Factor the Nspire Key
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Factor the Nspire Key
United-TI Archives -> Community News & Discuss Nspire
 
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smblackh


Newbie


Joined: 06 Nov 2010
Posts: 13
Posted: 06 Nov 2010 12:35:45 pm    Post subject:
I know of Ndless, but so far the only stable version supports OS 1.1, which doesn't work well due to the glitches turning it on, and it is still based off of TI's default operating system. Mad Yeah, the TI-84 and others support 3rd party OS's, but what can you get with a 15 Mhz processor and 1.5Mb of archive? With the Nspire theres possibilities of a real functional 3rd party OS, like some form of Linux!!!
Brute forcing is not much of an option, the RSA key is a 1024 bit (309 digit) monster. (Hackspire has some more info)
Factoring that with brute force would take centuries. Does anyone have any ideas?
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Levak


Advanced Newbie


Joined: 11 Nov 2009
Posts: 94
Posted: 06 Nov 2010 01:00:19 pm    Post subject:
Phryzly wrote:

Does anyone have any ideas?


Wait ?
Laughing
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smblackh


Newbie


Joined: 06 Nov 2010
Posts: 13
Posted: 06 Nov 2010 07:47:37 pm    Post subject:
Maybe when every computer has 192 cores and a clock speed of 8 Ghz... Neutral I actually programmed myself a program to brute factor it (too stupid to understand/program anything else right now) that supports multicore. I made it notify me when it was 0.000000000001 percent done and after 2 minutes of waiting and nothing happening I gave up. So assuming it was done in 2 minutes, that means this program will take around 380,250,000 years to complete...
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yifanlu


Newbie


Joined: 21 Mar 2010
Posts: 15
Posted: 07 Nov 2010 02:25:47 pm    Post subject:
The old TI calculators was cracked "easily" (and by easy I mean hundreds of volunteers contributing CPU for weeks) because the key was only RSA-512. The nspire has RSA-1024 with is twice as long, therefore 2^512 times longer.
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smblackh


Newbie


Joined: 06 Nov 2010
Posts: 13
Posted: 07 Nov 2010 06:30:33 pm    Post subject:
Yes the Nspire key would take much longer to crack meaning much more advanced and complex methods have to be used. If GNFS (General Number Field Sieve) was used, this would take around two months or so with community support, but GNFS is a very complex method to program.
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Lionel Debroux


Member


Joined: 01 Aug 2009
Posts: 170
Posted: 08 Nov 2010 12:32:33 am    Post subject:
(emphasis mine)
Quote:
If GNFS (General Number Field Sieve) was used, this would take around two months or so with community support, but GNFS is a very complex method to program.

No way. Even the leading-edge implementations of GNFS + post-processing that allowed factoring RSA-768 (in much more than two months) are, AFAICT, not public at the moment, and RSA-1024 is said to be at least one thousand times harder.
For more information, see:
* the long http://www.omnimaga.org/index.php?topic=3639.0 thread on Omnimaga, about the same topic;
* for the factoring community side of the story, see e.g. http://blogs.rsa.com/juels/rsa-768-factored/ and http://www.mersenneforum.org/showthread.php?t=12958
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smblackh


Newbie


Joined: 06 Nov 2010
Posts: 13
Posted: 08 Nov 2010 06:58:22 pm    Post subject:
Oh crap. Looks like I completely screwed up my calculations. Then this means the only way to crack the key would be to implement a virus during the install of a new OS.
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calc84maniac


Elite


Joined: 22 Jan 2007
Posts: 770
Posted: 08 Nov 2010 07:28:03 pm    Post subject:
Phryzly wrote:

Oh crap. Looks like I completely screwed up my calculations. Then this means the only way to crack the key would be to implement a virus during the install of a new OS.

The OS doesn't hold the key we need to sign our own OS's, just the one needed to validate OS's. We're not going to get the key that way.

Though, if we find an exploit in the boot code that will force it to run an OS without validating it, that would work for our purposes Smile
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xtjacob


Newbie


Joined: 15 Oct 2009
Posts: 17
Posted: 07 Dec 2010 10:02:19 pm    Post subject:
calc84maniac wrote:

Phryzly wrote:

Oh crap. Looks like I completely screwed up my calculations. Then this means the only way to crack the key would be to implement a virus during the install of a new OS.

The OS doesn't hold the key we need to sign our own OS's, just the one needed to validate OS's. We're not going to get the key that way.

Though, if we find an exploit in the boot code that will force it to run an OS without validating it, that would work for our purposes Smile



This is a crazy idea, but then again there are people who will do anything to crack their calculators. What if we tried something like this: http://www.engadget.com/2010/03/09/1024-bit-rsa-encryption-cracked-by-carefully-starving-cpu-of-ele/ or something like this http://techie-buzz.com/tech-news/1024-bit-rsa-cracked.html. I know they're crazy idea's, but I would love to see the look on TI's face if we manage to do something like this... If somebody can help me with this I do have a SPARC computer laying around. Smile
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Xeda112358


Active Member


Joined: 19 May 2009
Posts: 520
Posted: 08 Dec 2010 01:46:00 am    Post subject:
Ooh, wow, that is a very neat idea. I still want to attack prime numbers with the absolute brutal force of my mind, but I guess for now that could be useful. I think it will be more fun to create an algorithm to factor 2048-bit semi-prime numbers, though, in a timely manner. I am working on it! :D

Well, when I am bored or have nothing better to do...
Like the Riemann Hypothesis... Razz

Last edited by Guest on 08 Dec 2010 11:18:54 pm; edited 1 time in total
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Goplat


Advanced Newbie


Joined: 26 Jun 2007
Posts: 95
Posted: 08 Dec 2010 01:30:59 pm    Post subject:
xtjacob wrote:

This is a crazy idea, but then again there are people who will do anything to crack their calculators. What if we tried something like this: http://www.engadget.com/2010/03/09/1024-bit-rsa-encryption-cracked-by-carefully-starving-cpu-of-ele/ or something like this http://techie-buzz.com/tech-news/1024-bit-rsa-cracked.html

This "crack" requires physical access to the computer with the private key, so it's pretty useless.
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xtjacob


Newbie


Joined: 15 Oct 2009
Posts: 17
Posted: 08 Dec 2010 05:16:59 pm    Post subject:
Goplat wrote:

xtjacob wrote:

This is a crazy idea, but then again there are people who will do anything to crack their calculators. What if we tried something like this: http://www.engadget....ing-cpu-of-ele/ or something like this http://techie-buzz.c...sa-cracked.html

This "crack" requires physical access to the computer with the private key, so it's pretty useless.


Oh, I guess I misread it then... Razz
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Xeda112358


Active Member


Joined: 19 May 2009
Posts: 520
Posted: 08 Dec 2010 11:20:44 pm    Post subject:
Aww, but the article is still pretty cool! At least that means we still have an excuse to play with primes!

I ♥ Math! (and yes, that is a factorial)
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willrandship


Newbie


Joined: 16 Dec 2009
Posts: 10
Posted: 21 Jan 2011 05:38:41 pm    Post subject:
I hope this isn't too much of a necropost...some places have different rules regarding that.

I had a different idea, that I am rather unable to pursue not knowing any Arm Assembly, or even z80 assembly :P

At hackspire, there is a text file logging the communication over RS232 during startup of an nspire. In all types of startup (maintenance menu access, standard, deleting OS, etc.) there is a small list that is always the same.

Note that this is version 1.1 of the boot2, but since this is coming from the boot1 as well, it doesn't matter.

Boot Loader Stage 1 (1.1.8916)
Build: 2007/4/23, 23:37:16
Copyright (c) 2006, 2007 Texas Instruments Incorporated
Using production keys

Now, why say that if that is the only possible outcome? There is a possibility that there is a way to force the calculator to use other RSA keys for checking than the ones it comes with, or maybe even none at all. This might be though the serial, through some config file, or any number of different ways, but there must be some way to use this.

My idea is to look through the disassembled Boot2 code, and find what it does prior to outputting the fated serial message "Using Production Keys"

What do you think?
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Goplat


Advanced Newbie


Joined: 26 Jun 2007
Posts: 95
Posted: 21 Jan 2011 10:07:03 pm    Post subject:
That message doesn't mean anything. The code is just doing


Code:

print("\n\n\n\r");
print("Boot Loader Stage 1 (1.1.8916)\r\n)");
print("Build: 2007/4/23, 23:37:16\r\n");
print("Copyright (c) 2006, 2007 Texas Instruments Incorporated\r\n");
print("Using production keys\r\n");
print("\n");


Nothing more.
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willrandship


Newbie


Joined: 16 Dec 2009
Posts: 10
Posted: 22 Jan 2011 02:05:40 pm    Post subject:
but why say it at all if it's always that way? Are you sure that's all it can do?
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