# Generation and Distribution of Quantum Oblivious Keys for Secure Multiparty Computation
## 4 Conclusions  
Motivated by the usefulness of SMC as a privacy-protecting data mining tool, and identifying its OT cost as its main implementation challenge, we have proposed a potential solution for practical implementation of OT as a subroutine SMC. The scheme consists on pre-sharing an oblivious key pair and then using it to compute fast OT during the execution of the SMC protocol. We call this approach hybrid because it uses resources traditionally associated with classical symmetric cryptography (cryptographic hash functions), as well as quantum state communication and measurements on conjugate observables, resources associated with quantum cryptography. The scheme is secure as far as the chosen hash function is secure against quantum attacks. In addition, we showed that the overall time complexity of \(\pi_{HOK}\) is linear on all its security parameters, as opposed to the public-key based alternatives, whose time complexities are at least quadratic on their respective parameters. Finally, by comparing the state of current technology with the protocol requirements, we concluded that it has the potential to surpass current asymmetric cryptography based techniques. It was also noted that current experimental implementations of standard discrete-variable QKD can be adapted to perform \(\pi_{HOK}\). The same post-processing techniques of error correction and privacy amplification apply, however, fast hashing subroutines should be added for commitments during the parameter estimation step. Future work includes designing an experimental setup, meeting the implementation challenges, and experimentally testing the speed, correctness, and security of the resulting oblivious key pairs. This includes computing oblivious key rate bounds for realistic scenarios and comparing them with current alternative technologies. Real world key rate comparisons can help us understand better the position of quantum technologies in the modern cryptographic landscape. Regarding the use of quantum cryptography during the commitment phase; because of the impossibility theorem for unconditionally secure commitments in the quantum setting [17], one must always work with an additional assumption on top of needing quantum resources. The noisy storage model provides an example in which the commitments are achieved by noisy quantum memories [21; 22; 49]. The drawback of this particular assumption is the fact that advances in quantum storage technology work against the performance of the protocol, which is not a desired feature. The added cost of using quantum communication is a disadvantage. So far, to the knowledge of the authors, there are no additional practical quantum bit commitment protocols that provide advantages in security or efficiency compared to classical ones once additional assumptions (such as random oracles, common reference strings, computational hardness, etc.,) are introduced. Nevertheless, we are optimistic that such protocols can be found in the future, perhaps by clever design, or by considering a different a kind of assumption outside of the standard ones. Conceptualization, P.M. and A.N.P. ; methodology, M.F.R., N.A.S. and N.J.M. ; validation, M.L., N.P., and A.S.; formal analysis, M.L., P.Y., N.P., A.S. and P.M.; investigation, M.L., M.F.R., N.A.S. and N.J.M. ; writing--original draft preparation, M.L., N.P., P.Y., M.F.R., N.A.S., N.J.M. and A.N.P. ; writing--review and editing, M.L. and P.M.; visualization, M.F.R., N.A.S., N.J.M. and A.N.P. ; supervision, P.M. and A.N.P. ; project administration, P.M., A.S. and A.N.P. ; funding acquisition, P.M., A.S. and A.N.P. All authors have read and agreed to the published version of the manuscript. This work is supported by the Fundacao para a Ciencia e a Tecnologia (FCT) through national funds, by FEDER, COMPETE 2020, and by Regional Operational Program of Lisbon, under UIDB/50008/2020, UID/50008/2020, UID/CEC/00408/2013, POCI-0-0145-FEDER-031826, POCI-01-0247-FEDER-039728, PTDC/CCI-CIF/29877/2017, PD/BD/114334/2016, PD/BD/113648/2015, and CEECIND/04594/2017/CP1393/CT0006A.