1 Montgomery Modular Multiplication in Hard- ware

FEI KEMT
0,75
0,5
0,25
1
0
1 30 59 88 117 146 175 204
(a) KM /KD = 212/207
0,75
0,5
0,25
1
0
1 30 59 88 117 146 175
(b) KM /KD = 516/175
Figure 6 – 5 Distribution of mean values of ordered CLJ signal samples obtained during Q = 1000
periods TQ
On-chip reordering In order to make possible a better analysis of samples pro-
cessed in TRNG we implemented the following method for on-chip reordering of the
samples.
The structure of ordering logic is illustrated in Figure 6 – 6. Samples coming
from the TRNG are continually written in a dual-port memory block organised as
512 1-bit wide words (usually we do not use KD parameter, which determines the
number of samples in one period, bigger than 512). Writing address is initialised
with each new period TQ signalised by signal next tq. In order to read samples in a
way they create the CLJ clock waveform we need to set a correct reading address.
This operation is done by a LUT implemented as a ROM block. Input of the table
is identical with writing address, and output of LUT is used as a reading address
from samples memory. The content of ROM – the LUT can be easily generated
using Equation 5.12.
Signal sample ord was assigned to an output pin of DSP Stratix board and
measured by a scope (Tektronix TDS 3052), with trigger signal next tq. In Figure 6 –
7 we present the measured waveform. The parameters of the TRNG are following:
MCLK = 13, DCLK = 12, MCLJ = 14, DCLJ = 11, KM = 168, KD = 143, K −1
M = 103.
In the region of edge (in this particular case, on falling edge). Ordered samples
do not create ideal rectangular waveform, instead there can be observed more edges
in one period. Samples placed around a position of an ideal edge are sampled in
different timing instances (due to required reordering of the samples in time). Hence,
they may be influenced by different amount of jitter or said in other words, jitter
changes are faster than sampling frequency. This fact causes more than one change
(edge) of the signal. In order to make a better analysis of this phenomenon we need
to collect samples from the edge region for several hundreds of subsequent periods.
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