Attacks exploiting deviation of mean photon number in quantum key distribution and coin tossing

The security of quantum communication using a weak coherent source requires an accurate knowledge of the source's mean photon number. Finite calibration precision or an active manipulation by an attacker may cause the actual emitted photon number to deviate from the known value. We model effects of this deviation on the security of three quantum communication protocols: the Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol without decoy states, Scarani-Acín-Ribordy-Gisin 2004 (SARG04) QKD protocol, and a coin-tossing protocol. For QKD we model both a strong attack using technology possible in principle and a realistic attack bounded by today's technology. To maintain the mean photon number in two-way systems, such as plug-and-play and relativistic quantum cryptography schemes, bright pulse energy incoming from the communication channel must be monitored. Implementation of a monitoring detector has largely been ignored so far, except for ID Quantique's commercial QKD system Clavis2. We scrutinize this implementation for security problems and show that designing a hack-proof pulse-energy-measuring detector is far from trivial. Indeed, the first implementation has three serious flaws confirmed experimentally, each of which may be exploited in a cleverly constructed Trojan-horse attack. We discuss requirements for a loophole-free implementation of the monitoring detector.

Figure 1

Plug-and-play system, as implemented in Clavis2 [22, 26].

Figure 2

Optical pulses coming into Alice. (a) Trains of pulses (frames) generated by Bob. The frames are generated every $1\mathrm{m}\mathrm{s}$, are $340\mu \mathrm{s}$ long, and contain 1700 pulse pairs. (b) Beginning of the frame showing a synchronization pattern. The synchronization circuit checks for this specific pattern in every frame. (c) Two pulses per slot in the optical link. The energy of the first pulse is measured to be $150\mathrm{f}\mathrm{J}$, and the energy of the second (“calibrated signal pulse”) is measured to be $73\mathrm{f}\mathrm{J}$.

Figure 3

Pulse-energy-monitoring circuit and oscillograms. The six test points are marked “light,” “amplifier,” “reset,” “capacitor,” “comparator,” and “alarm” in (a), and the oscillograms at these points are shown (b) for normal operation and (c) for the case when light power is increased by $0.1\mathrm{d}\mathrm{B}$ (i.e., by $\approx 2\%$) above normal operation. During normal operation, when light pulses arrive with expected energy, the capacitor voltage always stays over the threshold level $V_{\text{th}}$. However, when the pulse's energy is higher than expected, due to higher gate pulse to FET1, deeper discharge of the integrating capacitor results. This causes its voltage go below $V_{\text{th}}$, which in turn creates an alarm. (a) Simplified circuit diagram of the pulse-energy-monitoring detector. See text for details. (b) Signals during normal operations. (c) Generation of an alert signal on injection of excess light.

Figure 4

Recovery of the front-end amplifier from the negative saturation to the normal operation. (a) Entire $340\mu \mathrm{s}$ long frame. A minor peak is visible in the amplifier output at $\sim 123\mu \mathrm{s}$, marking the recovery of the amplifier from the negative saturation. (b) Initial part of the recovery from the negative saturation. Even though light pulses are arriving at the input of the amplifier, no output is produced for $\sim 3\mu \mathrm{s}$. (c) A transient at $\sim 123\mu \mathrm{s}$ is the last irregularity, after which the amplifier fully recovers from the saturation.

Figure 5

Exploiting the low bandwidth of the front-end amplifier to break the security. (a) Suppression of three pulses out of four and the corresponding effect on the amplifier, capacitor, and comparator output. The pulse energy has been increased $8.5$ times from $73\mathrm{f}\mathrm{J}$ to $623\mathrm{f}\mathrm{J}$. (b) Pulse shape carrying the maximum injected energy using this method ($623\mathrm{f}\mathrm{J}$).

Figure 6

Energy multiplication factor $x$ for $(n+1)\mathrm{st}$ pulse vs number of blocked pulses $n$, in the amplifier saturation attack.

Figure 7

Attack exploiting the saturation effect of the front-end amplifier, blocking 100 pulses. The further into the frame the probe pulses are injected, the smaller the amplifier output becomes, because the amplifier stays into saturation for a longer period and more energy is required to bring it out of it. In the alarm plot, the first three pulses occurred because the energy of the probe (light) pulses was enough to produce an amplifier output strong enough to result in an alarm (as it has not yet been into a deep saturation). However, they occurred before the monitoring period and were not counted as an alarm signal by the FPGA. Similarly, the last pulse in the alarm plot occurred when the integrator was reset after the frame (after the end of monitoring period) and was not counted as an alarm.

Figure 8

Exploiting edge-triggered alarm monitoring. (a) Injection of very bright pulses and their effect on the circuit. Note that at the end of the frame when the amplifier output became zero, the capacitor voltage was still low. The reason is because after the end of the frame, the FPGA no longer generated the reset signal and hence the integrator did not reset. It reset at the beginning of the next frame after the reset signal was produced. (b) Pulse shape carrying the maximum injected energy using this method ($7150\mathrm{f}\mathrm{J}$ or 97 times more than the calibrated signal pulse).

Figure 9

Realistic attack scheme. With a probability $p_{\mathrm{attack}}^{\mathrm{USD}}$, pulses from Alice are measured by Eve using a 50:50 beam splitter followed by two copies of Bob's setup ${\mathrm{Bob}}^{\prime }$ that use different measurement bases. When the USD measurement is successful, Eve sends a pulse in the measured state using a source ${\mathrm{Alice}}^{\prime }$ placed next to Bob. SW1 and SW2 are optical switches. SW2 can in practice be replaced by an asymmetric beam splitter.

Figure 10

Fraction of secret key leaked to Eve in the BB84 protocol. The edge-trigger attack, which can increase $\mu$ in all pulses, allows Eve to gain full information with lower multiplication factor $x$ than the attacks that require suppression of pulses. At low $x$ (where the curve stops, marked by the crosses), Eve is unable to maintain the expected count rate at Bob (in the realistic attack) or induces too high QBER (in the strong attack), resulting in her presence being noticed and the key aborted. When the ratio is 0 (realistic attack), Eve is able to maintain the rate but cannot extract sufficient information to overcome privacy amplification. Channel loss is $3.4\mathrm{d}\mathrm{B}$, and, in the strong attack model, Eve is restricted to a maximum QBER of $8\%$ to avoid suspicion. This maximum QBER value was chosen because it is near the limit where Clavis2 can (sometimes) extract secure key [43].

Figure 11

Minimum $x$ to obtain partial and full information on the secret key in the edge-trigger attack (i.e., with no pulses suppressed) on the BB84 protocol. For the strong (realistic) attack model, Eve is able to extract partial information when between the saltire (cross) and circle (square), and full information above the circle (square). Again, Eve is restricted to a maximum QBER of 8% to avoid suspicion.

Figure 12

Fraction of secret key leaked to Eve in the SARG04 protocol. As with BB84, the attack that does not require Eve to suppress pulses performs better than the attacks that require pulse suppression. Once again, the missing points in the curve at low $x$ (marked by the crosses) occur when Eve is unable to maintain the expected count rate at Bob (in the realistic attack), or induces too high QBER (in the strong attack), resulting in her presence being noticed and the key aborted. When the ratio is 0 (realistic attack), Eve is able to maintain the rate but cannot extract sufficient information to overcome privacy amplification. Channel loss is $3.4\mathrm{d}\mathrm{B}$ and, in the strong attack model, Eve is restricted to a maximum QBER of 8% to avoid suspicion.

Figure 13

Bob's cheating probability versus honest abort probability in the coin-tossing protocol. The plot shows limits for the classical coin tossing and QCT (for $15\mathrm{k}\mathrm{m}$ and $\mu =0.0019$ [24]), as well as limits for the three attacks on QCT. We observe that all three Bob's attacks beat the classical limit, and QCT can therefore provide no provable advantage. Also plotted is factor $x$ required to reduce security of QCT to that of its classical counterpart.