Abstract
We propose a framework for analyzing classical sampling strategies for estimating the Hamming weight of a large string from a few sample positions, when applied to a multi-qubit quantum system instead. The framework shows how to interpret the result of such a strategy and how to define its accuracy when applied to a quantum system. Furthermore, we show how the accuracy of any strategy relates to its accuracy in its classical usage, which is well understood for the important examples. We show the usefulness of our framework by using it to obtain new and simple security proofs for the following quantum-cryptographic schemes: BB84 quantum-key-distribution, and quantum oblivious-transfer from bit-commitment.
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References
Bennett, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing, pp. 175–179 (1984)
Bouman, N.J., Fehr, S.: Sampling in a quantum population, and applications (2009), http://arxiv.org/abs/0907.4246
Bruss, D.: Optimal eavesdropping in quantum cryptography with six states. Physical Review Letters 81, 3018 (1998), http://arxiv.org/abs/quant-ph/9805019
Damgård, I., Fehr, S., Lunemann, C., Salvail, L., Schaffner, C.: Improving the security of quantum protocols via commit-and-open. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 408–427. Springer, Heidelberg (2009)
Hoeffding, W.: Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58(301), 13–30 (1963)
Lo, H.K., Chau, H.F., Ardehali, M.: Efficient quantum key distribution scheme and a proof of its unconditional security. J. Cryptol. 18(2), 133–165 (2005)
Renner, R.: Security of Quantum Key Distribution. Ph.D. thesis, ETH Zürich (Switzerland) (September 2005), http://arxiv.org/abs/quant-ph/0512258
Renner, R.S., König, R.: Universally composable privacy amplification against quantum adversaries. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 407–425. Springer, Heidelberg (2005)
Shor, P.W., Preskill, J.: Simple Proof of Security of the BB84 Quantum Key Distribution Protocol. Phys. Rev. Lett. 85, 441–444 (2000)
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Bouman, N.J., Fehr, S. (2010). Sampling in a Quantum Population, and Applications. 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_39
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DOI: https://doi.org/10.1007/978-3-642-14623-7_39
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