Parameter Considerations

• How should the false positive rate be determined? In some epoch, let $p$ be the false positive rate, $N$ be the total number of messages, $M$ be the number of true positives for some detection key, and $D$ be the number of detections for that detection key. Then $$E[D]=M+p(N-M)=pN+M(1-p),$$ and ideally $p$ should be chosen so that:

  1. $E[D]$ is bounded above;
  2. When $M$ is within the range of “normal use”, $E[D]$ is close enough to $pN$ that it’s difficult for a detector to distinguish (what does this mean exactly?);

• The notion of detection ambiguity only requires that true and false positives be ambiguous in isolation. In practice, however, a detector has additional context: the total number of messages, the number of detected messages, and the false positive probability. What’s the right notion in this context?

• What happens when an adversary manipulates $N$ (diluting the global message stream) or $M$ (by sending extra messages to a target address)? There is some analogy here to flashlight attacks, although with the critical difference that flashlight attacks on decoy systems degrade privacy of the transactions themselves, whereas here the scope is limited to transaction detection.