The concept of quantum cryptography(QC), which utilizes a quantum channel and classical TMs (Turing Machine) (as well as a classical channel) and some protocols such as oblivious transfer based on this concept have also been presented. QC is one of the solutions to the above-mentioned problem when a QTM (Quantum Turing Machine) is realized in the future: that is, QC will be used for key-distribution in place of public-key encryption if a QTM is realized. The major difference between QC and QPKC is that QC employs a quantum channel (and classical channel)while QPKC (Quantum Public Key Cryptosystem) employs only a classical channel. The security assumption for a QC scheme is quantum mechanics (believed by most physicists), while that fora QPKC scheme is a computational assumption (e.g., existence of a one-way function) in the QTM model.
Although several experimental QC systems have been already realized in the current technologies, recently reported security flaws of these systems are due to their realistic restrictions of quantum channels such as channel losses, realistic detection process, modifications of the qubits through channels, and fixed dark count error over long distance channels. In addition, it is likely that much more complicated communication networks will be utilized in the future, and it seems technically very hard and much costly to realize a quantum channel from end to end through such complicated networks even in the future.
Accordingly, the QPKC approach seems much more promising, since in many applications encryption and key-distribution should be realized by end-to-end communication through (classical) complicated communication networks. QC provides no solution to the problem of digital signatures when a QTM is realized: that is, QC cannot be used in digital signatures. Hence, our QPKC approach may be the only possible solution to the problem of digital signatures when a QTM is realized.