Cryptography Reference
In-Depth Information
100
Correct Computations
Faulty Computations
80
60
40
20
0
905.5 906.0 906.5 907.0 907.5 908.0 908.5 909.0 909.5 910.0 910.5 911.0 911.5 912.0
Measured CPU Input Voltage [mV]
10
3
Fig. 16.3
Percentage of correct and wrong computations averaged over 500
×
runs
computation. Since our goal was to inject single faults, we were interested in seeing
whether the errors in the outputs of the former computations were caused by one or
more faults during their executions. Reclassifying the faulted runs from the former
experiments according to the number of faults, it is possible to observe, as shown in
Fig.
16.4
, that there is a 1 mV wide voltage range where only a single fault happens
with dominant probability. Moreover, in the adjacent 1 mV range, the probability of
having a faulty computation triggered by a single fault ranges from 2 to 40 %. This
probability dwarfs the one of having multiple faults contributing to the erroneous
result, while in the voltage range where less than half of the computations are faulted.
When working under the 50 % faulty computation threshold, the number of possible
faults starts growing, and multiple fault scenarios start dominating the fault profile,
as can be expected in a degrading environment. After lowering the power supply
voltage even more, the board stops outputting data from the RS-232 interface used to
communicate, thus preventing the results from being collected. It is therefore clear
that, in the voltage region where the correct computations are the majority and faulty
ones begin to appear, the faults occurring in the computations are single and not
represented by small bursts.
Since the results until now have been obtained while keeping the number of
machine instructions per binary fixed for each measurement, and since there is no
specific timing for the insertion of the hazard causing faults, it is reasonable to assume
that a growth in the executable code size will be complemented by an analogous rise
in the probability of a fault appearing during the computation. This is not an obstacle
