UTXOs Linking Percentage to an address

[albert0bsd]

Hello

Have you ever wondered about the fascinating connections between inputs and outputs in a bitcoin Transaction?

I experimented with the Boltzmann tool, which proved to be quite effective when analyzing a single transaction.

However, my curiosity led me to develop a python tool (uxtotrack) to examine whether UTXOs share common addresses or TXIDs deep within their ancestry lines.
The question that brought me my interest here is: How closely related can supposedly two "independent" UTXOs be if they share a common link buried deep within their ancestry?

Example:

UXTO A and B have some common address in its ancestry line of transactions but in different levels just to put some tags and numbers, Address X is common in UXTO A ancestry Level 7 and Address X is common in UXTO  B ancestry Level 10.

Is there some formula/equationor work already written on that?

In this example we can imagine that some public exchange send balance to those addresses, or any other similar event, like those two address were paid by the same person or entity.

I already did some test with percentages backwards in some UXTO and most of them reach less than 0.01% percent of linkability after 6 or 7 levels of ancestry

So, what does this mean for the linkability of those address? Essentially, when we see less than 0.01% linkability after several levels of ancestry, it indicates that a specific address (in this case, Address X) contributed only a negligible fraction of the total balance in the UTXO we're examining.

I don’t know if this is a correct approach but I can't think of another way.

Now, the question arises: When does an ancestor become insignificant or unrelated to a specific UTXO? I propose two options for consideration:

• When it contributes less than a Satoshi of the Balance of the UXTO
• When it contributes less than 547 Satoshis of the balance of the UXTO

What are your thoughts about this topic?

[o_e_l_e_o]

How closely related can supposedly two "independent" UTXOs be if they share a common link buried deep within their ancestry?

If we make the assumption that addresses don't change hands, then all you can say is that maybe some part of those to UTXOs were owned by the same person a long time ago. I say maybe, because as soon as a transaction has more than one output, you cannot say "which" bitcoin ended up at which output, and indeed, such a concept does not exist at the protocol level.

The relevance of this is almost zero. Does it matter if you and I both own coins that 10 years ago were both owned by Mt Gox? Is that at all relevant to anything? Everyone will have handled cash at some point which was involved in a crime. What's that old statistic about 75% of bank notes having traces of cocaine on them?

Is there some formula/equationor work already written on that?

Maybe. Blockchain analysis companies have their own black box of algorithms and equations which they use to create links between addresses and outputs, but as we were just discussing on another thread, it is anything but scientific and often wildly inaccurate: https://bitcointalk.org/index.php?topic=5464886.0

I don’t know if this is a correct approach but I can't think of another way.

Here's a recent coinjoin transaction I just pulled: https://mempool.space/tx/54e5e265cad4a26bc64dd8ca439f0c62055d7e0a2ff3156f10166aeb17d631f8
Do we say that every output contains 12.5% of the coins of each input? Or do we say that each output contains 100% of the coins of one specific input, but we can only guess which input is linked to each output?

Both statements are wrong. At a protocol level there is no such distinction. So any guesses we make will be exactly that - guesses.

Now, the question arises: When does an ancestor become insignificant or unrelated to a specific UTXO? I propose two options for consideration:

• When it contributes less than a Satoshi of the Balance of the UXTO
• When it contributes less than 547 Satoshis of the balance of the UXTO

I think the first question is "What are you trying to achieve?" We can clearly say that UTXO X is a great-great-great-great-.....-grandparent of UTXO Y, just by following the ancestry and ignoring the amounts. What are you trying to achieve by classifying this based on amounts? Some compliance mechanism? An inference of common ownership? Your desired outcome will change the approach you want to take.

[albert0bsd]

Thank you for your reply

Here's a recent coinjoin transaction I just pulled: https://mempool.space/tx/54e5e265cad4a26bc64dd8ca439f0c62055d7e0a2ff3156f10166aeb17d631f8
Do we say that every output contains 12.5% of the coins of each input? Or do we say that each output contains 100% of the coins of one specific input, but we can only guess which input is linked to each output?

Nice Whirlpool

I think the first question is "What are you trying to achieve?"

what i want to achieve is having a way select the ideal uxtos in some Stonewall TX

For example if i select 4 UXTOs of different address, but two of them (A and B) have the relationship that i mentioned in the OP, It may means nothing but there may be also other factors (Time of that common Address do that transaction, block height, amounts like you mention, and maybe others)

But if the fourth selected UXTOs all have some Address in common the things may change.

What i want to determine is until what point of it is OK merge those UXTOs in a TX

[tbct_mt2]

What i want to determine is until what point of it is OK merge those UXTOs in a TX

If you can make your payments without merging UTXOs, why you don't do this?

You care about privacy and try to merge UTXOs, is it something worth to consider for your privacy?

If possible, I will use each UTXO for different transaction, for different receiver and I will never to merge those UTXOs like you want to do.

[o_e_l_e_o]

what i want to achieve is having a way select the ideal uxtos in some Stonewall TX

Great question! The bottom line is always going to be to wait as long as you can to get as many free remixes as possible.

Let's say you coinjoin six outputs of 0.05 BTC, and then after a single mix you create a stonewall transaction which spends all six of your new outputs together. That's pretty bad for your privacy, and potentially allows all your outputs to be linked. This is going to be the same for any coinjoin implementation.

Let's say you coinjoin six outputs of 0.05 BTC, but then let each one get 5 free remixes before you stonewall them. That's significantly better and much harder to track.

I don't think you can pinpoint a number of mixes and say "After this number it is safe, before this number it is not." It's just not that simple. The anonymity set you get from each individual remix will differ. Some will have 5 inputs/outputs. Others can have up to 8 inputs/outputs. Each other output in one of your mixes might be spent immediately after that remix, which decreases your forward looking anonymity set. Conversely, each other output in one of your mixes might go through another 50 free remixes, which vastly increases your forward looking anonymity set. Similar situation for a backward looking anonymity set - if all the other inputs in one of your mixes are very fresh, then your backward looking set is small. If the other inputs in one of your mixes have already remixed 50 times, then your backward looking set is much greater. Not only will the anonymity set change, but you need to consider your individual threat model as well. Are you wanting to hide your coins from your nosy neighbor next door? Or are you wanting to hide your coins from a nation state attacker? And how many outputs are your stonewalling together? Two might be OK after a couple of remixes; fifty UTXOs much less so.

You might be interested in looking at this: https://code.samourai.io/whirlpool/whirlpool_stats

As an example of my own practice:

I hit this milestone in Sparrow a few weeks ago, and decided to screenshot it for posterity:



I've added a few more to that count since then, and I've got a couple of such inputs in the same ballpark. It's turned in to an experiment now where I will just refuse to spend at least one of these outputs unless absolutely necessary just to see how high we can go.

As I mentioned above, just leave them in for as long as possible. Good luck to anyone trying to link those particular outputs together.

[albert0bsd]

You care about privacy and try to merge UTXOs, is it something worth to consider for your privacy?

Let's say you coinjoin six outputs of 0.05 BTC, but then let each one get 5 free remixes before you stonewall them. That's significantly better and much harder to track.

..... Good luck to anyone trying to link those particular outputs together.

Do you see that i am getting mixed anwsers ?

Well that debate will be endless.

I am goint to add the percentage script to the uxtotrack tool just to see if it is useful or not.

Regards!

[o_e_l_e_o]

Do you see that i am getting mixed anwsers ?

Absolutely. As I said above, I don't think there is a simple right and wrong answer here.

And no offense to tbct_mt2, but I think they have misunderstood the question. Yes, it is generally better if you can avoid consolidating UTXOs, but this is not the case when dealing with Stonewall transactions as you are here, where the whole point is to either coinjoin with another user or create a transaction which looks like you've coinjoined with another user.

[bitmover]

The relevance of this is almost zero. Does it matter if you and I both own coins that 10 years ago were both owned by Mt Gox? Is that at all relevant to anything? Everyone will have handled cash at some point which was involved in a crime. What's that old statistic about 75% of bank notes having traces of cocaine on them?

This percentage may be even higher,  90% as far a I know

https://www.acs.org/pressroom/newsreleases/2009/august/new-study-up-to-90-percent-of-us-paper-money-contains-traces-of-cocaine.html

EMBARGOED FOR RELEASE | August 16, 2009
New study: Up to 90 percent of U.S. paper money contains traces of cocaine

However,  I believe this is due to the fact that people use drug notes as a tool to consume cocaine