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CV Cryptography Using a Bidirectional Quantum Channel

CV Cryptography Using a Bidirectional Quantum Channel. Stefano Mancini. University of Camerino, Italy. in collaboration with S. Pirandola, S. Lloyd & S. Braunstein ( quant-ph/0611167). Outline. A general framework for QKD protocols with CV The security analysis

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CV Cryptography Using a Bidirectional Quantum Channel

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  1. CV Cryptography Using a Bidirectional Quantum Channel Stefano Mancini University of Camerino, Italy in collaboration with S. Pirandola, S. Lloyd & S. Braunstein (quant-ph/0611167)

  2. Outline • A general framework for QKD protocols with CV • The security analysis • From P&M protocols to PT&M protocols • The use of a bidirectional quantum channel • The security analysis and the superadditivity of security thresholds • Conclusions

  3. A general framework for CV QKD • modulated with variance V-1 (with V>>1) givesBob’s measurements give

  4. Xs are correlated random variables characterized by I(XA:XB). To access this information, either Bob estimates Alice’s encoding (direct reconciliation, DR), or Alice estimates Bob’s outcomes (reverse reconciliation, RR). • To get shared secret information the honest parties have to estimate the noise in the channel (by broadcasting and comparing part of their data) so to bound the information I(XA:E) or I(XB:E) which has been potentially stolen by Eve A secret key can be established iff (Csiszar & Korner, 1978)

  5. How to bound Eve’s information? • Collective Gaussian attacks are the most powerful for the Gaussian state protocols [M. Navascues et al., PRL 2006; R. Garcia-Patron & N. Cerf, PRL 2006] • Quadratures encode independent variables individual Gaussian interactions do not need to mix quadratures to be optimal individual Gaussian interaction can be modeled by entangling cloner [F. Grosshans et al., Nature 2003]

  6. Security thresholds (R = 0) Results in accordance with F. Grosshans, PRL 2005 and M. Navascues & A. Acin, PRL 2005.

  7. Prepare & Measure schemes vs Entanglement based schemes virtual entanglement Resources (energy or entanglement) are in the hands of Alice What is about distributing them among Alice and Bob? Remind dense coding protocol!

  8. A shift paradigm: from P&M to PT&M, use a two-way quantum channel b b+a Two-way quantum channel for QubitKD was put forward by K. Bostrom & T. Felbinger, PRL 2002; and M. Lucamarini & S. Mancini, PRL 2005.

  9. What are the advantages ? Eve is forced to a double perturbation of the quantum channel (double exploitment of uncertainty principle)

  10. Security thresholds (collective attacks) Quantities refer to a single use of the quantum channel

  11. Summary of the results Superadditivity behaviour of the security theresholds (the exception being Hom2 DR for T>Tc =0.86 in DR) When the channel is too noisy for one-way QKD, it can still be used to provide secure QKD!

  12. What is about a quantum Bob?

  13. Are there other dangerous attacks ? • Coherent attacks exploiting quantum interference between forward and backward path of the quantum channel • Quantum impersonation where Eve short-circuits the two paths of the quantum channel

  14. How to prevent them ? Alice and Bob have to check the coherence of the attacks, i.e. the memory of the quantum channel

  15. Towards unconditional scheme exploiting superadditivity of multiway quantum channel

  16. Conclusions • Virtual entanglement can be profitably used as a cryptographic primitive to assist QKD, when two-way quantum communication is used • Improvement of QKD security performances (superadditivity of security thresholds) • A class of attacks has been related to quantum memory channels predicting a link between correlated noise effects and privacy • The given formulation paves the way for the study of secure multi-way quantum communication • Apply two-(or multi)way quantum communication to other cryptographic tasks, secret sharing, data hiding etc.

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