Abstract
We prove the unconditional security of a quantum key distribution (QKD) protocol on a noisy channel against the most general attack allowed by quantum physics. We use the fact that in a previous paper we have reduced the proof of the unconditionally security of this QKD protocol to a proof that a corresponding Quantum String Oblivious Transfer (String-QOT) protocol would be unconditionally secure against Bob if implemented on top of an unconditionally secure bit commitment scheme. We prove a lemma that extends a security proof given by Yao for a (one bit) QOT protocol to this String-QOT protocol. This result and the reduction mentioned above implies the unconditional security of our QKD protocol despite our previous proof that unconditionally secure bit commitment schemes are impossible.
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References
C.H. Bennett, Quantum cryptography using any two nonorthogonal states, Physical Review Letters, vol. 68, no. 21, 25 May 1992, pp. 3121–2124.
C.H. Bennett, G. Brassard, Quantum Cryptography: Public key distribution and coin tossing, Proc. of IEEE International Conference on Computers, Systems, and Signal Processing, Banglore, India, December 1984, pp. 175–179.
C.H. Bennett and G. Brassard, The dawn of a new era for quantum cryptography: The experimental prototype is working!, Sigact News, vol. 20, no. 4, 1989, pp. 78–82.
C.H. Bennett, F. Bessette, G. Brassard, L. Salvail and J. Smolin, Experimental quantum cryptography, Journal of Cryptology, vol. 5, no. 1, 1992, pp. 3–28. Preliminary version in Advances in Cryptology-Eurocrypt’ 90 Proceedings, May 1990, Springer-Verlag, pp. 253–265.
C.H. Bennett, G. Brassard, C. Crépeau, M.-H. Skubiszewska, Practical Quantum Oblivious Transfer, In proceedings of CRYPTO’91, Lecture Notes in Computer Science, vol. 576, Springer-Verlag, Berlin, 1992, pp. 351–366.
G. Brassard, C. Crépeau, M. Sántha, Oblivious Transfers and Intersecting Codes, IEEE Transactions in Information Theory, 1996, (to appear).
C.H. Bennett, T. Mor, J. Smolin, The Parity Bit in Quantum Cryptography, Los Alamos preprint archive quant-ph/9604040, April 1996.
E. Biham, T. Mor, On the Security of Quantum Cryptography Against Collective Attacks Los Alamos preprint archive quant-ph/9605007, May 1996.
C.H. Bennett, G. Brassard and N.D. Mermin, Quantum cryptography without Bell’s theorem, Physical Review Letters, vol. 8, no. 5, 3 February 1992, pp. 557–559.
C.H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. Smolin and W.K. Wootters, Purification of Noisy Entanglement and Faithful Teleportation via Noizy Channels. Physical Review Letters, vol. 76, pp. 722 (1996).
C. Crépeau, Equivalence Between Two Flavors of Oblivious Transfers, Advances in Cryptology — Crypto’ 87 Proceeding, August 1987, Springer-Verlag, pp. 350–354.
C. Crépeau, Correct and Private Reductions among Oblivious Transfers, Ph.D. Thesis, Massachusetts Institute of Technology, 1990.
C. Crépeau, Quantum oblivious transfer, Journal of Modern Optics, vol. 41, no. 12, December 1994, pp. 2445–2454.
D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, A. Sanpera, Quantum privacy amplification and the security of quantum cryptography over noizy channels. Los Alamos preprint archive quant-ph/9604039, April 1996.
A.K. Ekert, Quantum cryptography based on Bell’s theorem, Physical Review Letters, vol. 67, no. 6, 5 August 1991, pp. 661–663.
R.J. Hughes, G. G. Luther, G. L. Morgan, C. G. Peterson and C. Simmons Quantum cryptography over underground optical fibers, Advances in Cryptology: Proceeding of CRYPTO’96.
D. Mayers, On the security of the Quantum Oblivious Transfer and Key Distribution protocols, Advances in Cryptology: Proceeding of CRYPTO’95, Lecture Notes in Computer Science, vol. 963, Springer-Verlag, Berlin, 1995, pp. 124–135.
D. Mayers explained the details of his attack against the BCJL protocol at the 4th workshop on quantum information theory organized by G. Brassard in Montréal, October 1995.
D. Mayers, The Trouble with Quantum Bit Commitment, Los Alamos preprint archive quant-ph/9603015, Mars 1996.
D. Mayers, Unconditionally Secure Quantum Bit Commitment is impossible (to be published).
D. Mayers and L. Salvail, Quantum Oblivious Transfer is Secure Against All Individual Measurements, Proceedings of the workshop on Physics and Computation, PhysComp’ 94, Dallas, Nov 1994, pp. 69–77.
A. Muller, J. Breguet and N. Gisin, Experimental demonstration of quantum cryptography using polarized photons in optical fibre over more than 1 km, Europhysics Letters, vol. 23, no. 6, 20 August 1993, pp. 383–388.
J.G. Rarity, P.C.M. Owens and P.R. Tapster, Quantum random number generation and key sharing, Journal of Modern Optics, vol. 41, no. 12, December 1994, pp. 2435–2444.
P.D. Townsend, J.G. Rarity and P.R. Tapster, Single photon interference in a 10 km long optical fibre interferometer, Electronics Letters, vol. 29, no. 7, April 1993, pp. 634–635.
P.D. Townsend, J.G. Rarity and P.R. Tapster, Enhanced single photon fringe visibility in a 10 km-long prototype quantum cryptography channel, Electronics Letters, vol. 29, no. 14, 8 July 1993, pp. 1291–1293.
M.N. Wegman, J.L. Carter, New hash function and their use in authentification and set equality, Journal of Computer and System Sciences, vol. 22, 1981, pp. 265–279.
A. Yao, Security of Quantum Protocols Against Coherent Measurements, in Proceedings of the 26th Symposium on the Theory of Computing, June 1995, pp. 67–75.
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Mayers, D. (1996). Quantum Key Distribution and String Oblivious Transfer in Noisy Channels. In: Koblitz, N. (eds) Advances in Cryptology — CRYPTO ’96. CRYPTO 1996. Lecture Notes in Computer Science, vol 1109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68697-5_26
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DOI: https://doi.org/10.1007/3-540-68697-5_26
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