The Bitcoin system only provides eventual consistency. For everyday life, the time to confirm a Bitcoin transaction is prohibitively slow. In this paper we propose a new system, built on the Bitcoin blockchain, which enables strong consistency. Our system, PeerCensus, acts as a certification authority, manages peer identities in a peer-to-peer network, and ultimately enhances Bitcoin and similar systems with strong consistency. Our extensive analysis shows that PeerCensus is in a secure state with high probability. We also show how Discoin, a Bitcoin variant that decouples block creation and transaction confirmation, can be built on top of PeerCensus, enabling real-time payments. Unlike Bitcoin, once transactions in Discoin are committed, they stay committed. CCS Concepts •Networks → Peer-to-peer protocols; Keywords Blockchain, Bitcoin, Byzantine Agreement