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Cryptography In the Bounded Quantum-Storage Model

Cryptography In the Bounded Quantum-Storage Model. Ivan Damgård, Louis Salvail, Christian Schaffner BRICS, University of Århus, DK Serge Fehr CWI, Amsterdam, NL. FOCS 2005 - Pittsburgh Tuesday, October 25 th 2005. Rabin Oblivious Transfer. b. b / ?. Bit Commitment. b. C b. b.

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Cryptography In the Bounded Quantum-Storage Model

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  1. Cryptography In theBounded Quantum-Storage Model Ivan Damgård, Louis Salvail, Christian SchaffnerBRICS, University of Århus, DK Serge Fehr CWI, Amsterdam, NL FOCS 2005 - Pittsburgh Tuesday, October 25th 2005

  2. Rabin Oblivious Transfer b b / ? Bit Commitment b Cb b b in Cb? Classical 2-party primitives • private • oblivious OT BC • binding • hiding • OT ) BC • OT is complete for two-party cryptography

  3. Known Impossibility Results • In the classical unconditionally secure model without further assumptions OT • In the unconditionally secure model with quantum communication [Mayers97, Lo-Chau97] BC

  4. ()  ()  Classical Bounded-Storage Model • random string which players try to store • a memory bound applies at a specified moment • protocol for OT [DHRS, TCC04]: memory size of honest players: k memory of dishonest players: <k2 • Tight bound [DM, EC04] • can be improved by allowing quantum communication OT BC

  5. Quantum Bounded-Storage Model • quantum memory bound applies at a specified moment. Besides that, players are unbounded (in time and space) • unconditional secure against adversaries with quantum memory of less then half of the transmitted qubits • honest players do not needquantum memory at all • honest players: 0 k dishonest players: <n/2 <k2 • ratio: 1 k OT  BC 

  6. Agenda • Quantum Bounded-Storage Model • Protocol for Oblivious Transfer • Protocol for Bit Commitment • Practicality Issues

  7. Quantum Mechanics (Toy Version) + basis £ basis Measurements: with prob. 1 yields 1 with prob. ½ yields 0 with prob. ½ yields 1

  8. memory bound: store < n/2 qubits Quantum Protocol for OT Bob Alice 0110… 0110… Example: honest players

  9. memory bound: store < n/2 qubits Quantum Protocol for OT II Bob Alice 0110… 0011…   honest players? private?

  10. … memory bound: store < n/2 qubits Obliviousness against dishonest Bob? Bob Alice 0110… … 11…

  11. Proof of Obliviousness: Tools • Purification techniques like in the Shor-Preskill security proof of BB84 • Privacy Amplification against Quantum Adversaries [RK, TCC05] • new min-entropy based uncertainty relation: OT  For a n-qubit register A in state A, let P+ and P£ be the probabilities of measuring A in the +-basis respectively £-basis. Then it holds P+1 + P£1· 1 + negl(n).

  12. Agenda • Quantum Bounded Storage Model • Protocol for Oblivious Transfer • Protocol for Bit Commitment • Practicality Issues

  13. memory bound: store < n/2 qubits Quantum Protocol for Bit Commitment Verifier Committer BC

  14. Quantum Protocol for Bit Commitment II Verifier Committer memory bound: store < n/2 qubits • one round, non-interactive • commit by receiving! • unconditionally hiding • unconditionally binding as long as Memcommitter < n / 2 BC ) proof uses same tools as for OT !

  15. Agenda • Quantum Bounded Storage Model • Protocol for Oblivious Transfer • Protocol for Bit Commitment • Practicality Issues

  16. Practicality Issues With today’s technology, we • can transmit quantum bits encoded in photons • cannot store them for longer than a few milliseconds OT BC Problems: • imperfect sources (multi-pulse emissions) • transmission errors

  17. Practicality Issues II Our protocols can be modified to • resist attacks based onmulti-photon emissions • tolerate (quantum) noise OT  • Well within reach of current technology. • makes sense over short distances (in contrast to QKD) BC 

  18. Summary Protocols for OT and BC that are • efficient, non-interactive • unconditionally secure against adversaries with bounded quantum memory • practical: • honest players do not need quantum memory • fault-tolerant OT  BC  Thank you for your attention!

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