LaurentMT

This document is an attempt to define metrics quantifying the degree of privacy provided by a bitcoin transaction.


Objectives

Definition of metrics measuring the resistance of a transaction to a set of attacks against users privacy.

Attacks considered in the scope of these metrics are:
- Merged Inputs Heuristic: methods identifying the inputs controlled by a same entity
- Coinjoin Sudoku: methods identifying the links existing between the inputs and outputs of a transaction 

LaurentMT

Context

In part 1 of this document, we've defined the entropy of a transaction.
This metric is a first good proxy to qualify the degree of privacy provided by a transaction but it fails to detect privacy leaks occuring at lower levels (1).
In this second part, we define 2 complementary fine-grained tools/metrics: the Link Probability of 2 utxos (LP) and the Link Probability Matrix (LPM) of a transaction.


Link Probability of 2 UTXOs

We call Link Probability of a tuple (tx input, tx output) the probability that a link exists between the 2 utxos.

LaurentMT

Context

This third part is about known and potential attacks against the privacy provided by tools like coinjoin.


Known attacks & weaknesses

- Linkability of inputs and outputs

A good illustration of this attack is Coinjoin Sudoku (see (1) for details).

LaurentMT

Back to home. As promised, here are some elements about the growth of activity observed during the last months. 
I apologize in advance for the long text and my crappy english.

A bit of context: I've been working on the development of OXT (an analytics platform dedicated to the bitcoin blockchain) during the last 12 months. It means that I've spent a part of this time observing charts to check if they make sense, are useful...
During this process I've learned one thing: bitcoin is still a small economy and therefore it's still possible that the activity of a single actor/service has a visible impact at global level.
For instance, some of these observations are related to well known events like the growth of #txs in 2012 (related to Satoshi Dice).
Some others are less known like this pattern in the growth of the utxo set which is likely to be caused by a small number of faucets doing weekly payments (https://bitcointalk.org/index.php?topic=1055594.msg11394989#msg11394989)
At last, some cases remain very myste

LaurentMT

depth;block;txid;receiver;amount_sent;amount_remaining;
0;400590;e26fa07a279f7d89ccb3f1a06a0e48ae0352c7eb4569eeef485f0370da075f73;;2049224;86979660465;
1;400590;49a3906606a37d7cd80ea35ab0f776f20e334306e2baf89929ad92f3bcc40a0b;ANON-543454272;2049224;86977581241;
2;400590;73fea04aaa60bdef18fd33e20f1738cba8f936a238c876669af0ba9743e62ff7;;10246122;86967305119;
3;400590;d8fb997145aae91ff7f8d2f9c3755e8d2b42d4af16447e4ed18b5ac1d0fd3b81;ANON-543454272;630819571;86336455548;
4;400590;6b020df2effde11fd8dba37d7757fe5e209cf38e8431801bc22c4e9535b48577;;53621371;86282804177;
5;400590;cba27ca7dac95ffc75ccc0be7b350f62e5910dba52362b7a2326abac6fde2c63;ANON-604635767;33129127;86249645050;
6;400590;dbdec93c617dad201cbcc5116aec5c15c2c3a58c9b50c255dca37648f4b664b0;;20833781;86228781269;
7;400590;44424153548ea72cd37bd13d568cbc8618d4073cb17a12d87bbd89812f9501a2;ANON-543454272;19126094;86209625175;
8;400590;8053b20f31d28e5ed3d95c1f7a57f70750751e39c2a5d34cb90df26221ec1916;ANON-543454272;11612271;86197982904;

LaurentMT

Keybase proof

I hereby claim:

• I am laurentmt on github.
• I am laurentmt (https://keybase.io/laurentmt) on keybase.
• I have a public key ASDiYbNA_9vdNN7-9VaxVosu5LZizw7Uz6Va-ZmMqYYnhwo

To claim this, I am signing this object:

LaurentMT

Addresses from alleged cold wallet
----------------------------------
1HyYMMCdCcHnfjwMW2jE4cv9qVkVDFUzVa
1JPtxSGoekZfLQeYAWkbhBhkr2VEDADHZB
1MhgmGaHwLAvvKVyFvy6zy9pRQFXaxwE9M
1ECUQLuioJbFZAQchcZq9pggd4EwcpuANe
1J9Fqc3TicNoy1Y7tgmhQznWrP5AVLXj9R


Addresses found with the merged inputs heuristic (no transitivity)

LaurentMT

TXS WITH AN INPUT CONTROLLED 1JZJaDDC44DCKLnezDsbW43Zf8LspCKBYP
-----------------------------------------------------------------------------------------
  ['117049c3eee4d0da5742738c084b83f2e1c467b461ce0dff6d4e612021e82fcd']
  ['b9cb6053f1c642b0f2aba6e3b21a954807f329edad62571c51e412d33b0d1af1']
  ['025189637c6519406d3f7a44d3338f84e3a698ee1fb9a6383437ebaf024cf092']
  ['2a1cb790f04a52d96a41753ff074de526154b3b827d924299964a1bf33f15b2e']
  ['a8520331a3fc0112b803d50609bf154ec2d6c036116fd25082aa572e318617ed']
  ['29ebaaa955a6c2e70fb369a464500a21bdf8a4fd5640403372b0f688e175a2b3']
  ['e0150e9e3c833001ffd107f4756096f2ef67acad9059f6dd8469e3a8a6a38ac4']
  ['2c88f50d126ee27836840ac47d6c33eeab1fe97fa61305230a53c33ce246d7f9']

LaurentMT

Addresses having an output spent with an output controlled by 1JZJaDDC44DCKLnezDsbW43Zf8LspCKBYP
-------------------------------------------------------------------------------------------------
  ['1JZJaDDC44DCKLnezDsbW43Zf8LspCKBYP']
  ['1MhgmGaHwLAvvKVyFvy6zy9pRQFXaxwE9M']
  ['1J9Fqc3TicNoy1Y7tgmhQznWrP5AVLXj9R']
  ['1ECUQLuioJbFZAQchcZq9pggd4EwcpuANe']
  ['1HyYMMCdCcHnfjwMW2jE4cv9qVkVDFUzVa']
  ['1JPtxSGoekZfLQeYAWkbhBhkr2VEDADHZB']
  ['1JTE7BiMW8isT2nA3j5RMb2EPY4eiuHphw']
  ['1K9iWhJxXb9HPWPjeNtCYKe4T4nAUcwxrG']

LaurentMT

3GWdttsNNZhujgR76nr9Y712njMUnRSMpV
3Kb1NQMA65jCKn61cuayMtzhpjNYmXSf3B
38fVmFdYjxaKcRNAT2on3kju6sCVf9XN1f
3C2fdFyqgvr5xCYVPZ3846jnh8DNiDZRwE
3Pg6z6TXLke1MUsVpUp5YHmoX278DyQNtu
34G1H4QLHddtj4zeJXJJBd7Nva9pYAybbe
3DsKxefZnGDcNpRRX46Tbfv1ZSXNRBTrjz
33HjoA3BiAJrEjD3Bvbg1wNUCcEamXLy9p
37YLkeBZd6uMZgW8V3gJpBDVqWFsDevptQ
3J5ZGTUQPDjUrcHwJWfhkyJEYEjDZYh3Fg