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#61
02-17-2018, 04:54
 contextrax Friend Join Date: Aug 2017 Posts: 43 Rept. Given: 0 Rept. Rcvd 17 Times in 7 Posts Thanks Given: 4 Thanks Rcvd at 66 Times in 18 Posts
Quote:
 Originally Posted by MrScotc Hi, is it possible to write down all your discovery and translate into a PDF ?
Be my guest
#62
02-18-2018, 02:36
 cjack Family Join Date: Jan 2002 Posts: 132 Rept. Given: 158 Rept. Rcvd 169 Times in 30 Posts Thanks Given: 191 Thanks Rcvd at 157 Times in 36 Posts
Thank's for sharing ECC Source contextrax!
Excuse me for my ignorance but, how to calculate the 8 ecc_curve_array[] parameters of an armadillo protected application?
#63
02-20-2018, 02:29
 contextrax Friend Join Date: Aug 2017 Posts: 43 Rept. Given: 0 Rept. Rcvd 17 Times in 7 Posts Thanks Given: 4 Thanks Rcvd at 66 Times in 18 Posts
Quote:
 Originally Posted by cjack Thank's for sharing ECC Source contextrax! Excuse me for my ignorance but, how to calculate the 8 ecc_curve_array[] parameters of an armadillo protected application?
The first four of them does not need to be changed for a amradillo protected target.
They are the hamming weight, A in the koblitz curve equation (y^2 + xy = x^3 + Ax^2 + B), point order and cofactor.
The last four is the x,y coordinate for the base point and public point in polynomial base.
Armadillo uses a 32 bit's seed for the base point so you will have to use arma source code to calc these values. They are however i the Type 2 Optimal Normal Base and you will have to do base conversion of them to go to x^113+x^9+1
But for testing speed or making a linux or GPU version then this is not necessary.

The test curve that I use have A in the equation set to "0". This result in a different curve used for testing only. The order of this curve is 0x2000000000000000480DCA1242B1C and contains the factors:
Prime factor : 2 - (2 bits)
Prime factor : 2 - (2 bits)
Prime factor : 18B9 - (13 bits)
Prime factor : 1A89A0F - (25 bits)
Prime factor : 31F1F2A998BD31AF391 - (74 bits)
(Found by schoof2 from miracl library. "schoof2.exe 0 1 113 9")

This makes is pretty good for testing (coz of the low order) and the test curve base point has a order of 0x31F1F2A998BD31AF391. (74 bit)
You will also notice that the equivalence classes is maintained in all these subgroup (They all contain 113*2 as factors of p-1) which of course is typical for a koblitz curve.

For base conversion you could make a matrix B=[1, b, b^2....,b^(m-1)] (m=113 for this base)
Multiplying b^m*B^-1 should give you a polynomial base and to go from this base to x^113+x^9+1 you can use one of the 113 roots.
For root finding you can use magma or sage or some other algo if you want to make one yourself.

Hope this helps.

Last edited by contextrax; 02-20-2018 at 03:17.
 The Following 3 Users Say Thank You to contextrax For This Useful Post: alekine322 (10-25-2018), cjack (02-25-2018), tonyweb (02-25-2018)
#64
02-20-2018, 03:46
 cdrom0 Friend Join Date: Jan 2018 Posts: 1 Rept. Given: 0 Rept. Rcvd 0 Times in 0 Posts Thanks Given: 0 Thanks Rcvd at 0 Times in 0 Posts
Hello! This is really cool, but isn't Armadillo discountinued? I am asking because I couldn't find it's homepage anymore.
#65
02-20-2018, 04:11
 contextrax Friend Join Date: Aug 2017 Posts: 43 Rept. Given: 0 Rept. Rcvd 17 Times in 7 Posts Thanks Given: 4 Thanks Rcvd at 66 Times in 18 Posts
Quote:
 Originally Posted by cdrom0 Hello! This is really cool, but isn't Armadillo discountinued? I am asking because I couldn't find it's homepage anymore.
Yes that is true but there is still allot of programs that uses it for protection and for licensing coz of the "unbreakable" elliptic curve system they use
#66
09-14-2018, 12:53
 cjack Family Join Date: Jan 2002 Posts: 132 Rept. Given: 158 Rept. Rcvd 169 Times in 30 Posts Thanks Given: 191 Thanks Rcvd at 157 Times in 36 Posts
Hi Contextrax, I have a VERY BAD target that I'm trying to reverse since a lot of time! The problem here is that it use A LOT of protected executables, so, maybe, the right way will be attacking the ECDSA certificate itself
Need support to calculate the last 4 ecc_curve_array[] parameters.
If you can help I'll extract the public certificate and post it here asap.
I think that a tool to calculate the 8 ecc_curve_array[] parameters will be AMAZING

Last edited by cjack; 09-14-2018 at 13:50.
#67
09-14-2018, 22:48
 Megin Banned User Join Date: Jul 2018 Posts: 31 Rept. Given: 0 Rept. Rcvd 4 Times in 4 Posts Thanks Given: 79 Thanks Rcvd at 78 Times in 31 Posts
Quote:
 Originally Posted by cjack Hi Contextrax, I have a VERY BAD target that I'm trying to reverse since a lot of time! The problem here is that it use A LOT of protected executables, so, maybe, the right way will be attacking the ECDSA certificate itself Need support to calculate the last 4 ecc_curve_array[] parameters. If you can help I'll extract the public certificate and post it here asap. I think that a tool to calculate the 8 ecc_curve_array[] parameters will be AMAZING
Maybe you share the target with us so we can check?
#68
09-15-2018, 04:47
 cjack Family Join Date: Jan 2002 Posts: 132 Rept. Given: 158 Rept. Rcvd 169 Times in 30 Posts Thanks Given: 191 Thanks Rcvd at 157 Times in 36 Posts

h**ps://mega.nz/#!V8RFxCDL!7JYuUUybRoJelyZwNvp8yB-LmkBGKEeJA_uUjfmxNls

I've put into the zip just the registration app and a trial key (expired on november 2017 but if you set the clock back it'll work).
As serial number use the string "Evaluation".

Hope to start the bruteforcing soon Curious to see how many time will take!
 The Following 2 Users Say Thank You to cjack For This Useful Post: gsaralji (09-17-2018), niculaita (09-15-2018)
#69
10-11-2018, 19:16
 contextrax Friend Join Date: Aug 2017 Posts: 43 Rept. Given: 0 Rept. Rcvd 17 Times in 7 Posts Thanks Given: 4 Thanks Rcvd at 66 Times in 18 Posts
Quote:
 Originally Posted by cjack Hi Contextrax, I have a VERY BAD target that I'm trying to reverse since a lot of time! The problem here is that it use A LOT of protected executables, so, maybe, the right way will be attacking the ECDSA certificate itself Need support to calculate the last 4 ecc_curve_array[] parameters. If you can help I'll extract the public certificate and post it here asap. I think that a tool to calculate the 8 ecc_curve_array[] parameters will be AMAZING
You want to break 4 113 bit's ECC curves by solving ECDSA?
We used like 6 months last time so unless you have access to a lot of CPU's this will take forever.
#70
10-21-2018, 20:39
 ismail Friend Join Date: Jul 2010 Posts: 7 Rept. Given: 22 Rept. Rcvd 11 Times in 5 Posts Thanks Given: 3 Thanks Rcvd at 0 Times in 0 Posts
can u share the target?
#71
10-22-2018, 15:27
 sendersu VIP Join Date: Oct 2010 Posts: 824 Rept. Given: 324 Rept. Rcvd 216 Times in 110 Posts Thanks Given: 162 Thanks Rcvd at 233 Times in 119 Posts
Quote:
 Originally Posted by contextrax You want to break 4 113 bit's ECC curves by solving ECDSA? We used like 6 months last time so unless you have access to a lot of CPU's this will take forever.

What is more important in bruteforcing - CPU GHz speed or # of cores?
#72
10-25-2018, 08:15
 alekine322 VIP Join Date: Apr 2011 Location: North America Posts: 180 Rept. Given: 934 Rept. Rcvd 58 Times in 31 Posts Thanks Given: 540 Thanks Rcvd at 50 Times in 25 Posts
Quote:
 Originally Posted by contextrax The first four of them does not need to be changed for a amradillo protected target. They are the hamming weight, A in the koblitz curve equation (y^2 + xy = x^3 + Ax^2 + B), point order and cofactor. The last four is the x,y coordinate for the base point and public point in polynomial base. Armadillo uses a 32 bit's seed for the base point so you will have to use arma source code to calc these values. They are however i the Type 2 Optimal Normal Base and you will have to do base conversion of them to go to x^113+x^9+1 But for testing speed or making a linux or GPU version then this is not necessary. The test curve that I use have A in the equation set to "0". This result in a different curve used for testing only. The order of this curve is 0x2000000000000000480DCA1242B1C and contains the factors: Prime factor : 2 - (2 bits) Prime factor : 2 - (2 bits) Prime factor : 18B9 - (13 bits) Prime factor : 1A89A0F - (25 bits) Prime factor : 31F1F2A998BD31AF391 - (74 bits) (Found by schoof2 from miracl library. "schoof2.exe 0 1 113 9") This makes is pretty good for testing (coz of the low order) and the test curve base point has a order of 0x31F1F2A998BD31AF391. (74 bit) You will also notice that the equivalence classes is maintained in all these subgroup (They all contain 113*2 as factors of p-1) which of course is typical for a koblitz curve. For base conversion you could make a matrix B=[1, b, b^2....,b^(m-1)] (m=113 for this base) Multiplying b^m*B^-1 should give you a polynomial base and to go from this base to x^113+x^9+1 you can use one of the 113 roots. For root finding you can use magma or sage or some other algo if you want to make one yourself. Hope this helps.
I see that you have a mathematical or physical profile.
You have tried to use your models to find the protection system of flex_LM
It also uses an ECC protection system.
(If I'm wrong, please correct me)
#73
10-26-2018, 14:17
 RedLord Friend Join Date: Nov 2016 Posts: 6 Rept. Given: 0 Rept. Rcvd 2 Times in 1 Post Thanks Given: 5 Thanks Rcvd at 30 Times in 5 Posts
Quote:
 Originally Posted by alekine322 I see that you have a mathematical or physical profile. You have tried to use your models to find the protection system of flex_LM It also uses an ECC protection system. (If I'm wrong, please correct me)
Yes, but flex uses more stronger ECC

Last edited by RedLord; 10-26-2018 at 14:54.

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