Signal Processing for Cryptography and Security Applications - Signal Processing Systems - page 230

1 2 3 4 5 6

Time [clock cycles]

Fig. 4 Measurements of supply current over time. Data dependent operations in clock cycles three
and four leak information about the operand(s)

The measurements of the side channel are susceptible to external and internal
noise contamination. Therefore, a first group of preprocessing techniques aims at
reducing the amplitude noise. The easiest preprocessing technique is averaging the
measurements. This was first pointed out by Kocher et al. in [ 45 ] . More noise
reduction can be achieved through filtering the data [ 7 ] . Results have been published
for the power side channel [ 55 ] as well as for the electromagnetic side channel [ 5 ] .
Another, more recently proposed technique is calculating the fourth-order cumu-
lant [ 46 ] . In some cases, the useful information is modulated onto a carrier. For this
type of data extraction, demodulation techniques are appropriate [ 5 , 41 , 60 ] .
Due to clock jitter, absence of a suitable trigger or simply due to countermea-
sures, measurements can suffer from temporal misalignment. Some publications
deal with this problem and try to remove the temporal misalignment. Homma
et al. explain the phase-based waveform matching procedure [ 37 ] and Gebotys
and White introduce the phase replacement technique [ 27 ] . Pelletier and Charvet
use wavelets to get rid of misalignment [ 63 ] . The rapid alignment method [ 59 ] of
Muijrers et al. also builds on wavelets. Woudenberg et al. propose to use dynamic
time warping [ 70 ] .
In the final phase of a side channel attack, the attacker uses a statistical tool to
find the correct key by analyzing the relation between the hypothetical leakage and
the measured leakage. The difference of means test was proposed by Kocher et al. in
their seminal paper [ 45 ] . Later, more advanced techniques were put forward: the T-
test [ 17 ] , the Pearson correlation coefficient [ 12 ] , Spearman rank correlation [ 9 ] ,
mutual information [ 28 ] , and maximum likelihood [ 14 ] . While all the previous
techniques are applied in the time domain, the differential frequency analysis
exploits the frequency information [ 26 ] .
Advanced signal processing techniques strengthen the adversary's capabilities
and raise the need for proper and better countermeasures against side channel
attacks.