🤖 Sibling output penalty

A privacy liability term of the cost function. Spending outputs of the same transaction together is wasteful, and more indicative of common ownership than spending unrelated coins together. It’s penalized heavily.

Definition

• $I$: the own inputs of the transaction under consideration.
• For each earlier transaction $T$, $j_T$ is the number of its outputs in $I$.
• Liability. ${\ell }_s=\sigma {\sum }_T\max (0,j_T-1)$, with $\sigma$ large.
• Neither the labels from the Consolidation penalty chapter nor subset sum density reduce it. Amounts can explain the values, but not two users spending outputs of one transaction together.

In the decision tree

• It’s a privacy-related term.
• Worst case: ${\ell }_s$ as defined. It depends only on the own inputs.
• Best case: ${\ell }_s=0$, which is used for pruning.
• ${\ell }_s\ge 0$ is unbounded, so it can exceed the remaining budget. The action is then taken only if other terms, e.g. a payment deadline, outweigh it.
• It applies to every own output of the transaction. The discount scales with value, not with the number of outputs.

After confirmation

• ${\ell }_s$ is fixed once the inputs are chosen.
• Once the action is taken, the resulting coins’ liability is capped at 1.

Open questions

• Should ${\ell }_s$ extend to coins with a common ancestor further back?