  Bitcoin, the first peer-to-peer electronic cash system, opened the door to
permissionless, private, and trustless transactions. Attempts to repurpose
Bitcoin's underlying blockchain technology have run up against fundamental
limitations to privacy, faithful execution, and transaction finality. We
introduce \emph{Strong Federations}: publicly verifiable, Byzantine-robust
transaction networks that facilitate movement of any asset between disparate
markets, without requiring third-party trust. \emph{Strong Federations} enable
commercial privacy, with support for transactions where asset types and amounts
are opaque, while remaining publicly verifiable. As in Bitcoin, execution
fidelity is cryptographically enforced; however, \emph{Strong Federations}
significantly lower capital requirements for market participants by reducing
transaction latency and improving interoperability. To show how this innovative
solution can be applied today, we describe \emph{\liquid}: the first
implementation of \emph{Strong Federations} deployed in a Financial Market.
