1 Montgomery Modular Multiplication in Hard- ware

FEI KEMT
6 True Random Number Generator
The chapter is dedicated to analysis of jitter-based random generator under various
aspects. Our work is based on the TRNG design proposed by Viktor Fischer and
Miloˇs Drutarovsk´y published in 2002 [60]. We enhance the already published results
summarised in the previous chapter. Our focus is put on analysis of the generator
in changing working conditions and configurations settings.
Results of the research were published in the following list of papers [47, 48, 61,
62,114–116,119]. The main achievements of our research were done in the following
areas:
• Analysis of PLL circuitry as a source of randomness – implementation issues,
possible PLL configurations, verification of vendor parameters,
• Analysis of TRNG implementation in different FPGAs – achievability study,
design consideration, practical results,
• Stochastic model of PLL-TRNG – proposal and practical verification,
• Temperature influence on PLL-TRNG – practical attack on TRNG with results
and suggestions for design.
The chapter is structured as follows. In the Section 6.1 we describe two ways
of clock synthesis in modern FPGAs and summarise the parameters of the clock
circuitry verified by practical measurements of the PLL parameters. The Section 6.2
provides an analysis of PLL configurations, practical results from Altera and Actel
FPGA implementations of the generator and a stochastic model of the generator.
In Section 6.3 we describe a non-invasive attack on the generator together with
practical outcomes. In the last part (Section 6.4) we discuss the obtained results
and provide ideas on the further research.
6.1 Clock Synthesis in FPGAs
In present-day integrated digital systems, there is a need for numerous clock sig-
nals with various frequencies. The synthesis of the clocks in separated circuits is
not effective and the frequencies are too high to be generated by an external crys-
tal. FPGA vendors offer for this purpose a clock circuitry embedded on the FPGA
chip. Beside synthesis of clock signals with required frequencies it provides addi-
tional functions making possible a processing of signals with very high frequencies.
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