Vernam's, Kotelnikov's, and Shannon's one-time pad and quantum cryptography

Quantum cryptography—quantum key distribution (QKD)—was one of the first fields of study of quantum information theory. It reached a mature scientific level and has been implemented in commercial systems for secure quantum communications. The key distribution problem is the central issue of symmetric cryptography. Quantum cryptography solves this problem on the basis of the fundamental laws of nature: the principles of quantum mechanics. Quantum key distribution is essentially matching two independent random sequences on the transmitting and receiving sides by exchanging quantum states. Required in addition to the quantum channel is an authentic classical communication channel. Both communication channels are open and vulnerable to a perpetrator's attack. To ensure the authenticity of the classical channel at initial system startup, a seed key is required, which is used to provide information-theoretic authentication. In essence, quantum cryptography systems are mechanisms for expanding this seed key. Subsequent sessions generate a quantum key, part of which is used for authentication, while another part is employed for other cryptographic purposes, such as encryption. An issue fundamental for quantum cryptography is the number of quantum key distribution sessions that can be conducted from the initial system launch until a new system reboot, when the cryptographic properties of the quantum keys reach a critical level, after which they can no longer be used for cryptographic purposes, and a new system reboot is needed. Although a number of reviews on quantum cryptography are currently available, this issue has not been discussed in detail. It is shown that for realistic parameters of quantum cryptography systems that are currently achievable, a QKD system can operate for virtually any length of time before the next reboot. This implies that QKD systems can implement a ‘one-time pad’—a set of one-time keys using only a single seed key. A brief historical overview is also presented, outlining some facts little known to the general public. This review, which is intended for a general audience, is comprehensible to undergraduate and graduate students who have completed university courses on quantum information science. The authors hope that it will provide a deeper understanding of the cryptographic underpinnings of state-of-the-art quantum key distribution systems.