Random Forests and Networks Analysis

D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a powerful tool in analyzing structures on networks and along this line of thinking, in recent works~\cite{AG1,AG2,ACGM1,ACGM2} we focused on applications of spanning rooted forests on finite graphs. The resulting main conclusions are reviewed in this paper by collecting related theorems, algorithms, heuristics and numerical experiments. A first foundational part on determinantal structures and efficient sampling procedures is followed by four main applications: 1) a random-walk-based notion of well-distributed points in a graph 2) how to describe metastable dynamics in finite settings by means of Markov intertwining dualities 3) coarse graining schemes for networks and associated processes 4) wavelets-like pyramidal algorithms for graph signals.Comment: Survey pape

FPGA-based true random number generation using circuit metastability with adaptive feedback control

13th International Workshop, Nara, Japan, September 28 – October 1, 2011. ProceedingsThe paper presents a novel and efficient method to generate true random numbers on FPGAs by inducing metastability in bi-stable circuit elements, e.g. flip-flops. Metastability is achieved by using precise programmable delay lines (PDL) that accurately equalize the signal arrival times to flip-flops. The PDLs are capable of adjusting signal propagation delays with resolutions higher than fractions of a pico second. In addition, a real time monitoring system is utilized to assure a high degree of randomness in the generated output bits, resilience against fluctuations in environmental conditions, as well as robustness against active adversarial attacks. The monitoring system employs a feedback loop that actively monitors the probability of output bits; as soon as any bias is observed in probabilities, it adjusts the delay through PDLs to return to the metastable operation region. Implementation on Xilinx Virtex 5 FPGAs and results of NIST randomness tests show the effectiveness of our approach

Sharp asymptotics for metastability in the random field Curie-Weiss model

In this paper we study the metastable behavior of one of the simplest disordered spin system, the random field Curie-Weiss model. We will show how the potential theoretic approach can be used to prove sharp estimates on capacities and metastable exit times also in the case when the distribution of the random field is continuous. Previous work was restricted to the case when the random field takes only finitely many values, which allowed the reduction to a finite dimensional problem using lumping techniques. Here we produce the first genuine sharp estimates in a context where entropy is important.Comment: 56 pages, 5 figure

A new TRNG based on coherent sampling with self-timed rings

Random numbers play a key role in applications such as industrial simulations, laboratory experimentation, computer games, and engineering problem solving. The design of new true random generators (TRNGs) has attracted the attention of the research community for many years. Designs with little hardware requirements and high throughput are demanded by new and powerful applications. In this paper, we introduce the design of a novel TRNG based on the coherent sampling (CS) phenomenon. Contrary to most designs based on this phenomenon, ours uses self-timed rings (STRs) instead of the commonly employed ring oscillators (ROs). Our design has two key advantages over existing proposals based on CS. It does not depend on the FPGA vendor used and does not need manual placement and routing in the manufacturing process, resulting in a highly portable generator. Our experiments show that the TRNG offers a very high throughput with a moderate cost in hardware. The results obtained with ENT, DIEHARD, and National Institute of Standards and Technology (NIST) statistical test suites evidence that the output bitstream behaves as a truly random variable.This work was supported in part by the Ministerio de Economia y Competitividad (MINECO), Security and Privacy in the Internet of You (SPINY), under Grant TIN2013-46469-R, and in part by the Comunidad de Madrid (CAM), Cybersecurity, Data, and Risks (CIBERDINE), underGrant S2013/ICE-3095

A Simple PLL-Based True Random Number Generator for Embedded Digital Systems

The paper presents a simple True Random Number Generator (TRNG) which can be embedded in digital Application Specific Integrated Circuits (ASICs) and Field Programmable Logic Devices (FPLDs). As a source of randomness, it uses on-chip noise generated in the internal analog Phase-Locked Loop (PLL) circuitry. In contrast to traditionally used free-running oscillators, it uses a novel method of randomness extraction based on two rationally related synthesized clock signals. The generator has been developed for embedded cryptographic applications, where it significantly increases the system security, but it can be used in a wide range of other applications. The functionality of the proposed solution is demonstrated for the Altera Apex FPLD family, but the same principle can be used for all recent ASICs or FPLDs that include an on-chip reconfigurable analog PLL. The quality of the TRNG output is confirmed by applying special DIEHARD and NIST statistical tests, which pass even for high output bit-rates of several hundreds of Kbits/s

The exit problem for diffusions with time-periodic drift and stochastic resonance

Physical notions of stochastic resonance for potential diffusions in periodically changing double-well potentials such as the spectral power amplification have proved to be defective. They are not robust for the passage to their effective dynamics: continuous-time finite-state Markov chains describing the rough features of transitions between different domains of attraction of metastable points. In the framework of one-dimensional diffusions moving in periodically changing double-well potentials we design a new notion of stochastic resonance which refines Freidlin's concept of quasi-periodic motion. It is based on exact exponential rates for the transition probabilities between the domains of attraction which are robust with respect to the reduced Markov chains. The quality of periodic tuning is measured by the probability for transition during fixed time windows depending on a time scale parameter. Maximizing it in this parameter produces the stochastic resonance points.Comment: Published at http://dx.doi.org/10.1214/105051604000000530 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

True random number generator based on the variability of the high resistance state of RRAMs

Hardware-based security primitives like True Random Number Generators (TRNG) have become a crucial part in protecting data over communication channels. With the growth of internet and cloud storage, TRNGs are required in numerous cryptographic operations. On the other hand, the inherently dense structure and low power characteristics of emerging nanoelectronic technologies such as resistive-switching memories (RRAM) make them suitable elements in designing hardware security modules integrated in CMOS ICs. In this paper, a memristor based TRNG is presented by leveraging the high stochasticity of RRAM resistance value in OFF (High Resistive) state. In the proposal, one or two devices can be used depending on whether the objective is focused on saving area or obtaining a higher random bit frequency generation. The generated bits, based on a combination of experimental measurements and SPICE simulations, passed all 15 National Institute of Standards and Technology (NIST) tests and achieved a throughput of tens of MHz.Postprint (published version

Delay Measurements and Self Characterisation on FPGAs

This thesis examines new timing measurement methods for self delay characterisation of Field-Programmable Gate Arrays (FPGAs) components and delay measurement of complex circuits on FPGAs. Two novel measurement techniques based on analysis of a circuit's output failure rate and transition probability is proposed for accurate, precise and efficient measurement of propagation delays. The transition probability based method is especially attractive, since it requires no modifications in the circuit-under-test and requires little hardware resources, making it an ideal method for physical delay analysis of FPGA circuits. The relentless advancements in process technology has led to smaller and denser transistors in integrated circuits. While FPGA users benefit from this in terms of increased hardware resources for more complex designs, the actual productivity with FPGA in terms of timing performance (operating frequency, latency and throughput) has lagged behind the potential improvements from the improved technology due to delay variability in FPGA components and the inaccuracy of timing models used in FPGA timing analysis. The ability to measure delay of any arbitrary circuit on FPGA offers many opportunities for on-chip characterisation and physical timing analysis, allowing delay variability to be accurately tracked and variation-aware optimisations to be developed, reducing the productivity gap observed in today's FPGA designs. The measurement techniques are developed into complete self measurement and characterisation platforms in this thesis, demonstrating their practical uses in actual FPGA hardware for cross-chip delay characterisation and accurate delay measurement of both complex combinatorial and sequential circuits, further reinforcing their positions in solving the delay variability problem in FPGAs