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I found a bug in Motorola DMRA ARC4

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doriboni

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Don't believe me? Record a few seconds from the middle of an EP or ADP transmission and I'll pull out the key. Raw source audio WAV recordings from DSD+ work best for me.
I'm curious to see if what you're saying is true, yes, if it's just to show off.
Here's the file you're requesting:

 

EI9BAB

Member
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Messages
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OK, but the same article also clarifies that although there are some digital signature vulnerabilities associated with the birthday attack, it cannot be used to break an encryption scheme any faster than a brute-force attack. This attack relates only to hashing functions and not IV collissions so I don't think it applies here and you are back to 2^18. In actuality a duplicate IV gives you very little information and in reality you are still dealing with a 2^40 keyspace. However, if you are brute forcing a key space of 2^40 then you generally will not have to exhaust the entire range of keys and will find the key halfway through on average. So if it were to take 3 months to search all keys then you can expect you will probably find the key you want in about 6 weeks - sometimes faster and sometimes slower. So in that context you are realistically moving from 2^40 to 2^39. Again, the IV collisions do not come into play here.

The main issue with a small IV pool is precalculation. At the end of the day, if you are confident that you can wait for a specific IV then you can precalculate all 2^40 keystreams for that given IV if you have a few terabytes and a little time. That means that when you encounter that particular IV then you can just look up the keystream and find the corresponding key. You are still presented with the issue though of working out what the keystream was before it was XORed against your svoice uperframe. (There is a way to do this in EP but we won't explicitly discuss that here.)

In reality, if you have worked out what the keystream is for a transmission that you have already decoded and presumably the IV is known, then brute forcing the keys might take a little time but I reckon you would find the key quicker than waiting for a specific radio to use the IV that you are waiting for. If you wanted to do many many different keys then precalculation might be cheaper but you might be waiting a very long time for that special IV to come along.

I don't think we are straying into anything unsavoury here. The discussion above is not telling anyone how to crack anything but clarifies how aa increase in IV collisions do not really aid the cause of a hacker in this attack.
On the other hand, we shoudl not completely dismiss the fact that you have identified the fact that there is potentially a much smaller pool of IVs being utilised. Frequent collisions do become an issue after a while. Some people have made entire YouTube videos about the concept of lack of IV randomisation and made a big deal about the purported vulnerabilites associated with this. It does seem that the actual IV space is smaller than all possible IVs. I'm just not sure if it resets back to the first key when you get to the end or if it loops around to a different number (modulo 2^32) but probably not.
 

EI9BAB

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Also, it should be noted that this is the recommended way under the standard to produce IVs rather than simply incrementing by 1. there may be some benefit to this (e.g. avoiding certain weak IVs). However, I don't think it could necessarily be simply classified as a bug. Maybe more as a known limitation.
 

jimmy9999

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Also, it should be noted that this is the recommended way under the standard to produce IVs rather than simply incrementing by 1. there may be some benefit to this (e.g. avoiding certain weak IVs). However, I don't think it could necessarily be simply classified as a bug. Maybe more as a known limitation.
I discovered that this loops and never goes to the end, which means that if you use a starting IV, it will loop after 294903 IV and some IVs will never appear. It's clearly visible when you start with the IV 00 00 00 01, you can see that there are some IVs that never appear.
45145144
04404405
11140510
15051014
41415154
01155040
01555114
50410154
14014411
54505444
11004054
44511411
11015444
44504054
05511411
41015444
01441111
44050150
54551551
05550415
10414010
14011445
05150541
There is no benefit to this bug, it does not prevent weak IVs because in a primitive LFSR there are no weak IVs, all IVs appear once and only once.


The literature clearly indicates that LFSR MUST be primitive to be reliable. So it's not a limitation, it's a malfunction. If we can't call it a bug, then it has to be a backdoor because no one can believe that MSI isn't capable of choosing a primitive LFSR for its standard.

If it's not a bug and it's intentionally present, it must have a definite advantage for quickly decoding without knowing the key (whether the technique behind it is the birthday attack or whatever).
 
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slicerwizard

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Toronto, Ontario
I'm curious to see if what you're saying is true, yes, if it's just to show off.
Here's the file you're requesting:

Well, not quite. That's much more than a few voice superframes - closer to 70+ (with all unique MIs) and over 25 seconds of audio - and includes a clean call start, so it should have some easy to test for silence frames (i.e. attackable plaintext); it can't be used to prove that only one or a few random superframes from the middle of a call are all that's required to extract a key.

Key extraction done, audio sounds like French language? Only one radio ID, but two different male speakers.
 

doriboni

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Oct 31, 2023
Messages
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And of course, that should be 360 ms (20 ms per voice frame x 3 voice frames per DMR burst x 6 bursts per DMR superframe)...
I can provide you with only one superframe but it takes more work than providing the whole thing. Prove to me already that you can decode that one by giving me the 40-bit key. Then I'll give you a single superframe.
 

mtindor

OH/WV DB Admin
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I can provide you with only one superframe but it takes more work than providing the whole thing. Prove to me already that you can decode that one by giving me the 40-bit key. Then I'll give you a single superframe.

We all know that isn't going to happen. #1 - not allowed on this website. #2 - you likely gave him info for a key that you _really_ want, and I'm positive you aren't getting it. He doesn't have to prove anything.
 
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