Accountable Private Set Cardinality for Distributed Measurement

We introduce cryptographic protocols for securely and efficiently computing the cardinality of set union intersection. Our private set-cardinality (PSC) are designed setting in which a large parties distributed system makes observations, small with more resources higher reliability aggregates observations. PSC allows secure useful statistics gathering privacy-preserving systems. For example, it operators anonymity networks such as Tor to answer questions: "How many unique users using network?" hidden services being accessed?". prove correctness security Universal Composability framework against an active adversary that compromises all but one aggregating parties. Although successful output cannot be guaranteed this setting, either succeeds or terminates abort, we furthermore make accountable causing abort by blaming at least malicious party. also show prevents adaptive corruption data from revealing past them victims targeted compromise, ensure safe measurements making outputs differentially private. present proof-of-concept implementation use demonstrate operates low computational overhead reasonable bandwidth. It can count tens thousands observations hundreds data-collecting while completing within hours. is thus suitable daily system.