The AZTEC protocol uses cutting-edge zero-knowledge proofs to enable private transactions on Ethereum. This enables the logic of transactions to be validated, whilst keeping the values encrypted. An efficient zero-knowledge privacy protocol and decentralised exchange. AZTEC protocol powers real world financial applications on ethereum mainnet today. AZTEC combines homomorphic encryption and range proofs. Homomorphic encryption allows arithmetic checks on encrypted numbers as if they weren’t encrypted. AZTEC's range proofs ensure that negative numbers (which in a finite field are large positive numbers) cannot subvert the double-spend check. Finally, AZTEC's commitment scheme is a unique method of encrypting data that enables fast and efficient verification of range proofs. This reduces the gas costs of AZTEC transactions on the Ethereum network. The AZTEC's trusted setup can be performed via a highly robust form of multiparty computation, where only one person in the protocol must act in good faith for the scheme to be secure.