Despite its title, this survey develops only two applications of cryptographic protocols in quantum computing: key distribution and bit commitment protocol, both of which relate to the BB84 protocol proposed in 1984 by Bennett and Brassard [1].
The first section is an introduction. Section 2 describes the fundamentals of classical cryptography, including easy examples. Section 3 provides some background on quantum mechanics. In section 4, the BB84 quantum key distribution protocol is presented and its security is discussed; in particular, the authors describe an entanglement-based version of BB84 (akin to Ekert’s protocol), providing a proof of its security (devised by Shor and Preskill) and showing that it is equivalent to the prepare-and-measure version of the classical BB84 protocol. Section 5 presents the BB84 quantum bit commitment protocol, based on the ideas of Bennett and Brassard, and shows that the security of unconditional quantum bit commitment is impossible. A brief outlook and some conclusions are provided in section 6.
The first two sections have many unnecessary details like the scytale encryption method and a definition of cryptosystems, and ignore some notions related to coding theory that are used later in the paper. However, the two main sections of the paper, 4 and 5, are interesting and offer fine information about some of the stages of such quantum cryptographic protocols.