Practical aspects of QKD security

Transcription

1 Practical aspects of QKD security Alexei Trifonov Audrius Berzanskis MagiQ Technologies, Inc.

2 Secure quantum communication Protected environment Alice apparatus Optical channel (insecure) Protected environment Bob apparatus Quantum cryptographic apparatus is located in the secure environment The task for the quantum cryptography is to protect the channel from the eavesdropping Quantum Cryptography Cryptography Security

3 Mutual information, key distillation criterion IAB (, ) 1 εlog ε 1 ε log 1 ε = ( ) 2( ) Bob information gain, ε - quantum bit error rate IAE (, ) = 1 + ξlog ξ + 1 ξ log 1 ξ ( ) ( ) 2 2 Eve information gain by Eve, ξ - error rate by Eve SAB (, E) max ( IAB (, ) IAE (, ), IAB (, ) IBE (, ))

4 Quantum channel Alice detector U1 U2 RNG EPR source E91 or BBM92 RNG Bob detector Alice source t U U2 1 RNG RNG BB84 Bob detector 1 2Φ + = t Φ + U U U U ( ) ( )

5 State estimation A B State distinguishability D ρ ρ + Likelihood of guessing correctly 1 + D L = max { w+, w } = 2 D = 1 p p ψ ψ + + Helstrom bound 2 Mutual information Likelihood of error 1 D ε = 1 L = 2 IAB (, ) = 1 + εlog ε + 1 ε log 1 ε ( ) ( ) 2 2

6 Mach-Zehnder interferometer 1 Relative phase shifter Eve detector 1 ξ = 1 D AE 2 0 Eve detector 2 φ Detector 1 ϕ = 0, π 1 ε = Detector 2 D AB 2 DAB = V

7 Complementarity relations A E B ε = 1 V 2 The main task is to break the symmetry in mutual information Quantum physics provides us with solution Bob Error rates 1 D ξ = 2 Alice D V 1 Complementarity relation Keeping V high enough we can make sure that IAB (, ) > max{ IAE (, ), IBE (, )} IAB (, ) = IAE (, ) D = V ε 1 2 = ξ = 15% 2 Error rate threshold for key distribution

8 What is good about QKD? Does not depend on mathematical complexity or any type of unproven computational algorithm Works as intrusion detector Unclonable leaves no copy of the information sent

9 What is bad about QKD? Intrinsically based upon single photon interferometry very sensitive to loss and decoherence Incompatible with optical amplifiers distance limitation! Uses single photon counters slow!

10 Major components affecting the Source performance of QKD system Ideally true single photon source really weak laser pulse, nonzero probability for more than one photon in a pulse Interferometer visibility up to 30 db is real Apparatus loss progress in telecom made it simple! Fiber loss typically db/km, affects the rate and distance - beyond the control Detector quantum efficiency and dark current noise rate and distance

11 The questions to the designer of the QKD system How to adjust average photon number? How to tune the performance of the single photon counter? Probability, log Photon number

12 Outline detector problem The main parameters of the detector of interest Requirements from security of QKD system Real detector characterization Comparison of true single photon and weak coherent pulse QKD Summary

13 Detector problem Good silicon detector for the first telecom window 830nm or free-space QKD Second and third telecom window are much more transparent: typical losses are db/km for 830nm, db/km for 1310nm, and db/km for 1550nm. Long-haul system (10+ km) can be built only with 1310 or 1550, the later is preferable. Ge detector can be used only for 1310nm (cooling -> > band gap shift). InGaAS detectors have huge afterpulsing -> > decrease in capacity. Solution: careful detector selection, short pulse gating, plus electronic e suppression of the gating pulses after the event.

14 Main parameters of the single photon detector Quantum efficiency the probability of getting a response from a single quanta Dark current probability - the probability of the false click η p DC The speed of recharging the detector maximum rate Afterpulsing probability the increase probability of getting a subsequent false click

15 Performance of the QKD system with true single photon source Single photon source Gain per pulse 1e-1 1e-2 1e-3 1e-4 1e-5 1e-6 Parameters µ B 0.3 η = 10% p DC α = η B = = db / km = 0.5 1e Distance, km

16 Performance Dark current probability is high, solution fast gating + cooling. Detector is below the breakthrough voltage and is gated above only within the time window containing the photon Parameters Base voltage Gate pulse width Gate pulse amplitude Working temperature

17 Detector performance 1.E+05 T=-40degC pw=10ns 1.E+04 MaxC/DC 1.E+03 1.E+02 4V 5V 6V 8V 1.E Bias voltage Ratio of Max Count/ Dark count vs Bias voltage for 10ns gating pulse

18 Gating Amplitude Dependence -80deg C, Gating 2ns 1.00E E-03 T=-80degC, 2ns 4 V 6 V 8 V 1.00E-04 DCR 1.00E E E QE, %

19 Gating Pulse Width Dependence -60deg C, Gating amplitude 8V T = -60 degrees C, Vp = 8 V 1.00E E-04 Tp = 2 ns Tp = 4 ns Tp = 6 ns Tp = 10 ns DCR 1.00E E E QE (%)

20 Gating Pulse Width Dependence: normalized -60deg C, Gating amplitude 8V 1.00E-04 T = 60 degrees C, Vp = 8 V normalized /ns 1.00E-05 DCR 1.00E E-07 Tp = 2 ns Tp = 4 ns Tp = 6 ns Tp = 10 ns 1.00E QE (% )

21 Temperature Dependence Gating 2ns, 8V Tp = 2 ns Vp = 8 V 1.00E E-04 DCR 1.00E E E-07 0 degrees C -40 degrees C -60 degrees C -80 degrees C QE (%)

22 APD AfterPulsing Testing Parameters V gate: 8V T gate: 2ns Temperature: -80 and -40 deg C Laser λ=1553.4nm P into APD =-122dBm 1photon/pulse (@5kHz) Discriminator trigger pulse 200ns Delay APD Gating Laser Trigger

23 APD AfterPulsing Testing Afterpulsing -40deg C, 2ns, 8V, f=5khz\ 1photon/pulse 1e-2 Afterpulse probability 1e-3 1e-4 1e-5 QE=12.9% DCR=2.2e-5 QE=9.1% DCR=1.2e-5 QE=7% DCR=7e-6 1e Delay, µs Bias 47.5V Bias 47.0V Bias 46.75V

24 APD AfterPulsing Testing Afterpulsing -80deg C, 2ns, 8V, f=5khz 1e-1 1e-2 Afterpulse probability 1e-3 1e-4 1e-5 QE=13% DCR=4e-5 QE=11% DCR=3e-6 1e-6 QE=7.9% DCR=1.5e Delay, µs Bias 43.53V Bias 43.2V Bias 42.5V 2exp fit Fit parameters: f=y0+a*exp(-bx)+c*exp(-dx) B=1.7 D=0.3

25 Conclusion detector problem Both quantum efficiency and dark current are decreasing with cooling At the same time afterpulsing effect becomes significant at low temperature To maximize the system performance careful tweaking of the parameters must be done with respect to actual experimental conditions

26 Quantum Key Distribution: w/ Attempted Eavesdropper

27 Algorithms Authentication Sifting Error correction Privacy amplification Final key 1 psift = psignal 2 H = εlog2 ε 1 ε log2 1 ε ( 1 2 τ = 1+ log ) 2 + 2ε 2ε 2 G = p ( 1 τ f H ) sift ( ) ( ) ε - quantum bit error rate H - Shannon entropy

28 Performance of the QKD system with true single photon source Single photon source Gain per pulse 1e-1 1e-2 1e-3 1e-4 1e-5 1e-6 Parameters µ B 0.3 η = 10% p DC α = η B = = db / km = 0.5 1e Distance, km

29 Eavesdropping model Eve can perform POVM attack (cloning) Eve has QND apparatus to distinguish total photon number of the pulse Eve can use photon number splitting PNS attack (PNS + quantum memory) Eve can substitute the fiber with the loss-free channel or use quantum teleportation to deliver the (unknown) single photon state to Bob Probability, log Photon number

30 Photon number splitting attack Alice µ PNS Bob µ ( 1 L) Quantum memory Classical channel Eve can use only channel loss, not Bob apparatus loss or detector QE

31 How dangerous is the PNS attack?? Can Eve get use of all the loss in the system or she can modify and take advantage only upon the channel loss? Alice and Bob apparatus assume to be physically protected from intrusion, Eve cannot use any type of amplification Conclusion: only the channel loss should be taken into account

32 Gain per pulse 1e-1 1e-2 1e-3 1e-4 1e-5 WCP QKD performance Parameters µ B optimum! η = 10% 5 pdc = 10 α = 0.2 db / km η = 0.5 B 1e Distance, km Sifted bits After error correction After EC and privacy amplification Optimum photon number 1.0 Distance, km vs Optimum PN Distance, km

33 The influence of the dark current on the distance of QKD Gain per pulse / QE QE*DC=10^-2 QE*DC=10^-3 QE*DC=10^ Distance, km QE*DC=10^-5

34 Conclusion Secure QKD is possible with commercially available components Performance of the system depends on the combination of parameters and should be optimized for a certain experimental conditions Future progress in performance of QKD systems depends significantly on the progress in single photon counting technique, this is probably the most obvious and feasible source of improvement Thanks to Thanks to Norbert Luetkenhaus Darius Subacius Anton Zavriyev