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Author Topic: New RSA Algorithm discussion  (Read 65364 times)

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Offline AngelFish

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Re: New RSA Algorithm discussion
« Reply #195 on: August 15, 2011, 05:48:24 pm »
Boot1 is held in ROM, which is currently impossible to modify.

Also, the Nspire could indeed decrypt the OS if it wanted to (thank god it doesn't). It's enabled by something called Public-key cryptography, which basically allows anyone to verify/decrypt the data, but only those possessing the secret keys to sign the data so that it can be verified.
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Offline sammyMaX

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Re: New RSA Algorithm discussion
« Reply #196 on: August 15, 2011, 05:50:55 pm »
OS 2.1 and OS 3 modify the boot1 though; how does that happen?

EDIT: Fail. They modify the boot2.
« Last Edit: August 15, 2011, 05:51:31 pm by sammyMaX »
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Offline ExtendeD

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Re: New RSA Algorithm discussion
« Reply #197 on: August 15, 2011, 05:56:47 pm »
Quote from: Qwerty.55 on August 15, 2011, 05:48:24 pm
Boot1 is held in ROM, which is currently impossible to modify.
It's actually a NOR chip. I thought some TI-Nspire diags software suggested the boot1 could be updated.
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Offline sammyMaX

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Re: New RSA Algorithm discussion
« Reply #198 on: August 15, 2011, 05:57:30 pm »
Yes. Here is the link: http://ourl.ca/8594
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Offline AngelFish

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Re: New RSA Algorithm discussion
« Reply #199 on: August 15, 2011, 05:57:58 pm »
That's why I said it's "currently impossible." To the best of my knowledge, no one knows how to do it.
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Offline jnesselr

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Re: New RSA Algorithm discussion
« Reply #200 on: August 15, 2011, 06:22:29 pm »
Right now, directly modifying it is impossible.  It is also not within this discussion's range, as this is about generally breaking RSA, not necessarily the nSpire's RSA.  Although, of course, it would be immediately applied to that.

Anyway, let me say this, since I have seen this question posed several times, and asked it several times myself before I knew completely about it.

There is currently no non-mathematical way of discovering the private keys

That is all. :D  Well, actually, that's a lie. TI has them, but we don't advocate... retrieving... them.

But yeah, this is in the Math and Science sub-forum, so really should be pertaining to it.  There is this which is about bypassing the RSA signatures.
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Offline sammyMaX

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Re: New RSA Algorithm discussion
« Reply #201 on: August 15, 2011, 06:28:49 pm »
Quote from: graphmastur on August 15, 2011, 06:22:29 pm
That is all. :D  Well, actually, that's a lie. TI has them, but we don't advocate... retrieving... them.

ROFL  :hyper:
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Offline sammyMaX

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Re: New RSA Algorithm discussion
« Reply #202 on: August 17, 2011, 05:30:15 pm »
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Offline AngelFish

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Re: New RSA Algorithm discussion
« Reply #203 on: August 17, 2011, 05:58:55 pm »
Sorry to disappoint you, but verifying perfect squares is still far too computationally intensive to be practical.

To quote part of my post from the other page on the scale of the problem:

Quote
Given the current 2048 bit keys and classical computations, the scale of the problem is vastly more difficult than even the largest keys broken today (768 bits). By vast, I mean volume of the known universe measured in nanometers cubed vast*. The chance that anyone will solve it is so exceedingly slim that the only mathematical tool I have available to calculate it has to work with arbitrary precision operations simply in order to present it. Unless someone gets their hands on a massive quantum computer running Shor's algorithm**, it is, in short, an impossible problem.

*Even this is an understatement.

**It'd take about 30 seconds for a quantum computer to break the code, since the computations necessary increase according to (lg n)^3 for an n bit key.

Basically, trial integer factorization isn't going to work.
« Last Edit: August 17, 2011, 06:02:17 pm by Qwerty.55 »
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Offline sammyMaX

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Re: New RSA Algorithm discussion
« Reply #204 on: August 17, 2011, 08:20:42 pm »
True, but you're missing the point here. I myself don't expect to find an algorithm that factors in polynomial time. But perhaps someone else could take my ideas and improve them. Knowledge is power, and I contributed what I did.
« Last Edit: August 17, 2011, 08:20:52 pm by sammyMaX »
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