Abstract
We describe how any two-party quantum computation, specified by a unitary which simultaneously acts on the registers of both parties, can be privately implemented against a quantum version of classical semi-honest adversaries that we call specious. Our construction requires two ideal functionalities to garantee privacy: a private SWAP between registers held by the two parties and a classical private AND-box equivalent to oblivious transfer. If the unitary to be evaluated is in the Clifford group then only one call to SWAP is required for privacy. On the other hand, any unitary not in the Clifford requires one call to an AND-box per R-gate in the circuit. Since SWAP is itself in the Clifford group, this functionality is universal for the private evaluation of any unitary in that group. SWAP can be built from a classical bit commitment scheme or an AND-box but an AND-box cannot be constructed from SWAP. It follows that unitaries in the Clifford group are to some extent the easy ones. We also show that SWAP cannot be implemented privately in the bare model.
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References
Aharonov, D., Ben-Or, M.: Fault-tolerant quantum computation with constant error. In: 29th Annual ACM Symposium on Theory of Computing (STOC), pp. 176–188 (1997)
Ambainis, A., Mosca, M., Tapp, A., de Wolf, R.: Private quantum channels. In: 41st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 547–553 (2000)
Ben-Or, M., Crépeau, C., Gottesman, D., Hassidim, A., Smith, A.: Secure multiparty quantum computation with (only) a strict honest majority. In: 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 249–260 (2006)
Broadbent, A., Fitzsimons, J., Kashefi, E.: Universal blind quantum computation (December 2009), http://arxiv.org/abs/0807.4154
Crépeau, C., Gottesman, D., Smith, A.: Secure multi-party quantum computation. In: 34th Annual ACM Symposium on Theory of Computing (STOC), pp. 643–652 (2002)
Gottesman, D., Chuang, I.L.: Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999)
Gottesman, D., Chuang, I.L.: Quantum teleportation is a universal computational primitive (August 1999), http://arxiv.org/abs/quant-ph/9908010
Gutoski, G., Watrous, J.: Quantum interactive proofs with competing provers. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 605–616. Springer, Heidelberg (2005)
Kilian, J.: Founding cryptography on oblivious transfer. In: 20th Annual ACM Symposium on Theory of Computing (STOC), pp. 20–31 (1988)
Lo, H.-K.: Insecurity of quantum secure computations. Physical Review A 56(2), 1154–1162 (1997)
Lo, H.-K., Chau, H.F.: Is quantum bit commitment really possible? Physical Review Letters 78, 3410–3413 (1997)
Mayers, D.: Unconditionally secure quantum bit commitment is impossible. Physical Review Letters 78, 3414–3417 (1997)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Popescu, S., Rohrlich, D.: Quantum nonlocality as an axiom. Foundations of Physics 24(3), 379–385 (1994)
Popescu, S., Rohrlich, D.: Causality and nonlocality as axioms for quantum mechanics. In: Symposium on Causality and Locality in Modern Physics and Astronomy: Open Questions and Possible Solutions (1997), http://arxiv.org/abs/quant-ph/9709026
Renner, R., König, R.: Universally composable privacy amplification against quantum adversaries. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 407–425. Springer, Heidelberg (2005)
Salvail, L., Sotáková, M., Schaffner, C.: On the power of two-party quantum cryptography. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 70–87. Springer, Heidelberg (2009)
Shor, P.W.: Fault-tolerant quantum computation. In: 37th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 56–65 (1996)
Smith, A.: Techniques for secure distributed computing with quantum data. Presented at the Field’s institute Quantum Cryptography and Computing Workshop (October 2006)
Watrous, J.: Limits on the power of quantum statistical zero-knowledge. In: 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 459–468 (2002)
Wolf, S., Wullschleger, J.: Oblivious transfer and quantum non-locality. In: International Symposium on Information Theory (ISIT 2005), pp. 1745–1748 (2005)
Yao, A.: How to generate and exchange secrets. In: 27th Annual IEEE Symposium on Foundations of Computer Science (FOCS) (1986)
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Dupuis, F., Nielsen, J.B., Salvail, L. (2010). Secure Two-Party Quantum Evaluation of Unitaries against Specious Adversaries. In: Rabin, T. (eds) Advances in Cryptology – CRYPTO 2010. CRYPTO 2010. Lecture Notes in Computer Science, vol 6223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14623-7_37
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