Abstract
In this paper, we define a class of special two-party private summation (S2PPS) problems and present a common quantum solution to S2PPS problems. Compared to related classical solutions, our solution has advantages of higher security and lower communication complexity, and especially it can ensure the fairness of two parties without the help of a third party. Furthermore, we investigate the practical applications of our proposed S2PPS protocol in many privacy-preserving settings with big data sets, including private similarity decision, anonymous authentication, social networks, secure trade negotiation, secure data mining.
Similar content being viewed by others
References
Yao, A.C.: Protocols for secure computations. In: Proceedings of the 23rd IEEE Symposium on Foundations of Computer Science (FOCS’ 82), p. 160 (1982)
Goldreich, O., Micali, S., Wigderson, A.: How to play ANY mental game. In: Proceedings of the 19th Annual ACM Symposium on Theory of Computing (STOC’87), p. 218 (1987)
Yao, A.C.: How to generate and exchange secrets. In: Proceedings of the 27th Annual Symposium on Foundations of Computer Science (FOCS’86), p. 162 (1986)
Lindell, Y., Pinkas, B.: A proof of Yao’s protocol for secure two-party computation. J. Cryptol. 22, 161 (2009)
Lindell, Y., Pinkas, B.: Secure multiparty computation for privacy-preserving data mining. J. Priv. Confid. 1, 59 (2009)
Goldreich, O.: Secure Multi-Party Computation (Final (incomplete) Draft, Version 1.4). http://www.wisdom.weizmann.ac.il/~oded/PSX/prot.pdf
Atallah, M.J., Du, W.: Secure multi-party computational geometry. In: Proceedings of the 7th International Workshop on Algorithms and Data Structures, LNCS 2125, p. 165 (2001)
Freedman, M.J., Nissim, K., Pinkas, B.: Efficient private matching and set intersection. In: Proceedings of the Advances in Cryptology—Eurocrypt 2004, LNCS 3027, p. 1 (2004)
Cristofaro, E.D., Gasti, P., Tsudik, G.: Fast and private computation of cardinality of set intersection and union. In: Proceedings of the Cryptology and Network Security, LNCS 7712, p. 218 (2012)
Wu, M.E., Chang, S.Y., Lu, C.J., Sun, H.M.: A communication-efficient private matching scheme in Client–Server model. Inf. Sci. 275, 348 (2014)
Vaidya, J., Shafiq, B., Fan, W., Mehmood, D., Lorenzi, D.: A random decision tree framework for privacy-preserving data mining. IEEE Trans. Dependable Secur. Comput. 11, 399 (2014)
Debnath, S.K., Dutta, R.: Secure and efficient private set intersection cardinality using bloom filter. In: Proceedings of the Information Security, LNCS 9290, p. 209 (2015)
Chan, P., Lucio-Martinez, I., Mo, X.F., Simon, C., Tittel, W.: Performing private database queries in a real-world environment using a quantum protocol. Sci. Rep. 4, 5233 (2014)
Tan, S.H., Kettlewell, J.A., Ouyang, Y.K., Chen, L., Fitzsimons, J.F.: A quantum approach to homomorphic encryption. Sci. Rep. 6, 33467 (2016)
Brassard, G.: Modern Cryptology: A Tutorial. Lecture Notes in Computer Science, vol. 325. Springer, New York (1988)
Shor, P.W.: Algorithms for quantum computation—discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, p. 124 (1994)
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on Theory of Computing, p. 212 (1996)
Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, p. 175 (1984)
Boykin, P.O., Roychowdhury, V.: Optimal encryption of quantum bits. Phys. Rev. A 67, 042317 (2003)
Lai, H., Zhang, J., Luo, M.X., Pan, L., Pieprzyk, J., Xiao, F.Y., Orgun, M.A.: Hybrid threshold adaptable quantum secret sharing scheme with reverse Huffman–Fibonacci-tree coding. Sci. Rep. 6, 31350 (2016)
Farouk, A., Zakaria, M., Megahed, A., Omara, F.A.: A generalized architecture of quantum secure direct communication for N disjointed users with authentication. Sci. Rep. 5, 16080 (2015)
Wang, T.Y., Cai, X.Q., Ren, Y.L., Zhang, R.L.: Security of quantum digital signatures for classical messages. Sci. Rep. 5, 9231 (2015)
Crépeau, C., Gottesman, D., Smith, A.: Secure multi-party quantum computation. In: Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, p. 643 (2002)
Ben-or, M., Crépeau, C., Gottesman, D., Hassidim, A., Smith, A.: Secure multiparty quantum computation with (only) a strict honest majority. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, p. 249 (2006)
Unruh, D.: Universally composable quantum multi-party computation. In: Proceedings of the Advances in Cryptology—EUROCRYPT 2010, LNCS 6110, p. 486 (2010)
Jakobi, M., Simon, C., Gisin, N., et al.: Practical private database queries based on a quantum key distribution protocol. Phys. Rev. A 83, 022301 (2011)
Gao, F., Liu, B., Wen, Q., Chen, H.: Flexible quantum private queries based on quantum key distribution. Opt. Express 20, 17411 (2012)
Gao, F., Liu, B., Huang, W., Wen, Q.: Post-processing of the oblivious key in quantum private queries. IEEE. J. Sel. Top. Quantum Electr. 21, 6600111 (2015)
Liu, B., Gao, F., Huang, W., Wen, Q.: QKD-based quantum private query without a failure probability. Sci. China Phys. Mech. Astron. 58, 100301 (2015)
Wei, C., Wang, T., Gao, F.: Practical quantum private query with better performance in resisting joint-measurement attack. Phys. Rev. A 93, 042318 (2016)
Lo, H.K.: Insecurity of quantum secure computations. Phys. Rev. A 56, 1154 (1997)
Colbeck, R.: Impossibility of secure two-party classical computation. Phys. Rev. A 76, 062308 (2007)
Buhrman, H., Christandl, M., Schaffner, C.: Complete insecurity of quantum protocols for classical two-party computation. Phys. Rev. Lett. 109, 160501 (2012)
Hardy, L., Kent, A.: Cheat sensitive quantum bit commitment. Phys. Rev. Lett. 92, 157901 (2004)
Giovannetti, V., Lloyd, S., Maccone, L.: Quantum private queries. Phys. Rev. Lett. 100, 230502 (2008)
Olejnik, L.: Secure quantum private information retrieval using phase-encoded queries. Phys. Rev. A 84, 022313 (2011)
Shi, R.H., Mu, Y., Zhong, H., Zhang, S.: Quantum oblivious set-member decision protocol. Phys. Rev. A 92, 022309 (2015)
Shi, R.H., Mu, Y., Zhong, H., Cui, J., Zhang, S.: Secure multiparty quantum computation for summation and multiplication. Sci. Rep. 6, 19655 (2016)
Brassard, G., Høyer, P., Tapp, A.: Quantum counting. In: Proceedings of the 25th International Colloquium on Automata, Languages and Programming, LNCS 1443, p. 820 (1998)
Mosca, M.: Counting by quantum eigenvalue estimation. Theor. Comput. Sci. 264, 139 (2001)
Diao, Z.J., Huang, C.F., Wang, K.: Quantum counting: algorithm and error distribution. Acta. Appl. Math. 118, 147 (2012)
Kent, A.: Quantum bit string commitment. Phys. Rev. Lett. 90, 237901 (2003)
Holevo, A.: Probabilistic and Statistical Aspects of Quantum Theory. Publications of the Scuola Normale Superiore. Springer, New York (2011)
Acknowledgements
This wok was supported by National Natural Science Foundation of China (No. 61173187) and Talents Youth Fund of Anhui Province Universities (No. 2013SQRL006ZD).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shi, RH., Zhang, S. Quantum solution to a class of two-party private summation problems. Quantum Inf Process 16, 225 (2017). https://doi.org/10.1007/s11128-017-1676-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-017-1676-x