Armadillo ECDSA-113

[contextrax]

Originally Posted by MrScotc

Hi, is it possible to write down all your discovery and translate into a PDF ?

Be my guest

[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?

[contextrax]

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.

[cdrom0]

Hello! This is really cool, but isn't Armadillo discountinued? I am asking because I couldn't find it's homepage anymore.

[contextrax]

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

[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

[Megin]

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?

[cjack]

Yes sure! Here the link:

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!

[contextrax]

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.

[ismail]

can u share the target?

[sendersu]

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?

[alekine322]

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)

[RedLord]

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

[Apuromafo]

Originally Posted by cjack

Yes sure! Here the link:

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!

im think there is not necesary do many with that app , i will send some private msj
x64dbg (no plugins)
hide command
bp in 00402A90 as hw bp and start to check
is posible use the values (provided) or any fake.
here must be the end:

00403251 68 50714100 PUSH reg3.00417150
00403256 6A 06 PUSH 6
00403258 8B0D 18714100 MOV ECX,DWORD PTR DS:[417118]
0040325E 51 PUSH ECX
0040325F E8 EC2B0000 CALL reg3.00405E50
00403264 83C4 0C ADD ESP,0C
00403267 B9 06000000 MOV ECX,6
0040326C BE 40584100 MOV ESI,reg3.00415840 ; ASCII "Thank you for registering."
00403271 8DBD E0FEFFFF LEA EDI,DWORD PTR SS:[EBP-120]
00403277 F3:A5 REP MOVS DWORD PTR ES:[EDI],DWORD PTR DS>
00403279 66:A5 MOVS WORD PTR ES:[EDI],WORD PTR DS:[ESI]
0040327B A4 MOVS BYTE PTR ES:[EDI],BYTE PTR DS:[ESI]
0040327C 6A 00 PUSH 0
0040327E 68 00534100 PUSH reg3.00415300 ; ASCII "Encryptionizer Key Registration"
00403283 8D95 E0FEFFFF LEA EDX,DWORD PTR SS:[EBP-120]
00403289 52 PUSH EDX
0040328A 8B45 08 MOV EAX,DWORD PTR SS:[EBP+8]
0040328D 50 PUSH EAX
0040328E FF15 74214100 CALL DWORD PTR DS:[412174]
00403294 C705 BC6C4100 00>MOV DWORD PTR DS:[416CBC],0
0040329E 6A FF PUSH -1
004032A0 8B4D 08 MOV ECX,DWORD PTR SS:[EBP+8]
004032A3 51 PUSH ECX
004032A4 FF15 64214100 CALL DWORD PTR DS:[412164]
004032AA C745 F8 01000000 MOV DWORD PTR SS:[EBP-8],1

if not have the program, will call to program regedit values , im think there not must be a normal app with armadillo (minimum protection)

BR, Apuromafo

[Apuromafo]

About the importance of privatevalue in the example before exposed:
generating a licence for apuromafo for x86+x64 (is the same cert shortv3 lv10)

->

tool:ATK 0.4
Ecdsa Public: 1570789295,4089747062247003654720736468506441,10111618751385367037406972360317044
(Curve SEED : 1570789295
Base Point x : 4089747062247003654720736468506441
Base Point y : 10111618751385367037406972360317044)
Private:1984557253727814641989266002264698
name:apuromafo
Sym:BDA4FA1C
press generate and see:

name:apuromafo
serial:000017-MC8PXU-6U3PC3-3V93J6-Y9MCJ5-7GF1E8-TRWK3F-JUGJV6-4QFZNC-TW0YVM


in advanced log

KeyBytes (Len: 6, 0x6):
1CC8BDA4FA1C
NextRandomRange Array (Seed=37577C32)
F40CE61ECC9B
Encrypted KeyBytes:
E8C45BBA3687
Cooked Name (Len: 9, 0x9):
APUROMAFO
Message (Len: 15, 0xF):
E8C45BBA3687415055524F4D41464F
Message Hash (Len: 16, 0x10):
F1AAF5EC593C2E208C91E2BFA9ED06F7
Random point:
x=747BC033ABFF5D62B6845ABE3139, y=11EE604E9C851EBF14BF56807DCD8,
prvt=CD79505FC0D0A18FD75A5F355CD8
Signature (Len: 28, 0x1C):
660C7B48E46F268C914F0785C8CE3931BE5A84B6625DFFAB33C07B74
Signed KeyBytes (Len: 34, 0x22):
E8C45BBA3687660C7B48E46F268C914F0785C8CE3931BE5A84B6625DFFAB33C07B74

in my pc, both armadillo was registred with my user+serial generated using atk0.4

BR, Apuromafo