Very nice! If it allows apps, couldn't an asm shell also be made in an app without having to send a modified backup?

Yes. I half-finished a TI-73 shell in 2002 that was an app. However since TI has not yet released the freeware signing key for the 73, it would have been a pain to update new versions.

That shell was called DuckIE (Duck Interface Environment). You may find that "Mallard" makes more sense if you know that :)

yeah, why didn't they release a signing program for 73 apps?

TI-73 apps are signed using the same scheme as are TI-83+ apps.

What has not been released for the 73 (1) is the private key (number 0102) needed to sign apps. If you have a real TI-73 (2), you can (with some effort) retrieve the *public* key which is the 512-bit product of two large prime numbers; those two numbers are the private key, and they are needed to sign apps (3).

It is beyond the capability (4) of any current computer (5) to factor a 512-bit number; whether there exists an efficient algorithm for doing so with a conventional computer is unknown (6); and forging a Rabin signature is computationally equivalent to factoring the key (7).

(1) Yes, the private key for the 83+ (number 0104) is available. No, the TI-73 does not accept apps signed with it.

(2) Yes, it probably is possible to retrieve it from the boot page as well.

(3) Yes, there are MD5 collisions known; no, they won't help us yet.

(4) With the possible exception of the NSA.

(5) Or even massive distributed computing project.

(6) With the possible exception of the NSA.

(7) Because if you can forge an arbitrary signature, you can sign a chosen square, in which case you have a 50% chance of finding two square roots of the same number which are not negatives of each other, and given those you can find the factors fairly easily.

The NSA can't do it either, unless there's a "back-door" in the algorithm TI has chosen.

There isn't, unless you count MD5 itself. I'm not qualified to say what the NSA can and can't do, but they are well ahead of the rest of the world in all matters cryptographic.

No. Just give'em a the encrypted source code of a virus. According to Dan Brown, the NSA-Supercomputer will automatically

1. decrypt it
2. compile it
3. run it
4. die.

Darn, this book was so unrealistic.

"Digital Fortress." That book was hilarious.

One question. Don't arbitrary-length floating point math libraries exist? If so, why would 512-bit factoring be impossible??

Takes too long. Too long as in decades.

Well, in a best-case scenario according to your numbers, we could have had it done three years from now, had we started right away :P

Why would you want to use floats? Factoring a number can be done with integers too. And since integer arithemetic (especially the arbitrary length kind) is a *lot* faster than floating point arithmetic, I'd say you really don't want to use floating point numbers.
In theory, you could just tell Mathematica (or Matlab, or Maple, or a version of Cabamap extended with a Factor-command) to FactorInteger[publickey]. The only problem is that you're probably dead before the calculation is done (and in the case of using Cabamap, the batteries will most certainly be dead before it's done ;) ).

Hogwash! A massive distributed computing project? Using NFS, a group factored a 512 bit number in 3.7 months using 300 computers. I'm sure by today's standards you could get that down to 100 computers, or less if you were willing to sacrifice some time. I hardly call that massive.

There's no way Ticalc could host such a project. However, as long as you're only out to crack a freeware key, there might be visitors of this site willing to participate... It could be feasible (and *w*ould be illegal!) to do this. (Interest for such an attempt would probably be a lot bigger if somebody went after the 68k freeware keys.)
Note: this is not meant as "inspiration" for anyone to actually try to hack any keys. Personally, I think TI has not been all that unfriendly to us (they did put the Send(9 easter egg into the 83 and gave us ZASMLOAD, they put full assembly support in the 83+ and beyond and they released 0104.key to name just a few things), so I don't think they'd deserve 'us' hacking their keys. What I wrote above was merely intended as a thought experiment (think Schrodinger's Cat), I'm very curious whether we *could* pull it of, that's all.
(Hmm, the disclaimer is longer than the actual contents of my post...)

68K keys, yeah!

I really don't think cracking a key is illegal -- although if they say it's a trade secret, I suppose it could be under the DMCA.

Oh yes, that's most definitely under the DMCA. It might very well already be illegal under another law, because you'd essentially be forging a signature.

My mistake, then. If somebody wants to try, I don't want to discourage it, merely point out that it would be rather difficult.

And of course, though I don't discourage large-scale mathematical exercises, I don't support electronic "forgery" of any kind.

Oh yeah. For efficiency's sake, I would recommend that any mathematical effort be directed at key 02 rather than 0102. :)

Thought you didnt support forgery?

I suppose he meant he doesn't support "using" the forgery's successful outcome :) which doesn't disallow him from providing experience, advice and other miscellaneous tips, or even working towards this success :-)

We all know how genius minds are welcome in this wonderful community :)

Is this why TI doesn't want to link to us? Because we talk about stuff like this? *chuckles*

Actually because some dumbass made a secret porn level for a game on the Ticalc CD and someone's mom found out... :/

That was you, right?

what's the difference?

0102 is the 73 freeware key. 02 is the OS key. :)

Are those keys the same length? That's odd, I'd think the OS key would be longer, to stimulate people to break a less important key.
I mean, if they're the same length, why bother cracking the freeware key if you can get the jackpot with the same amount of effort?

They're the same length, 512. Besides having different factors, the only difference is that the OS key is for an RSA signature and the freeware app key is a Rabin signature. Of course Rabin is a special, easy to computer, case of RSA.

No, it's not. The two systems are similar in that both are validated by raising a number to a given power. But the math behind them is quite different.

For one thing, only one quarter of the numbers mod n can actually *be* Rabin-signed (since there are *four* Rabin signatures for every number 1 <= x < n). That's what the f-transforms are for. And the f-transforms only work if one of your primes is congruent to 3 and one is congruent to 7 mod 8 -- hence that restriction on the format of TI's Rabin keys, which needn't apply to their OS keys.

For another thing, the RSA transformation relies on being able to find e and d whose product is 1 mod (p-1)(q-1). Since both (p-1) and (q-1) are even, you'd have a hard time finding an integer which you can multiply by 2 to get 1 mod (p-1)(q-1).

Right theres a lot of restrictions for Rabin that there arent for RSA. Thats why its a "special case".

The fact is that the RSA algorithm simply does not work with e=2, because squaring is not a 1-1 operation in *any* nontrivial modulus. So there can be no decryption exponent, because you can't decrypt the message (without additional information) in the first place!

So I guess if you define RSA as "raising a number to some power in some modulus," then yes, Rabin is RSA. But there's a lot more to both algorithms than that, and a lot of mathematical beauty that you're ignoring...