The phase-locked loop-based true random number generator (PLL-TRNG) extracts randomness from clock jitter. It is an interesting construct because it comes with a stochastic model, making it certifiable by certification bodies. However, bringing it to good performance is difficult since it comes with multiple parameters to tune. This article proposes to use backtracking to determine these parameters. Compared to existing methods, based on genetic algorithms or exhaustive search of a feasible set of parameters, backtracking has several advantages. Indeed, since this method is expressible by constraint programming, it provides very good readability. Constraints can be specified in a very straightforward and maintainable way. It also exhibits good performance and generates PLL-TRNG configurations rapidly. Finally, it allows to integrate new exploratory design constraints for the PLL-TRNG very easily. We provide experimental results with a PLL-TRNG implemented on three FPGA families that come with different physical constraints, showing that the method allows to find good parameters for every one of them. Moreover, we were able to obtain configurations that lead to an increase 59 % in throughput and 82 % in jitter sensitivity on average, thereby generating random numbers of higher quality at a faster rate. This approach also paves the way for new design exploration strategies for PLL-TRNG. The source code of our implementation is open source and available online for reproducibility and reuse.

Security in random number generation for cryptography is closely related to the entropy rate at the generator output. This rate has to be evaluated using an appropriate stochastic model. The stochastic model proposed in this paper is dedicated to the transition effect ring oscillator (TERO)-based true random number generator (TRNG) proposed by Varchola and Drutarovsky (in: Cryptographic hardware and embedded systems (CHES), 2010, Springer, 2010 ). The advantage and originality of this model are that it is derived from a physical model based on a detailed study and on the precise electrical description of the noisy physical phenomena that contribute to the generation of random numbers. We compare the proposed electrical description with data generated in two different technologies: TERO TRNG implementations in 40 and 28 nm CMOS ASICs. Our experimental results are in very good agreement with those obtained with both the physical model of TERO’s noisy behavior and the stochastic model of the TERO TRNG, which we also confirmed using the AIS 31 test suites.

Several recent designs show that the phase locked-loops (PLLs) are well suited for building true random number generators (TRNG) in logic devices and especially in FPGAs, in which PLLs are physically isolated from the rest of the device. However, the setup of the PLL configuration for the PLL-based TRNG is a challenging task. Indeed, the designer has to take into account physical constraints of the hardwired block, when trying to achieve required performance (bit rate) and security (entropy rate per bit). In this paper, we introduce a method aimed at choosing PLL parameters (e.g. input frequency, multiplication and division factors of the PLL) that satisfy hardware constraints, while achieving the highest possible bit rate or entropy rate according to application requirements. The proposed method is fast enough to produce all possible configurations in a short time. Comparing to the previous method based on a genetic algorithm, which was able to find only a locally optimized solution and only for one PLL in tens of seconds, the new method finds exhaustive set of feasible configurations of one-or two-PLL TRNG in few seconds, while the found configurations can be ordered depending on their performance or sensitivity to jitter.

The objective of this paper is to provide insight on the design, evaluation and testing of modern True Random Number Generators (TRNGs) aimed towards certification. We discuss aspects related to each of these stages by means of two illustrative TRNG designs: PLL-TRNG and DC-TRNG. Topics covered in the paper include: the importance of formal security evaluations based on a stochastic model of the entropy source, the development of suitable and lightweight embedded tests to detect failures, the implementation and testing of TRNGs in dedicated FPGA platforms, and a robustness assessment to environmental and/or physical modifications.

Security in true random number generation in cryptography is based on entropy per bit at the generator output. The entropy is evaluated using stochastic models. Several recent works propose stochastic models based on assumptions related to selected physical analog phenomena such as noise or jittery signal and on the knowledge of the principle of randomness extraction from the obtained analog signal. However, these assumptions simplify often considerably the underlying analog processes, which include several noise sources. In this paper, we present a new comprehensive multilevel approach, which enables to build the stochastic model based on detailed analysis of noise sources starting at transistor level and on conversion of the noise to the clock jitter exploited at the generator level. Using this approach, we can estimate proportion of the jitter coming only from the thermal noise, which is included in the total clock jitter.

True Random Number Generators (TRNG) are cryptographic primitives that exploit intrinsic noise sources in electronic devices. Their quality is linked to the underlying technology, activity of the neighboring circuitry and device environment (temperature, power supply, electromagnetic emanations). Consequently, when comparing TRNGs, they should be tested in identical technology, system architecture and operating conditions. We present a unified hardware platform and related open source tools aimed at fair benchmarking of TRNGs implemented in different FPGA technologies. The platform is accessible remotely. Designers can download related tools from the web site and they can upload their configuration bitstream to the remote FPGA and download random data generated in the same hardware and in the same conditions as other concurrent designs and state-of-the-art generators. The proposed tools were approved in many applications and they guarantee safe acquisition of random sequences at data rates of up to 400 Mbits/s.

The paper deals with the characterization of sources of randomness in true random number generators aimed at cryptographic applications implemented in Field Programmable Gate Arrays (FPGA). One of the most often used source of randomness in logic devices is the timing jitter present in clock signals, generated using ring oscillators (RO). In order to estimate the entropy of the generated random bit-stream, it is necessary to characterize the employed timing jitter. Using the simulation of the clock jitter injection into the gates of RO we show that the proportion of jitter from uncorrelated and correlated noise sources on the overall period jitter depends on the number of delay elements (inverters). We also propose a new and precise method of the jitter measurement outside the device based on the use of the differential device outputs in conjunction with a differential oscilloscope probe. The measured standard deviation of the clock period is more than two times smaller than the one obtained using traditional methods. Employing the proposed measurement method we show that the jitter profile of the RO-generated clock and its sensitivity to global jitter sources (e. g. deterministic jitter) is strongly dependent on the architecture and topology of the oscillator.

Random number generators are one of basic cryptographic primitives used in cryptographic protocols. Most of true random number generators in field programmable gate arrays (FPGAs) employ the timing jitter from ring oscillator clocks as a source of randomness. The paper analyses the jitter generated in ring oscillators and it uses a simple physical model of jitter sources to show that the random jitter accumulates slower than the global and manipulable deterministic jitter. This fact, which can be used to attack generators, is not considered even in most recent designs considered to be secure. The paper proposes simple but efficient countermeasure against these attacks. The method is validated using the proposed behavioral VHDL model and it is shown to be efficient also in hardware.