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fullmetalcoder


Member


Joined: 01 Aug 2009
Posts: 139

Posted: 13 Nov 2009 11:45:32 am    Post subject:

1) Evolution of home computers processing power
2) Determination of FloppusMaximus to break the first key
3) Momentum in the community caused by that first cracking

The fact that TI used 512 bit keys cannot really be considered as silliness considering how old these calcs are. The biggest silliness IMHO was to even use signing keys but that's debatable ;)

@brandon : do we really have any *exploitable* exploit? AFAIK we're still unable to run native code on the nspire.
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brandonw


Advanced Member


Joined: 12 Jan 2007
Posts: 455

Posted: 13 Nov 2009 01:39:36 pm    Post subject:

Not yet, but we're getting there. The door's wide open now for it.
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Lionel Debroux


Member


Joined: 01 Aug 2009
Posts: 170

Posted: 13 Nov 2009 02:04:46 pm    Post subject:

Indeed, 512-bit RSA keys (a 154 or 155-digit composite number, a.k.a C154-C155) were very hard to factor in the end of the 1990s. At the end of 2009:
* as shown by Benjamin Moody, factoring a 512-bit RSA key (C154-C155) by GNFS is a few months of CPU time for a single dual-core computer of a slightly older generation, and requires ~10 GB of space... in other words, it's trivial;
* factoring a 768-bit RSA key (C231-C232) by GNFS is definitely hard, but probably doable: people at MersenneForum are currently factoring a C280 by SNFS, a task which isn't THAT much easier than factoring a C232 by GNFS. Two bottlenecks: finding a polynomial for an integer of that size (AFAICS, could be distributed across computers), and having a single computer with enough RAM for the post-processing (no FLOSS currently implements a distributed post-processing);
* factoring a 1024-bit RSA key (C308-C309) remains completely impractical, and will remain impractical for years, unless there's a theoretical breakthrough on integer factorization (e.g., P = NP - that would be cool Very Happy)... Unfortunately, that's what the Nspires use - but now that the boot2 was decompressed, and soon after it, the OS was decrypted, it probably won't be long before we can run the software we wish to run, on the devices we own.
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Mapar007


Advanced Member


Joined: 04 Oct 2008
Posts: 365

Posted: 13 Nov 2009 03:50:22 pm    Post subject:

Amen.
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fullmetalcoder


Member


Joined: 01 Aug 2009
Posts: 139

Posted: 14 Nov 2009 06:08:26 am    Post subject:

Lionel Debroux wrote:
unless there's a theoretical breakthrough on integer factorization (e.g., P = NP - that would be cool Very Happy)

P=NP wouldn't help that much actually. We would know that an efficient algorithm exists but we wouldn't necessarily find it. A more probable breakthrough IMHO would be one focusing on factoring RSA keys using their specific properties instead of factoring them using a general algorithm but I'm not aware of any such research... (actually I found a paper on the topic a while back but it relied on quantum computing so it's unlikely to be of much use before a long while).


Last edited by Guest on 14 Nov 2009 06:08:50 am; edited 1 time in total
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Galandros


Active Member


Joined: 29 Aug 2008
Posts: 565

Posted: 14 Nov 2009 09:27:19 am    Post subject:

fullmetalcoder wrote:
Lionel Debroux wrote:
unless there's a theoretical breakthrough on integer factorization (e.g., P = NP - that would be cool Very Happy)

P=NP wouldn't help that much actually. We would know that an efficient algorithm exists but we wouldn't necessarily find it. A more probable breakthrough IMHO would be one focusing on factoring RSA keys using their specific properties instead of factoring them using a general algorithm but I'm not aware of any such research... (actually I found a paper on the topic a while back but it relied on quantum computing so it's unlikely to be of much use before a long while).

Yep, there is a algorithm that uses quantum computing in factoring, but just a part of the algorithm. Other part is just plain usual programming.
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fullmetalcoder


Member


Joined: 01 Aug 2009
Posts: 139

Posted: 14 Nov 2009 09:55:10 am    Post subject:

Galandros wrote:
fullmetalcoder wrote:
Lionel Debroux wrote:
unless there's a theoretical breakthrough on integer factorization (e.g., P = NP - that would be cool Very Happy)

P=NP wouldn't help that much actually. We would know that an efficient algorithm exists but we wouldn't necessarily find it. A more probable breakthrough IMHO would be one focusing on factoring RSA keys using their specific properties instead of factoring them using a general algorithm but I'm not aware of any such research... (actually I found a paper on the topic a while back but it relied on quantum computing so it's unlikely to be of much use before a long while).

Yep, there is a algorithm that uses quantum computing in factoring, but just a part of the algorithm. Other part is just plain usual programming.

Well, the *crucial* part relies on quatum computing so that rules it out for our purpose...
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Galandros


Active Member


Joined: 29 Aug 2008
Posts: 565

Posted: 14 Nov 2009 10:40:50 am    Post subject:

fullmetalcoder wrote:
Well, the *crucial* part relies on quatum computing so that rules it out for our purpose...

Yes, and I know but forgot to mention that. Still cool to think that not all of it depends on quantum computing.
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alexrudd
pm me if you read this


Bandwidth Hog


Joined: 06 Oct 2004
Posts: 2335

Posted: 16 Nov 2009 10:20:21 am    Post subject:

My dad just called me today and told me I should read the Wall Street Journal article about TI.

"What, you mean the one with the DMCA takedown?"
"How did you know?!?"


I haven't found the actual article yet.
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Mapar007


Advanced Member


Joined: 04 Oct 2008
Posts: 365

Posted: 16 Nov 2009 11:00:12 am    Post subject:

I think it's this: http://online.wsj.com/article/SB1258325812...p_sections_tech
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jasonp


Newbie


Joined: 21 Aug 2009
Posts: 4

Posted: 16 Nov 2009 01:41:14 pm    Post subject:

Nice article, but "a process that involved factoring two huge prime numbers" ?

News media never get this terminology correct. So what does this mean when you read something on a topic you know nothing about?


Last edited by Guest on 16 Nov 2009 01:42:55 pm; edited 1 time in total
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Mapar007


Advanced Member


Joined: 04 Oct 2008
Posts: 365

Posted: 16 Nov 2009 01:51:07 pm    Post subject:

Factoring a prime number is impossible, dear WSJ... (I spotted that one too) One word makes the difference.
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Weregoose
Authentic INTJ


Super Elite (Last Title)


Joined: 25 Nov 2004
Posts: 3976

Posted: 16 Nov 2009 03:13:15 pm    Post subject:

Wait, so that actually appeared in a magazine? It's mostly empty talk from someone who was given the information but didn't figure it out responsibly enough. Because, you know, hacking the calculator to perform larger calculations is really what this is all about. I should submit this to MathWorld, as the Wall Street Journal has definitely joined ranks with The New York Times in having butchered a secondary school concept.
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calcdude84se


Member


Joined: 09 Aug 2009
Posts: 207

Posted: 16 Nov 2009 04:46:35 pm    Post subject:

Well, at least we get the publicity, I need to buy a copy to show everyone I know...
My vision (and a lot of other people's too) is to turn these calculators into general-purpose computers. They basically are computers anyway, it's just that the OS is math-centric (I do know that it is a calculator).
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ztrumpet


Active Member


Joined: 06 May 2009
Posts: 555

Posted: 16 Nov 2009 05:16:31 pm    Post subject:

That's a neat vision.
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DigiTan
Unregistered HyperCam 2


Super Elite (Last Title)


Joined: 10 Nov 2003
Posts: 4468

Posted: 16 Nov 2009 07:40:41 pm    Post subject:

Prime factors, schmime factors. I'm just glad to be one step closer to my dream of UTI being a clue in the New York Times crossword. And man O man, you gotta love those headline puns!
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thornahawk
μολών λαβέ


Active Member


Joined: 27 Mar 2005
Posts: 569

Posted: 17 Nov 2009 04:50:29 am    Post subject:

A nice e-mail to that [email=dionne.searcey@wsj.com]article's writer[/email] would be nice to inform her of her little error. ;)

thornahawk
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ah-blabla


Newbie


Joined: 28 Oct 2009
Posts: 26

Posted: 17 Nov 2009 04:59:17 am    Post subject:

calcdude84se wrote:
Well, at least we get the publicity, I need to buy a copy to show everyone I know...
My vision (and a lot of other people's too) is to turn these calculators into general-purpose computers. They basically are computers anyway, it's just that the OS is math-centric (I do know that it is a calculator).

You might as well take one of today's modern "smartphones", since they are more powerful and also have colour screens, albeit no specific maths-friendly keypad. One of the android based phones would probably be best.

What I think would be interesting is creating an open calculator standard, where everything is easily modifiable. Since everything is open, manufacturers wouldn't try protecting all their code / limiting their hardware, and try to stop people putting their own software on their devices. Additionally, a direct standardised hardware access port could be built in to allow teachers to easily "take control" of calculators, i.e. before tests be able to reset a calculator, in other words put a new OS on, without worrying that software can fool them -- thus limiting everyone to the same functionality in a test (i.e. disabling cas if necessary for a test). (To make all sides happy, one would have an automatic software which backs up the calc, resets it, and after the test allows the backup to be restored -- this would make an automatic system whereby you dock the calc in before and after a test.) That should make teachers more confident in calculators since they can't be easily fooled, whereas now that the NSpire is almost cracked, they can't be sure whether they can trust it or not, since there is no easy way to verify what is on the calculator, since it is so locked up.
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Mapar007


Advanced Member


Joined: 04 Oct 2008
Posts: 365

Posted: 17 Nov 2009 02:52:09 pm    Post subject:

Nah, I want to be able to control my calc at any time I want ... Smile No teachers meddling with it!
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brandonw


Advanced Member


Joined: 12 Jan 2007
Posts: 455

Posted: 18 Nov 2009 01:35:04 am    Post subject:

thornahawk wrote:
A nice e-mail to that [email=dionne.searcey@wsj.com]article's writer[/email] would be nice to inform her of her little error. ;)

thornahawk


I think you guys might be a little harsh, like you said, one word makes the difference. She does know about it. The first time I read it, I didn't catch it, someone else pointed it out to me.

Weregoose wrote:
Because, you know, hacking the calculator to perform larger calculations is really what this is all about.


I'm (at least one of) the one(s) that said that. It's a perfectly legitimate reason (maybe the most) for wanting to replace the operating system. Everything else can already be done through assembly programs and Flash applications.


Last edited by Guest on 18 Nov 2009 01:36:49 am; edited 1 time in total
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