Fun Number Theory Facts

[squalyl]

Hi,

For those of you who don't know it yet, a BOINC distributed project was set up to help sieving the keys.

We currently have 100 CPU cores registered, we need more!

Please join , you can help us in 3 clicks under windows and linux :biggrin:

http://boinc.unsads.com/rsals

Would it be interesting to add other keys? Now we have all ti68ks and k0A.

[fullmetalcoder]

[rromfog]

Just downloaded BOINC to help, but it seems like the project is out of work units.

[squalyl]

yes it is, I'll add even more workunits tomorrow, I was on vacation.

The number of users tripled during the weekend, and so did the computation speed, so the 5000 workunits I added last friday have been quickly depleted ^^

[FloppusMaximus]

Good to see you again, squalyl. Did you get my mail?

[Synthesis2k2]

Had a slight problem with the BOINC client at work. I thought it was calculating, but all 5-8 work units I "completed" were sent in and were pronounced "bad". Just wanted to give a heads-up, so the head of the project can take the necessary steps (if any). They were submitted by Synthesis2k2. My bad. :(

-Syn

[FloppusMaximus]

According to this, you've got some kind of permission error, so you have not actually been doing any work.

[squalyl]

I have none.

But I'm glad to see the BOINC dispatcher created another result (unsent yet) to conclude the validation:
http://boinc.unsads.com/rsals/workunit.php?wuid=3901

That's nice to see that this sort of problem is taken care autonomously, I was afraid we would have to resend particular workunits to complete the failed ranges

[Synthesis2k2]

Well, thankfully its taking care of the trouble units I messed up. I'll probably start this up on my home computer tonight or tomorrow, where I know exactly what privileges I have and what I don't. Thanks guys.

-Syn

[squalyl]

Well, it will be time to add other keys to the system.

Lionel proposed the '0102' key with the following polynomial:

[Lionel Debroux]

Between 02 and 0102, I think we should start with 0102, because 0102.poly (from polys.tar.gz) has a Murphy score of 2.70e-12 (good score is 2.16e-12), while 02.poly has a Murphy score of 2.39e-12.
I can't do that myself right now because I have a number of BOINC WUs queued, but I guess the polynomial selection for 02 could be pushed up to 20M leading coefficients ?

[squalyl]

the first workunits have been pushed for the ti73-flashapps key, in the 10-15M range.

[FloppusMaximus]

My PC isn't busy right now, so I guess I'll work on 02 polynomials.

What about the 68k application keys? Any interest there?

[squalyl]

Yes, we have a nice number of relations, around 30 millions now.

I've stopped counting regularly because wc -l is quite long to count lines in ~ 3GB*5 of files
I'll run it tomorrow however, to check the counts.

FYI: http://boinc.unsads.com/rsals_data/allstats.PNG

If you have time and space to backup the results in this directory, don't hesitate to do so. There are tarballs for boinc results, and "preboinc" files.

[Lionel Debroux]

Besides the tarballs, one can make incremental backups of all individual BOINC result files for the "0A" key and the TI-68k OS keys by using e.g.:

mkdir -p 73FA ; cd 73FA ; wget -O - http://boinc.unsads.com/rsals_data/list_73FA | awk '{print "http://boinc.unsads.com/rsals_data/73FA/" $0}' | wget -nc -i - ; cd ..

mkdir -p 84P ; cd 84P ; wget -O - http://boinc.unsads.com/rsals_data/list_84P | awk '{print "http://boinc.unsads.com/rsals_data/84P/" $0}' | wget -nc -i - ; cd ..

mkdir -p 89 ; cd 89 ; wget -O - http://boinc.unsads.com/rsals_data/list_89 | awk '{print "http://boinc.unsads.com/rsals_data/89/" $0}' | wget -nc -i - ; cd ..

mkdir -p 89T ; cd 89T ; wget -O - http://boinc.unsads.com/rsals_data/list_89T | awk '{print "http://boinc.unsads.com/rsals_data/89T/" $0}' | wget -nc -i - ; cd ..

mkdir -p 92P ; cd 92P ; wget -O - http://boinc.unsads.com/rsals_data/list_92P | awk '{print "http://boinc.unsads.com/rsals_data/92P/" $0}' | wget -nc -i - ; cd ..

mkdir -p V200 ; cd V200 ; wget -O - http://boinc.unsads.com/rsals_data/list_V200 | awk '{print "http://boinc.unsads.com/rsals_data/V200/" $0}' | wget -nc -i - ; cd ..

(if you have a high-bandwidth connection, you may want to pass --limit-rate=<n> to the wget on the receiver side of the pipe, so as to make the server's life a bit smoother )

[EDIT1: fix a typo.]



As for the TI-68k FlashApp keys: I have identified five call sites of BN_power17Mod in AMS 2.01, 2.05 and 3.10 (the OS itself, not the boot code). Four of them are rather close to each other, the address of the fifth one varies widely. But I haven't yet investigated further (I mean, retrieving their third argument).
Some clues can probably be found by executing Flashappy, which makes Flashapp signature validation ineffective by modifying the OS code. But for now, I'm going to bed :)



[EDIT2, 20090823: add the 73 FlashApp (0102) folder; use -nc instead of -N for wget, it's more efficient because the folders are in add-only mode.]

[FloppusMaximus]

As I think I've mentioned before, I've already found (by analyzing existing app signatures) what I believe to be the public keys for signing TI-89/92+ Flash apps. They are:

Key 0101 (TI-92+ / V200):
BC747C4065E96E3B79B9BCC1A441BC3692E264CF681C9962B763C19824D84FB0474D567CF2FE5547
3378A18DB2E875BCE87F0022B6B9CC1E1FD455D9FACD0461

Key 0103 (TI-89 / Titanium):
916BDE593CC9F21B07F72033A92D6DC6DCCE8622705E9F7B4C4235A00B0A0DEA4F9827960CF2676C
3F25F987C4BACD38A8F849A5CFCEC188BA0C8B3DFD3602ED

Someone with an actual ROM dump should confirm these numbers. They are probably stored in the boot code, somewhere near where the OS keys are stored.

Edit: Never mind, they are stored in the OS upgrade itself. Offset 0x39BA6 in os209.9xu, 0x39F66 in os209.89u. I think it's fair to assume these are the actual keys.

I don't know if there are also 0108 and 0109 keys; I haven't seen any apps signed with those keys. Like 010A, those keys would not be particularly useful.

[Lionel Debroux]

Indeed, it's fair to assume these are the actual keys. Good job :)

On 89, 89T, 92+ and V200, 0101 and 0103 are stored right after the timestamp key (A3E3..1E15).
They're indirectly referenced by a move.l #32-bit,(a2), a2 being an output area of that routine (this is AMS 2.05 for 92+):

[squalyl]

well, let's add this key. The only thing I need is the polynomial.

[Lionel Debroux]

I have started polynomial selection on 0103:

[squalyl]

hem, by analyzing the outcome of the received results, it seems that the failure rate is very high (28.2099% for windows, much less for linux - 7.5463% ) and I know why.

Among the latest users registered, a lot of them participate in multiple projects. So the BOINC client has to stop calculations and my application cannot resume, because checkpointing is not implemented.

I would love if the author of GGNFS could behave as the msieve's one, and help us with this part. I don't know what has to be saved, when the backup has to be done, how to restore it, etc.

The global algorithm should be as follow: