it is?

really, you only have to find one number that has the same number of digits that the square root of the public key has.

go ahead, test it out if you want. there is no simple way to crack rsa encryption but there are a lot of things that could help you, and more than likely if you found the number of digits that one of the keys has to be, just search a dvd for all the numbers that have that many digits.

im thinking that the key would be at a very early part in the dvd, if somebody looked at the lens in the dvd drive as the xbox read a non-xbox game it might shed some light as to where to look for those 2 keys.

you guys are grossly overestimating how many numbers you would need to check, you can create a seive to find just primes first, so you arent checking numbers that would result in false positives, and you can easily find the number of digits you need, i dont know how much that removes from all of the equations but i know it decreases the time to calculate a key dramatically.

like i said, you only need 1 of them. its pretty unrealistic to try but if anyone wants to just say so

i wouldnt approach it witha brute force approach, there are a few tricks you can do with math to find the approximate location of the key but still you need a big calculating program.

unspoiledpuma · « **Reply #41 on:** December 11, 2005, 09:49:00 AM »

QUOTE(adam7288 @ Dec 11 2005, 05:18 PM)

Voice of Reason - If we had quantum computing available, how long would it take?

probably a few month

The encryption is awsome!

CMB · « **Reply #42 on:** December 11, 2005, 12:21:00 PM »

QUOTE(Drunkn_Munky @ Dec 11 2005, 09:42 AM)

What we really need is a super computer like in Digital Fortress. I have $500, anyone else want to chip in?

If the Xbox checks that the 2 numbers on the DVD multiply to make that big long number, why not use that big long number and 1 as the keys?

lol, i highly doubt that would ever work as everyone was saying before. But that would be funny if we just did that. And anyways we need 2 prime numbers and if i remember correctly 1 is neither prime nor composite.

TheRandomDude · « **Reply #43 on:** December 12, 2005, 12:46:00 AM »

Alright, the only thing that confuses me now is about signing. What I believed was that the private key was built into the code using an algorithim. If this is true, and you have enough code, doesn't that make it possible to crack the private key by narrowing down what the 2 primes could possibly be? I keep on hearing about random bits of data to confuse that sort of thing, but wouldn't that wreck the signing altogeather?

VoiceOfReason · « **Reply #44 on:** December 12, 2005, 11:35:00 AM »

[quote name='adam7288' date='Dec 11 2005, 08:18 AM' post='3106392']

Author Topic: Why Can't We Get A Digital Signature? (Read 752 times)