Quantum Cryptography

Transcription

1 svozil/publ/2005-qcrypt-pres.pdf Institut für Theoretische Physik, University of Technology Vienna, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria

2 References History & References References History WIE83 Stephen Wiesner, Conjugate coding, Sigact News, 15, (1983) [manuscript written circa 1970] BBSS92 Charles H. Bennett and F. Bessette and G. Brassard and L. Salvail and J. Smolin, Experimental Quantum Cryptography, Journal of Cryptology, 5, 3-28 (1992) Charles H. Bennett and Gilles Brassard and Artur K. Ekert,, Scientific American, 267, (1992) GRTZ02 Nicolas Gisin, Grégoire Ribordy, Wolfgang Tittel, and Hugo Zbinden, Quantum cryptography, Rev. Mod. Phys. 74, (2002) David Mermin, Lecture Notes on Quantum Computation, [Cornell University, Physics , CS 483; Spring, 2005] mermin/qcomp/chap6.pdf

3 History History & References References History 1970 Stephen Wiesner, Conjugate coding: noisy transmission of two or more complementary messages by using single photons in two or more complementary polarization directions/bases BB84 Protocol: key growing via quantum channel & additional classical bidirectional communication channel 1991 EPR-Ekert protocol: maximally entangled state, three complementary polarization directions; additional security confirmation by violation of Bell-type inequality through data which cannot be directly used for coding

4 Wiesner s conjugate coding scheme Wiesner s conjugate coding scheme BB84 Protocol EPR-Ekert protocol Interferometric protocols

5 BB84 Protocol History & References Wiesner s conjugate coding scheme BB84 Protocol EPR-Ekert protocol Interferometric protocols

6 EPR-Ekert protocol History & References Wiesner s conjugate coding scheme BB84 Protocol EPR-Ekert protocol Interferometric protocols Parametrization of ψ = x + + y by two angles 0 θ π (azimutal) and 0 ϕ 2π. Let the expectation value measured by a pair of particles along the directions a i and b j be E(a i, b j ) = P ++ (a i, b j ) + P (a i, b j ) P + (a i, b j ) P + (a i, b j ). Consider the Clauser-Horne-Shimony-Halt (CHSH) term S = E(a 1, b 1 ) E(a 1, b 3 ) + E(a 3, b 1 ) + E(a 3, b 3 ). With the six measurement directions corresponding to ϕ = 0 (for all six), and θ1 a = 0, θa 2 = π/4, θa 3 = π/2, θb 1 = π/4, θb 2 = π/2, and θ3 b = 3π/4 (three per side), S = 2 2 is maximally violated by the Tsirelson bound. Constant monitoring of S certifies the absence of an eavesdropper.

7 Interferometric protocols Wiesner s conjugate coding scheme BB84 Protocol EPR-Ekert protocol Interferometric protocols

8 Single particle events Complementarity No-cloning (no-copy) theorem Man-in-the-middle attack Single particle production, manipulation & detection It is essential to use single particle states, otherwise Eve could eavesdrop on the extra particles.

9 Complementarity History & References Single particle events Complementarity No-cloning (no-copy) theorem Man-in-the-middle attack Eavesdropping randomizes the state transmitted from Alice to Bob.

10 No-cloning (no-copy) theorem Single particle events Complementarity No-cloning (no-copy) theorem Man-in-the-middle attack Ideally, a perfect Qcopy device A, acting upon an arbitrary state ψ and some arbitrary blank state b, would do this: ψ b A i ψ ψ A f. Suppose it would copy the two quasi-classical state + and accordingly: +, b, A i +, +, A f,, b, A i,, A f. By the linearity of quantum mechanics, the state 1 2 ( + + ) is copied according to 1 ( + + ) b, A i 1 ( +, +, A f +,, A f ) ( + + ) 1 2 ( + + ) A i.

11 Single particle events Complementarity No-cloning (no-copy) theorem Man-in-the-middle attack Man-in-the-middle attack using both the classical & quantum channels Eve Alice c box-in-the-middle fake Bob fake Alice c Bob q copy or misinform q from

12 Single particle events Complementarity No-cloning (no-copy) theorem Man-in-the-middle attack Man-in-the-middle attack using both the classical & quantum channels Compare: Standard quantum key distribution protocols are provably secure against eavesdropping attacks, if quantum theory is correct. (from To: The need for the public (non-quantum) channel in this scheme to be immune to active eavesdropping can be relaxed if the Alice and Bob have agreed beforehand on a small secret [[classical cryptographic]] key,.. (from BB84: C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India (IEEE Computer Society Press, 1984), pp ) In accordance with our general philosophy that QKD forms a part of an overall cryptographic architecture, and not an entirely novel architecture of its own, the DARPA Quantum Network currently employs the standardized authentication mechanisms built into the Internet security architecture (IPsec), and in particular those provided by the Internet Key Exchange (IKE) protocol. (from

13 Techniques & gadgets Techniques & gadgets 1989 IBM Yorktown Heights 1993 Lake Geneva & 2004 Vienna 2003-present DARPA Network Boston Photon sources: faint laser pulses, photon pairs generated by parametric downconversion, photon guns,... Quantum channels: single-mode fibers, free-space links,... Single-photon detection: photon counters,... (Quantum) Random number generators: calcite prism,...

14 1989 IBM Yorktown Heights Techniques & gadgets 1989 IBM Yorktown Heights 1993 Lake Geneva & 2004 Vienna 2003-present DARPA Network Boston

15 1993 Lake Geneva History & References Techniques & gadgets 1989 IBM Yorktown Heights 1993 Lake Geneva & 2004 Vienna 2003-present DARPA Network Boston

16 2004 Vienna History & References Techniques & gadgets 1989 IBM Yorktown Heights 1993 Lake Geneva & 2004 Vienna 2003-present DARPA Network Boston

17 2003-present DARPA Network Boston Techniques & gadgets 1989 IBM Yorktown Heights 1993 Lake Geneva & 2004 Vienna 2003-present DARPA Network Boston

18 Techniques & gadgets 1989 IBM Yorktown Heights 1993 Lake Geneva & 2004 Vienna 2003-present DARPA Network Boston Thank you for your attention!