1 Montgomery Modular Multiplication in Hard- ware

FEI KEMT
Figure 6 – 11 Amount of sampled ones during 1000 sampling periods for TRNG with configuration
B, with low-pass loop filter (detail of the raising edge).
amplitude of the jitter are significant as are the differences in probability values
between particular samples. The configuration B is characterised by smaller changes
of the jitter amplitude which are in addition more flat. In such case the probability
changes uniformly for the most critical samples and does not have any unwanted
impact on the generated random sequence. Described higher level of robustness was
observed in configuration B and confirmed by positive output of all statistical tests.
From the obtained results and suggestions for PLL-TRNG design we can con-
clude that the design tested in [98] with parameters KM/KD = 270/203 is not
suitable for usage in changing temperature. From the Table 6 – 8 we get the number
of critical samples that is 22, 11 per edge. As we proposed in the suggestions above,
more important is the number of highly critical samples that should be more than 10.
This condition is not met in this configuration and the generator behaves similarly
to the Configuration A in our experiments during simulated attack on PLL-TRNG.
6.4 Conclusions and Further Research
The chapter provided an analysis of the PLL based TRNG. We focused on implemen-
tation aspects and relations between the target platform FPGA and PLL circuitry
and achievable technical parameters of the generator in devices from vendors Actel
and Altera. In the second part of the chapter we brought our proposal for stochastic
model of the TRNG and proposed additional steps in PLL-TRNG design in order
to achieve a robustness of the generator in changing environment.
120