Quantum cryptography: Public key distribution and coin tossing

TL;DR

The paper introduces quantum cryptography as a foundation for distributing secret randomness without prior shared keys, using non-orthogonal photon states and the uncertainty principle to detect eavesdropping. It formalizes the polarization-based qubit framework, explains conjugate bases, and leverages this to enable secure key distribution via a quantum channel complemented by authenticated public communication. A concrete protocol for quantum public-key distribution is presented, including basis reconciliation, eavesdropping detection, and Wegman–Carter authentication, with claims of security even against adversaries with unlimited computational power, albeit with practical limitations on transmission strength. The work also discusses a quantum coin-tossing protocol and highlights potential quantum-cheating strategies (notably EPR-based) while emphasizing the protocol’s current attainability and constraints, such as lack of digital signatures and amplification-free transmission.

Abstract

When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media, e.g. a communications channel on which it is impossible in principle to eavesdrop without a high probability of disturbing the transmission in such a way as to be detected. Such a quantum channel can be used in conjunction with ordinary insecure classical channels to distribute random key information between two users with the assurance that it remains unknown to anyone else, even when the users share no secret information initially. We also present a protocol for coin-tossing by exchange of quantum messages, which is secure against traditional kinds of cheating, even by an opponent with unlimited computing power, but ironically can be subverted by use of a still subtler quantum phenomenon, the Einstein-Podolsky-Rosen paradox.