This paper presents a proof that quantum key distribution (QKD) can be made unconditionally secure over arbitrarily long distances, even in the presence of noise. The proof reduces the security of a noisy quantum scheme to a noiseless quantum scheme, and then to a noiseless classical scheme, which can be analyzed using classical probability theory. The authors show that, given fault-tolerant quantum computers, QKD can be made secure against eavesdropping, even when the quantum channel is noisy. They also address the problem of distinguishing malicious eavesdropping from noise, and show that classical probability theory can be used to establish the security of QKD. The paper discusses the use of quantum repeaters and fault-tolerant quantum computation to extend the range of secure QKD. It also presents a quantum verification scheme that is similar to a classical verification scheme, and shows that classical arguments can be used to analyze quantum problems. The authors conclude that their proof of security is robust and applicable to a wide range of quantum cryptographic protocols.This paper presents a proof that quantum key distribution (QKD) can be made unconditionally secure over arbitrarily long distances, even in the presence of noise. The proof reduces the security of a noisy quantum scheme to a noiseless quantum scheme, and then to a noiseless classical scheme, which can be analyzed using classical probability theory. The authors show that, given fault-tolerant quantum computers, QKD can be made secure against eavesdropping, even when the quantum channel is noisy. They also address the problem of distinguishing malicious eavesdropping from noise, and show that classical probability theory can be used to establish the security of QKD. The paper discusses the use of quantum repeaters and fault-tolerant quantum computation to extend the range of secure QKD. It also presents a quantum verification scheme that is similar to a classical verification scheme, and shows that classical arguments can be used to analyze quantum problems. The authors conclude that their proof of security is robust and applicable to a wide range of quantum cryptographic protocols.