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We introduce Zef, the first Byzantine-Fault Tolerant (BFT) protocol to support payments in anonymous digital coins at arbitrary scale. Zef follows the communication and security model of FastPay: both protocols are asynchronous, low-latency, linearly-scalable, and powered by partially-trusted sharded authorities. Zef further introduces opaque coins represented as off-chain certificates that are bound to user accounts. In order to hide the face values of coins when a payment operation consumes or creates them, Zef uses random commitments and NIZK proofs. Created coins are made unlinkable using the blind and randomizable threshold anonymous credentials of Coconut. To control storage costs associated with coin replay prevention, Zef accounts are designed so that data can be safely removed once an account is deactivated. Besides the specifications and a detailed analysis of the protocol, we are making available an open-source implementation of Zef in Rust. Our extensive benchmarks on AWS confirm textbook linear scalability and demonstrate a confirmation time under one second at nominal capacity. Compared to existing anonymous payment systems based on a blockchain, this represents a latency speedup of three orders of magnitude, with no theoretical limit on throughput.