1 Montgomery Modular Multiplication in Hard- ware

FEI KEMT
extraction. In other words, the principle of random numbers generation has to be
described for better understanding and for better analysis of possible attacks on the
TRNG.
Startup Test, Online Test, TOT Tests If RNG prototype in a lab generates
acceptable random numbers this may not be true for each TRNG of the same type
during the whole operation time. The reason for this could be found in tolerances
of components of the noise source, ageing effects, or outside attacks. In the worst
case the TRNG breaks down totally and the output numbers are constant from that
moment on. Therefore, the developer of the TRNG should implement also tests
that will detect similar cases of the randomness degradation of the output bits. We
distinguish between 3 types of tests [74]:
1. startup test is used to verify the principle functionality of the noise source
when the TRNG has been started.
2. online test should detect if the quality of the random numbers is not sufficient
for this particular TRNG or deteriorates in the course of the time.
3. tot test (’tot’ stands for ’total failure of the noise source’) should detect a total
breakdown of the noise source.
Implementation of the tests For implementation of the tests one has to consider
the limitations that are given by the platform on which the TRNG is implemented.
Not rarely the implementation target are smart cards, or field programmable gate
arrays (FPGAs) with limited memory space. Therefore the chosen tests should
require only small additional logic resources. Moreover the tests should be selected
according to the features of the TRNG and the basic principle of the random source.
It is possible to create also new tests that are more suitable for the particular TRNG
and detect better the possible defects.
Due to the limited memory resources of target platforms it is impossible to test
the statistical properties on very long sequences (up to Mbits of data) as some tests
(e.g. [97]) require. The goal is to find tests that are able continually evaluate the
quality of the random source without the need of storing the output bits. Require-
ments which appropriate online tests should fulfil are formulated in [100].
Two another requirements are given on the tests. On one side we expect detection
of even small deviation from ideal random source, but on the other side often random
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