Anonymity Experiments

Tx2OutMergeProbability
----------------------

pick a random 2-out tx from the blockchain during month of July 2020
search for direct or indirect merges
repeat n times, report how many of the pairs had >=1 merges detected

result:
[1, 72, 100] of 100 iterations
meaning:
direct merges:  1 of 100
1 churn merges: 72 of 100
2 churn merges: 100 of 100

experiment repeated, this time with 2 entirely random outputs chosen from month of July 2020
result:
merges: [0, 30, 100] of 100 iterations


MergeAnonymitySetSize
---------------------
key question: if you send me two poisoned outputs, and I intend to merge them (i.e. spend them together in the same transaction), 
  how many other ways will the blockchain also report that they might have been merged by chance?

procedure:

pick two random outputs on the blockchain created during month of July 2020
count the number of direct or indirect merges observed

repeat for several pairs of two random poisoned outputs

result:
(churn window means: for each output, the observation window during which all successive churns of that ouput collectively occur)
(direct means spent together directly in a transaction, level 1 means each output churned at most once prior to merge tx. 
 level 1 can thus include situations where the first output was never churned at all, but the second output was churned once)

====================================================
 Possible merges of 2 random outputs, detected with churn window = 2 hours
====================================================
 Direct |  Level 1 |  Level 2 |  Level 3 |  Level 4
--------|----------|----------|----------|----------
      0 |        0 |        0 |        0 |        0
      0 |        0 |        0 |        0 |        0
      0 |        0 |        0 |        1 |        3
      0 |        0 |        1 |        1 |        1
      0 |        0 |        0 |        0 |        0
====================================================

====================================================
 Possible merges of 2 random outputs, detected with churn window = 4 hours
====================================================
 Direct |  Level 1 |  Level 2 |  Level 3 |  Level 4
--------|----------|----------|----------|----------
      0 |        0 |        2 |        8 |       25
      0 |        0 |        0 |        0 |        4
      0 |        0 |        0 |        0 |        4
      0 |        0 |        0 |        1 |        1
      0 |        0 |        1 |        9 |       42
====================================================

====================================================
 Possible merges of 2 random outputs, detected with churn window = 24 hours
====================================================
 Direct |  Level 1 |  Level 2 |  Level 3 |  Level 4
--------|----------|----------|----------|----------
      0 |        0 |        0 |       27 |      358
      0 |        0 |        0 |       69 |      562
      0 |        0 |        2 |       51 |      267
      0 |        0 |        6 |       80 |      642
      0 |        1 |        5 |      378 |     2730
====================================================

====================================================
 Possible merges of 2 random outputs, detected with churn window = 48 hours
====================================================
 Direct |  Level 1 |  Level 2 |  Level 3 |  Level 4
--------|----------|----------|----------|----------
      0 |        0 |       90 |     1902 |    13584
      0 |        0 |       42 |     1036 |     6775
      0 |        0 |        1 |       76 |     1191
      0 |        0 |        5 |      294 |     2740
      0 |        0 |        1 |      111 |     1110
===================================================

====================================================
 Possible merges of 2 random outputs, detected with churn window = 96 hours
====================================================
 Direct |  Level 1 |  Level 2 |  Level 3 |  Level 4
--------|----------|----------|----------|----------
      0 |        0 |        6 |      192 |     2776
      0 |        0 |       29 |     1256 |    11102
      0 |        0 |        5 |      257 |     3314
      0 |        0 |        7 |      420 |     3465
      0 |        0 |       64 |     2987 |    24700
====================================================

Conclusion: Churn incoming inputs at least 3 times, and do not merge churned outputs within 24 hours of receipt