Adaptive Variation-Resilient Random Number Generator for Embedded Encryption

The gist The adaptive RNG extracts unbiased encryption-grade random number streams from physically driven entropy sources, mitigating variations in process and supply voltage through an adaptive digitizer.

Entropy Sources and Challenges

Entropy sources are core components in RNGs, providing the source of randomness. Deterministic PRNGs are regarded as RNGs with low-quality randomness. TRNGs based on conventional CMOS technology employ noise in devices, such as thermal noise or random telegraph noise. Hardware TRNG implementations are based on utilization of devices with unique properties or exploitation of intrinsic noise in classical electronic devices. The challenge in using TRNGs is that they are adversely affected by variations in the fabrication process of the device technology used, leading to bias in generated bit streams. Moreover, in IoT devices, which are mainly battery powered, fluctuations in the supply voltage can also adversely affect TRNGs. Emerging devices utilizing stochastic switching mechanisms have been proposed as promising entropy sources for TRNGs due to their inherent stochastic nature. Notably, devices with stochastic temporal dynamics driven by fluctuations in thermal energy, such as stochastic magnetic tunnel junctions (sMTJs), do not require voltage pulsing or forced switching mechanisms to trigger their stochastic response. However, a major challenge in these device technologies is their limited resilience to process-induced and supply voltage variations.

Adaptive Digitizer Mechanism

The system’s key feature is its adaptive digitizer with an adaptive reference voltage. Once a stochastic signal is generated by the entropy source, the signal needs to be converted from analog to digital, and this is the role of the digitizer. Ideally, the desired output of the digitizer would be a random bit stream that is 50 % ones (1’s) and 50 % zeros (0’s) on average. In this design, instead of applying a fixed VREF to the comparator, a low-pass filter generates an adaptive moving VREF from the stochastic signal corresponding to its short-term average. An important novelty is this VREF that adapts to changes in the stochastic signal, such as voltage drift or mismatch from the designed-for voltage levels due to process-induced or supply voltage variations, and represents a real-time short-term average of the stochastic signal itself. This correction and adaptation of the reference voltage take place before the comparator and without needing any information about the output of the comparator. The LPF that generates this adaptive VREF can be implemented using a resistor (R) and a capacitor (C) in a simple RC LPF configuration. The time constant τLPF of the RC circuit determines how quickly the reference voltage adapts to changes in Vstochastic.

Post-Processing and Randomness Enhancement

Due to the enhanced randomness qualities of the generated bitstreams, light-weight postprocessing is sufficient for acceptable encryption-grade randomness, allowing further savings in hardware. After the adaptive digitizer, post-processing is needed to ensure statistical randomness properties of the bitstream are encryption-grade. For conventional TRNG designs, a commonly employed post-processing circuit is the Trivium cipher. The Mini Trivium is a modified lower-hardware-cost version of the Trivium cipher used for post-processing. This simplified circuit reduces the three Nonlinear Feedback Shift Registers into a single 19-bit shift register, thus reducing complexity.

Variation Resilience and Performance

The adaptive RNG is designed to eliminate any bias, enhancing the resilience of the system to process-induced and supply-voltage variations. Simulation results show that the proposed adaptive TRNG dynamically tracks Vstochastic and tunes itself to adapt to entropy source variations. The system demonstrates enhanced resilience of the adaptive TRNG to variations in VDD, G0 and TMR compared to a conventional TRNG, reaching up to an enhancement in the variation-resilience range of 40 %, 75 % and 17 %, respectively. The system can support a wide range of throughputs from 5 to 182 Mbps. Experimental results confirm that the LFSR-based adaptive RNG implementation using off-the-shelf components results in the generation of high quality random numbers with properties suitable for embedded encryption. The system consistently passed all 16 tests of the NIST SP 800-22 test suite with a 100% pass rate.

Conclusion and Applicability

The presented adaptive RNG has great potential for use in embedded encryption within IoT devices, making data encryption accessible locally. The approach does not need voltage pulsing as required in other designs. It is important to highlight the generality of our adaptive RNG concept beyond MTJs only, as it can be implemented using various entropy sources (e.g., CMOS, RRAM, MTJ), as demonstrated through our LFSR implementation in the FPGA experiments. The presented adaptive RNG offers a wide - relatively high - throughput range of 5 Mbps to 182 Mbps. The system is implementable using off-shelf component implementations. The presented adaptive RNG consistently passed all NIST SP 800-22 tests with a 100% pass rate. The obtained P-values are indeed comparable to the results obtained for the sMTJ-based adaptive TRNG system at nominal conditions.

How it works

1. The system employs an entropy source, such as a stochastic magnetic tunnel junction (sMTJ) or a Linear Feedback Shift Register (LFSR).

2. An adaptive digitizer is employed to eliminate any bias, enhancing the resilience of the system to process-induced and supply-voltage variations.

3. The adaptive digitizer generates an adaptive moving VREF from the stochastic signal corresponding to its short-term average.

4. This process of conversion and subsequent adaptive digitization processes infuses more noise (randomness) into the signal.

5. The output will then undergo post-processing to produce a digital random bit stream with randomness qualities that fulfil the basic requirements of embedded cryptography applications.

How it works

The adaptive digitizer is implemented using a low-pass filter circuit where the time constant τLPF determines how quickly the reference voltage adapts to changes in Vstochastic. The selection of R and C depends on how fast the system needs to adapt to fluctuations in Vstochastic. The LPF circuit is used to generate an adaptive moving VREF from the stochastic signal.

How it works

The post-processing circuit uses a simplified Mini Trivium cipher to reduce hardware resources for energy-constrained IoT devices.

1. Adaptation of Entropy Source Tracking for Process Resilience: The system uses an adaptive digitizer with an adaptive reference voltage that dynamically tracks any stochastic signal drift or deviation, which mitigates variations in the entropy source, leading to unbiased random bit stream generation.

2. Enhanced Pseudo-Randomness from Weak Sources: The adaptive RNG demonstrates the ability to enhance lower-quality sources, as shown by its success with a pseudo-random source like an LFSR, where the digital output from the LFSR is converted to an analog signal serving as VStochastic, and is then fed into the adaptive digitizer that converts it back to digital.

3. Reduced Hardware Complexity for Cryptography: The system utilizes a simplified post-processing circuit called the Mini Trivium, which reduces complexity by reducing its three Nonlinear Feedback Shift Registers (NFSRs) into a single 19-bit shift register, thus reducing complexity, without compromising core cryptographic properties.

4. Increased Robustness to Supply Voltage Fluctuations: The adaptive RNG exhibits significant resilience, with simulation results showing an enhancement in the variation-resilience range of 40 % for supply voltage variations (VDD), allowing consistent operation across a wide range of throughputs from 5 to 182 Mbps.

5. Versatile Entropy Source Utilization: The adaptive RNG architecture is generalizable, as it can be implemented using various entropy sources, including CMOS, RRAM, MTJ, demonstrating its potential for use in diverse IoT applications beyond just sMTJs.

With a growing interest in securing user data within the internet-of-things (IoT), embedded encryption has become of paramount importance, requiring light-weight high-quality Random Number Generators (RNGs). Emerging stochastic device technologies produce random numbers from stochastic physical processes at high quality, however, their generated random number streams are adversely affected by process and supply voltage variations, which can lead to bias in the generated streams. In this work, we present an adaptive variation-resilient RNG capable of extracting unbiased encryption-grade random number streams from physically driven entropy sources, for embedded cryptography applications. The system's key feature is its adaptive digitizer with an adaptive reference voltage. As a proof of concept, we employ a stochastic magnetic tunnel junction (sMTJ) device as an entropy source. The impact of variations in the sMTJ is mitigated by the adaptive digitizer, which generates an adaptive short-term average reference voltage that dynamically tracks any stochastic signal drift or deviation, leading to unbiased random bit stream generation. The generated bit streams, due to their higher entropy, then only need to undergo simplified post-processing. A prototype of the adaptive RNG system was experimentally implemented using discrete electronic components and an FPGA for entropy source emulation. Statistical randomness tests based on the National Institute of Standards and Technology (NIST) test suite are conducted on bit streams obtained using the simulations as well as the discrete electronic component implementation, demonstrating that the bit streams consistently pass all 16 tests of the NIST SP 800-22 test suite with a 100% pass rate. Leveraging its simplified post-processing, the adaptive RNG shows consistent operation across a wide range of throughputs from 5 to 182 Mbps.