During the tests of a bit exchange the noise was ramped down linearly before making the switching of the resistors and then ramped up. The ramping time was 8% of the whole bit exchange time (clock period). After switching and noise ramp-up another 8% of clock period was elapsed before taking samples from the noise in order to do the statistical key extraction.
Figure 6.4 shows the voltage and current distributions obtained by evaluating 74497 clock cycles. One can easily see that the HH and LL distributions are quite well separated from the LH distribution considering the voltage or current, respectively, therefore Alice and Bob can extract the key with high success rate of 99,98%. The eavesdropper (Eve) has no information, since the LH and HL states yield almost identical distribution.
Figure 6.5 shows the statistical data obtained during the exchange of a single bit.
Several attack tests were performed to check the security of the realized system including the Bergou- Scheuer-Yariv test utilizing wire resistance [9]; Hao’s test [11];
Kish’s tests based on of resistor inaccuracy and current pulse injection [4,12] and we have found no more than 0,19% of information leak.
0
0,30 0,40 0,50 0,60 0,70
Counts
Voltage [V]
HL LH
Figure 6.4. Empirical voltage and current histograms seen by Alice and Bob (top left and top right, respectively) and voltage counts seen by Eve (bottom) at one end of the line for the two different secure bit arrangements (LH and HL) during the whole span of security checks utilizing 74497 clock cycles. It is obvious from the strong overlap of the two curves that Eve has virtually zero information even with fixed bit arrangement for 74497 clock cycles.
After the successful tests we have designed microcontroller based KLJN units in order to make the communicator units more compact. The units have a single mixed signal microcontroller with on-chip precision ADCs and DACs and some additional analog signal conditioning to scale the bipolar signals into the range of the single supply data converters. The USB port is used to connect to the host computer and power the units. The small switching units and model KLJN line is integrated on a small plug-in card printed circuit board. Figure 6.7 depicts the schematic and the photo of the units.
The tests of these units were successful, only a slight decrease in the communication speed was observed.
0 20 40 60 80
-2 -1 0 1 2
Count
Voltage [V]
LL HL LH HH
0 50 100 150
-10 -5 0 5 10
Count
Current [mA]
LL HL LH HH
0 10 20 30 40 50 60 70 80 90
-2,0 0,0 2,0
Counts
Voltage [V]
Figure 6.5. Empirical histograms of the voltage and current counts seen by Alice and Bob (top left and top righ, respectively); voltage counts seen by Eve (bottom) at end of the line at the two different secure bit arrangements, LH and HL, three of each one. These functions correspond to the situation when the bit arrangement is fixed (LH or HL) and then the two distribution functions are the voltage counts measured at the two ends of the line to execute a Bergou- Scheuer-Yariv type of attack. The poor statistics seen in the top left and top right figures are enough for Alice and Bob to identify secure bit alignment with 0.02% error rate (99.98%
fidelity). However when Eve tries to identify the bits from the two histogram recorded at the two ends of the line (bottom) she must work with these distributions which are very stochastic, almost identical and totally overlapping with a less than 1% shift of their centers [7] which results in 0.19% eavesdropped bit/transmitted secure bit.
6.5 Conclusions
We have developed DSP based units to realize the theoretically unconditionally secure Kirchhoff Loop Johnson Noise communication method. Our aim was to demonstrate the performance, to find the practical limitations of security and to make several security tests.
As a competitor of secure quantum communicators the KLJN system is much smaller, simpler and cheaper. We have carried out many experiments using our hardware and model communication line equivalent to lengths from 2km to 2000km.
Our results indicate unrivalled fidelity and security levels among existing physical secure communicators. There are straightforward ways to improve security, fidelity and communication range further, such as proper choice of resistors, thicker cable, enhanced statistical tools for bit decision.
INTERFACE FT232RL 16-bit ADC
C8051F060 16-bit ADC
USB REFERENCE
AD780 VOLTAGE
8051 CORE 25 MIPS
+5V -5V
TMR0521 DC
GND DC POWER IN
BS62LV4006 512K SRAM
LTC6484
15-PIN CONNECTOR
12-bit DAC 12-bit DAC
PGA112 PGA PGA112
PGA LTC6482
Figure 6.7. Block diagram (top left) and photo (top right) of the compact microcontroller based KLJN communicator data acquisition and control unit. The simplified schematic of the KLJN switching and signal conditioning unit is shown at the bottom.
7 Summary and theses
The six chapters of this dissertation review my most important research results related to basic and applied noise research. The aim of the theoretical and experimental investigations, the analog and numerical simulations, the instrumentation hardware and related embedded and host computer software developments was to contribute to the knowledge of random processes and of the behavior of fluctuating systems. The emphasis was always on the efforts to find new ways in which noise can be used as an information source; how signal-to-noise ratio can be increased or in which we can use even noise as a tool to improve the operation of devices, to enhance the accuracy of measurement and to control and to optimize information transfer.
Most of the results were achieved in active cooperation with the members of my noise research group that I have been leading since 1997 and within the framework of various international and domestic collaborations. The following theses present my contribution to the work and are supported by 51 papers, 18 invited talks and 208 independent citations.