1 Montgomery Modular Multiplication in Hard- ware

FEI KEMT
Figure 6 – 8 Sampled waveform of a clock signal for TRNG for Configuration A for temperatures
in range −40 ◦ C + 30 ◦ C.
The random sequences were tested by simple statistical tests defined in FIPS
standard [57]. The test suite can reveal a bias or unbalanced distribution of zeros
and ones in generated sequence by application of 4 basic tests (monobit test, poker
test, runs and long runs tests). If at least one test from the set was not passed, the
result is denoted as FAILED, otherwise we put OK mark.
In Table 6 – 9 we summarise the results of statistical tests at different FPGA chip
temperatures. It can be seen that while the configuration A has produced by some
temperatures the sequences that did not pass the statistical tests, the configuration
B is reliable in the whole range of temperatures.
The columns with critical samples number show the number of samples influenced
by jitter. It can be observed that in case of the configuration B, when we have set
a low bandwidth of the loop filter, the number of influenced samples is significantly
higher.
We further investigate the number and position of critical samples for both con-
figurations in dependency on the chip temperature. Crucial impact on the statistical
parameters of the generated sequence have the samples with probability around 0.5.
In case we eliminate the almost constant samples, with less than 100 by jitter in-
fluenced values during 1000 periods, there are 4-6 and 12-13 highly critical samples
per edge for configuration A and B, respectively.
The Figures 6 – 10 and 6 – 11 show in details the area of rising edge of the sampled
waveform. We can observe how during the measuring period the number of sampled
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