Oscillator-based True Random Number Generator Research Articles

Entropy Model of Rosin Autonomous Boolean Network Digital True Random Number Generator

A True Random Number Generator (TRNG) is an important component in cryptographic algorithms and protocols. The Rosin Autonomous Boolean Network (ABN) digital TRNG has been widely studied due to its nice properties, such as low energy consumption, high speed, strong platform portability, and strong randomness. However, there is still a lack of suitable entropy models to deduce the requirement of design parameters to ensure true randomness. The current model to evaluate the entropy of oscillator-based TRNGs is not applicable for Rosin ABN TRNGs due to low-frequency noise. This work presents a new, suitable stochastic model to evaluate the entropy of Rosin ABN TRNGs. Theoretical analysis and simulation experiments verify the correctness and the effectiveness of the model, and, finally, the appropriate sampling parameters for Rosin ABN TRNGs are given for sufficient entropy per random bit to ensure true randomness.

Entropy Computation for Oscillator-based Physical Random Number Generators

In this paper, we provide a complete set of algorithms aimed at the design and security evaluation of oscillator-based True Random Number Generators (TRNG). While depending on some TRNG design assumptions, the proposed algorithms use as inputs the statistical parameters of the underlying random physical process such as the clock jitter originating from the thermal noise and give a lower bound of the entropy rate of the generated bit stream as output. We describe the general structure of a TRNG composed of multiple free-running oscillators and samplers, the outputs of which are post-processed by an entropy conditioner. Depending on the specification of the entropy conditioner, which can usually be any Boolean function, we describe several algorithmic optimizations. We then explain how to compute and efficiently manage the entropy rate at the output of such a post-processing block and at the output of the generator as a whole.

Implementation and Evaluation of Ring Oscillator-based True Random Number Generator

Implementation and Evaluation of Ring Oscillator-based True Random Number Generator

Can Deep Learning Break a True Random Number Generator?

True Random Number Generators (TRNGs) create a hardware-based, non-deterministic noise that is used for generating keys, initialization vectors, and nonces in a variety of applications requiring cryptographic protection. A compromised TRNG may lead to a system-wide loss of security. In this brief, we show that an attack combining power analysis with bitstream modification is capable of classifying the output bits of a TRNG implemented in FPGAs from a single power measurement. We demonstrate the attack on the example of an open source AIS-20/31 compliant ring oscillator-based TRNG implemented in Xilinx Artix-7 28nm FPGAs. The combined attack opens a new attack vector which makes possible what is not achievable with pure bitstream modification or side-channel analysis.

Sequence‐Oriented Stochastic Model of RO‐TRNGs for Entropy Evaluation

Ring oscillator-based true random number generators (RO-TRNGs) are widely used to generate unpredictable random numbers for cryptographic systems. Entropy is usually adopted to quantitatively measure the unpredictability of a TRNG. There have been several stochastic models such as the time-oriented and phaseoriented ones built to evaluate the entropy of ElementaryRO-TRNGs with single oscillator. However, these models are not suitable for the TRNGs composed of multiple oscillators (Multiple-RO-TRNGs), which can obtain more randomness and higher throughput. Considering this, we propose a sequence-oriented stochastic model for the entropy evaluation of RO-TRNGs, named the first-order stationary Markov source model. This model is extensible for the Multiple-RO-TRNGs. Based on that, we present a detailed method to determine the entropy of Multiple-ROTRNGs. Our proposed model is verified by experiments. Besides, our method can also be a guide to design ROTRNGs with both high entropy and high throughput.

Anti aging controllable true random number generator for secured AES-based crypto system

A tetrahedral oscillator-based true random number generator for secret key generation in cryptosystem has been proposed. The circuit is made to behave correctly for a long time. By applying pass transistors, the aging effects due to hot carrier injection (HCI) and negative bias temperature instability (NBTI) are reduced. This fact is helpful to achieve the goal and its performances have also been improved. Pass transistor makes the transistors to operate only at enabling times. Thus, bit flipping in normal designs are reduced. Due to the complexity in the tetrahedral oscillator hacking will be very tough. The secret key generated from TRNG circuit is adopted in advanced encryption standard (AES) cryptosystem to maintain an off-chip database. Moreover, controlling circuits for TRNG have been introduced because in any of the cryptosystem man-in-middle attack is possible. To avoid this controlling circuits are used to identify the authenticity of customers. Simulation results explain that our aging resistant design can be used for generating more reliable keys. Although the operating conditions changes, the DC operating point of the system does not change more. The randomness is also shown through NIST tests.

On the Entropy of Oscillator-Based True Random Number Generators under Ionizing Radiation.

The effects of ionizing radiation on field-programmable gate arrays (FPGAs) have been investigated in depth during the last decades. The impact of these effects is typically evaluated on implementations which have a deterministic behavior. In this article, two well-known true-random number generators (TRNGs) based on sampling jittery signals have been exposed to a Co-60 radiation source as in the standard tests for space conditions. The effects of the accumulated dose on these TRNGs, an in particular, its repercussion over their randomness quality (e.g., entropy or linear complexity), have been evaluated by using two National Institute of Standards and Technology (NIST) statistical test suites. The obtained results clearly show how the degradation of the statistical properties of these TRNGs increases with the accumulated dose. It is also notable that the deterioration of the TRNG (non-deterministic component) appears before that the degradation of the deterministic elements in the FPGA, which compromises the integrated circuit lifetime.

Stochastic Insulator-to-Metal Phase Transition-Based True Random Number Generator

An oscillator-based true random number generator (TRNG) is experimentally demonstrated by exploiting inherently stochastic threshold switching in the insulator-to-metal transition (IMT) in vanadium dioxide. Through experimentation and modeling, we show that the origin of stochasticity arises from small perturbations in the nanoscale domain structure, which are then subsequently amplified through a positive feedback process. Within a 1T1R oscillator, the stochastic cycle-to-cycle variations in the IMT trigger voltage result in random timing jitter, which is harnessed for a TRNG. The randomness of the IMT TRNG output is validated using the NIST SP800-22 statistical test.

Modeling Random Telegraph Noise as a Randomness Source and its Application in True Random Number Generation

The random telegraph noise (RTN) is becoming more serious in advanced technologies. Due to the unpredictability of the physical phenomenon, RTN is a good randomness source for true random number generators (TRNG). In this paper, we build fundamental randomness models for TRNGs based on single trap- and multiple traps-induced RTN. We theoretically derive the autocorrelation coefficient, bias, and bit rate for RTN-based TRNGs. Two representative RTN-based TRNG schemes are simulated to verify the proposed randomness models. An oscillator-based TRNG is also studied based on the theoretical randomness model of multiple traps-induced RTN. We also provide basic guidelines for designing RTN-based TRNGs.

Fault model of electromagnetic attacks targeting ring oscillator-based true random number generators

Many side channels including power consumption, electromagnetic emanation, optical radiation, and even sound have been studied since the first publication of a side channel attack at the end of the 1990s. Most of these channels can be relatively easily used for an overall analysis of the cryptographic system (implementation of efficient passive attacks) or for injection of faults. Until recently, only the optical channel allowed both analysis of locally leaked information and precise injection of faults (single-bit errors). Recent works showed that the near-field electromagnetic channel enables similar results to be obtained. Like the optical channel, the near-field electromagnetic channel allows both active and passive attacks, which, in addition, can be theoretically non-invasive and contactless. However, the cost of the attack bench that is needed to exploit the near-field electromagnetic channel is less than that of an optical channel. Recently, we showed that it is possible to use the near-field electromagnetic channel to perform an efficient active attack targeting the true random number generator (TRNG) based on ring oscillators. In cryptography, TRNGs are chiefly used to generate encryption keys and other critical security parameters, so the proposed active attack could have serious consequences for the security of the whole cryptographic system. Here, we present the coupling of a passive attack and an active attack. The proposed coupled attack first uses a spectral differential analysis of the TRNG electromagnetic radiation to obtain valuable information on the position of ring oscillators and their frequency range. This information is then used to tune the electromagnetic harmonic signal to temporarily synchronize the ring oscillators. In this paper, we propose a fault model of the entropy extractor which shows that the behavior of the ring oscillators changes, and that it occurs additional and unwanted “fake rising edges” of the clock signal which disturb the flip-flops involved in such TRNGs. The effectiveness of our proposed coupled attack questions the use of ring oscillators in the design of TRNGs.

A Process and Temperature Tolerant Oscillator-Based True Random Number Generator

This paper presents an oscillator-based true random number generator (TRNG) that dynamically unbiases 0/1 probability. The proposed TRNG automatically adjusts the duty cycle of a fast oscillator to 50%, and generates unbiased random numbers tolerating process variation and dynamic temperature fluctuation. A prototype chip of the proposed TRNG was fabricated with a 65nm CMOS process. Measurement results show that the developed duty cycle monitor obtained the probability of ‘1’ 4,100 times faster than the conventional output bit observation, or estimated the probability with 70 times higher accuracy. The proposed TRNG adjusted the probability of ‘1’ to within 50±0.07% in five chips in the temperature range of 0°C to 75°C. Consequently, the proposed TRNG passed the NIST and DIEHARD tests at 7.5Mbps with 6,670µm2 area.

A Worst-Case-Aware Design Methodology for Noise-Tolerant Oscillator-Based True Random Number Generator With Stochastic Behavior Modeling

This paper presents a worst-case-aware design methodology for an oscillator-based true random number generator (TRNG) that produces highly random bit streams even under deterministic noise. We propose a stochastic behavior model to efficiently determine design parameters, and identify a class of deterministic noise under which the randomness gets the worst. They can be used to directly estimate the worst χ value of a poker test under deterministic noise without generating bit streams, which enables efficient exploration of design space and guarantees sufficient randomness in a hostile environment. The proposed model is validated by measuring prototype TRNGs fabricated with a 65-nm CMOS process.

Jitter Amplifier for Oscillator-Based True Random Number Generator

We propose a jitter amplifier architecture for an oscillator-based true random number generator (TRNG). Two types of latency-controllable (LC) buffer, which are the key components of the proposed jitter amplifier, are presented. We derive an equation to estimate the gain of the jitter amplifier, and analyze sufficient conditions for the proposed circuit to work properly. The proposed jitter amplifier was fabricated with a 65nm CMOS process. The jitter amplifier with the two-voltage LC buffer occupied 3,300µm2 and attained 8.4x gain, and that with the single-voltage LC buffer achieved 2.2x gain with an 1,700µm2 area. The jitter amplification of the sampling clock increased the entropy of a bit stream and improved the results of the NIST test suite so that all the tests passed whereas TRNGs with simple correctors failed. The jitter amplifier attained higher throughput per area than a frequency divider when the required amount of jitter was more than two times larger than the inherent jitter in our test-chip implementations.

Improving the Robustness of Ring Oscillator TRNGs

A ring oscillator-based true-random number generator design (Rings design) was introduced in Sunar et al. [2007]. The design was rigorously analyzed under a simple mathematical model and its performance characteristics were established. In this article we focus on the practical aspects of the Rings design on a reconfigurable logic platform and determine their implications on the earlier analysis framework. We make recommendations for avoiding pitfalls in real-life implementations by considering ring interaction, transistor-level effects, narrow signal rejection, transmission line attenuation, and sampler bias. Furthermore, we present experimental results showing that changing operating conditions such as the power supply voltage or the operating temperature may affect the output quality when the signal is subsampled. Hence, an attacker may shift the operating point via a simple noninvasive influence and easily bias the TRNG output. Finally, we propose modifications to the design which significantly improve its robustness against attacks, alleviate implementation-related problems, and simultaneously improve its area, throughput, and power performance.

True-Randomness and Pseudo-Randomness in Ring Oscillator-Based True Random Number Generators

The paper deals with true random number generators employing oscillator rings, namely, with the one proposed by Sunar et al. in 2007 and enhanced by Wold and Tan in 2009. Our mathematical analysis shows that both architectures behave identically when composed of the same number of rings and ideal logic components. However, the reduction of the number of rings, as proposed by Wold and Tan, would inevitably cause the loss of entropy. Unfortunately, this entropy insufficiency is masked by the pseudo-randomness caused by XOR-ing clock signals having different frequencies. Our simulation model shows that the generator, using more than 18 ideal jitter-free rings having slightly different frequencies and producing only pseudo-randomness, will let the statistical tests pass. We conclude that a smaller number of rings reduce the security if the entropy reduction is not taken into account in post-processing. Moreover, the designer cannot avoid that some of rings will have the same frequency, which will cause another loss of entropy. In order to confirm this, we show how the attacker can reach a state where over 25% of the rings are locked and thus completely dependent. This effect can have disastrous consequences on the system security.