Byzantine agreement requires a set of parties in a distributed system to agree on a value even if some parties are corrupted. A new protocol for Byzantine agreement in a completely asynchronous network is presented that makes use of cryptography, specifically of threshold signatures and coin-tossing protocols. These cryptographic protocols have practical and provably secure implementations in the “random oracle” model. In particular, a coin-tossing protocol based on the Diffie-Hellman problem is presented and analyzed.The resulting asynchronous Byzantine agreement protocol is both practical and nearly matches the known theoretical lower bounds. More precisely, it tolerates the maximum number of corrupted parties, runs in constant expected time, has message and communication complexity close to the maximum, and uses a trusted dealer only in a setup phase, after which it can process a virtually unlimited number of transactions. Novel dual-threshold variants of both cryptographic protocols are used.The protocol is formulated as a transaction processing service in a cryptographic security model, which differs from the standard information-theoretic formalization and may be of independent interest.