CHAOTIC PHYSICAL TRUE RANDOM NUMBER GENERATOR AND ASSOCIATED METHOD

Description

TECHNICAL FIELD

[0001] The present invention relates to the field of devices and methods for generating true random numbers. More particularly, in two aspects, the present invention relates to a chaotic physical generator of true random numbers and the associated generation method. For example, the generation of true random numbers is essential to modern cryptography, generating the keys that enable secure communication. STATE OF THE ART

[0002] To obtain a sequence of true random numbers, it is known to rely on an intrinsically random physical process. Since the amplitude of the associated signals can be weak, it may be necessary to amplify them before converting them into a sequence of true random numbers. This quest for sources of amplified randomness leading to a random numerical sequence is a constantly evolving field of research.

[0003] The physical generation of true random numbers is based on such intrinsically random physical processes. It is particularly known to exploit various physical phenomena, including: thermal noise [SK Mathew et al., “2.4 Gbps, 7 mW All-Digital PVT-Variation Tolerant True Random Number Generator for 45 nm CMOS High-Performance Microprocessors,” in IEEE Journal of Solid-State Circuits, vol. 47, no. 11, pp. 2807-2821, Nov. 2012], or the variation of the frequency of a clock [Fischer V. et al. (2003) True Random Number Generator Embedded in Reconfigurable Hardware. In: Kaliski BS, Koç .K., Paar C. (eds) Cryptographic Hardware and Embedded Systems - CHES 2002. Lecture Notes in Computer Science, vol 2523. Springer, Berlin, Heidelberg].

[0004] These phenomena can be observed directly on resonant components, or resonators, of an electrical circuit, but can also be observed directly on resonators equipping devices belonging to other fields.

[0005] For example, it has been shown that the chaotic behavior of optical components can be exploited, in particular by using lasers and photodetectors as resonators [Uchida, A., Amano, K., Inoue, M., Hirano, K., Naito, S., Someya, H., ... & Yoshimura, K. (2008). Fast physical random bit generation with chaotic semiconductor lasers. Nature Photonics, 2(12), 728].

[0006] Micro / Nano-Electro-Mechanical Systems (M / NEMS) are another example of resonant devices. Some of their resonant components exploit mechanical properties, allowing the direct conversion of mechanical displacement into an electrical signal. These components are ubiquitous in modern technologies and are notably used as sensors in the form of accelerometers, gyroscopes, and magnetometers [Tanaka, M. (2007). An industrial and applied review of new MEMS device features, Microelectronic engineering, 84(5-8), 1341-1344]. Among the various intrinsic properties of these resonators, some are sources of uncertainty, including: thermomechanical noise [TB Gabrielson et al. "Mechanical-thermal noise in micromachined acoustic and vibration sensors", in IEEE Transactions on Electron Devices, vol. 40, no. 5, pp. 903-909, May 1993, doi: 10.1109 / 16.210197], and the 1 / f noise of their resonance frequency [M. Sansa et al. Frequency fluctuations in silicon nanoresonators, Nat. Nanotechnol. 11, 552-558 (2016)].

[0007] Thanks to their intrinsic non-linearity, it is possible to put these resonators into a chaotic regime [YC Wang et al. "Chaos in MEMS, parameter estimation and its potential application," in IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 45, no. 10, pp. 1013-1020, Oct. 1998].

[0008] As mentioned above, in order to create a physical generator of true random numbers, it is necessary to amplify the intrinsic noise of the resonator being used. In the field of electronic circuits, it is possible to amplify noise, as a source of randomness, notably by exploiting the sensitivity of the chaotic regime to the conditions in which the resonator is initially located [ME Yalcin et al. "True random bit generation from a double-scroll attractor," in IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 51, no. 7, pp. 1395-1404, July 2004].

[0009] Furthermore, oscillating devices exist. Such devices are described, for example, in the article by Ghosh Dia et al., entitled "Generation & control of chaos in a single loop optoelectronic oscillator," published in the journal Optik. These devices are not comparable to the resonant devices introduced earlier. Indeed, an oscillating device generally comprises a closed loop, responding to well-defined constraints; its very physics is fundamentally different from that of a resonant device. In particular, an oscillator "affects itself" in the sense that its circuit is closed, whereas a resonant device or resonator has no feedback loop.

[0010] Qingfei Chen's dissertation at Arizona State University, titled "Nonlinear dynamics, control and shock mitigation in microelectromechanical and nanoelectromechanical resonant devices", exposes the technological background on miniaturized resonant devices.

[0011] One object of the present invention is to overcome at least one drawback of physical generators of known true random numbers.

[0012] More particularly, an object of the present invention is to provide a chaotic physical generator of true random numbers allowing a gain in simplicity of implementation, in size and / or in manufacturing cost, relative to existing chaotic physical generators of true random numbers.

[0013] Another object of the present invention is to provide a physical generator of true random numbers compatible with many existing technologies, and in particular CMOS technologies (for "Complementary Metal Oxide Semiconductor" according to Anglo-Saxon terminology), preferably without additional bulk or manufacturing cost.

[0014] The other objects, features, and advantages of the present invention will become apparent from an examination of the following description and accompanying drawings. It is understood that other advantages may be incorporated. SUMMARY

[0015] To achieve this objective, according to a first aspect of the invention, an excitation system is provided for a resonant physical component, the system comprising an excitation device configured to: Excite the resonant physical component with a specific excitation signal to bring, or even maintain at least temporarily, the resonant physical component in a state of dynamic multi-stability, and modulate the excitation signal. so that the resonant physical component has chaotic behavior and an analog signal from the resonant physical component is directly or indirectly representative of the chaotic behavior of the resonant physical component.

[0016] The excitation system is also free of a feedback loop.

[0017] Note that the modulation of the excitation signal can include modulation in phase and / or in frequency and / or in amplitude, by a modulating signal.

[0018] According to a second aspect of the invention, a chaotic physical generator of true random numbers is provided, comprising: A resonant physical component, an analog-to-digital converter configured to convert an analog signal from the resonant physical component into a digital signal representative of the analog signal, a digital processing device configured to generate a sequence of true random numbers from said digital signal.

[0019] The generator also includes an excitation device for the resonant physical component configured to: Excite the resonant physical component with a determined excitation signal to bring, or even to maintain at least temporarily, the resonant physical component into a regime of dynamic multi-stability, and modulate the excitation signal.

[0020] The excitation device is free of a feedback loop.

[0021] Thus, the resonant physical component exhibits chaotic behavior, and the analog signal to be converted is directly or indirectly representative of the chaotic behavior of the resonant physical component.

[0022] By placing the resonant physical component in a dynamic multistability regime through the application of an excitation signal, and by further modulating the excitation signal, the behavior of the resonant physical component can become chaotic. The intrinsic noise sources of the resonant physical component are then amplified, for example exponentially, resulting in high-amplitude noise. The analog signal from the resonant physical component is then representative of its chaotic behavior. It is therefore possible to use it to generate a sequence of true random numbers.Considering that, with few exceptions, every microelectromechanical system includes a physical component capable of acting as a resonator for the generator according to the second aspect of the invention, it is understood that the excitation system according to the first aspect of the invention offers advantages in terms of ease of implementation, size, and / or manufacturing cost for the realization of chaotic physical generators of true random numbers, particularly compared to generators based on oscillating devices (with feedback loops). It is further understood that the excitation system according to the first aspect of the invention is compatible with many existing technologies, including CMOS technologies, potentially with a small size or limited additional manufacturing cost.

[0023] According to a third aspect of the invention, a method for generating true random numbers is provided, in particular implementing a chaotic physical generator as presented herein, comprising the following steps: Excitation of a resonant physical component with a specific excitation signal to bring, or even at least temporarily maintain, the resonant physical component in a state of dynamic multistability; Modulation of the excitation signal so that the resonant physical component exhibits chaotic behavior. The excitation and modulation stages are implemented by an excitation device free from a feedback loop, Acquisition of an analog signal, and more particularly an electrical signal, from the resonant physical component and directly or indirectly representative of the chaotic behavior of the resonant physical component, Conversion of the analog signal into a digital signal representative of the acquired analog signal, then Generation from said digital signal of a sequence of true random numbers.

[0024] According to a fourth aspect of the invention, a computer program product is provided, comprising instructions which, when executed by at least one processor, performs at least the steps of the true random number generation process as hereinafter introduced.

[0025] According to a fifth aspect of the invention, a microelectromechanical system is provided comprising a resonant physical component, an analog / digital converter and a digital processing device, further comprising an excitation device configured to excite the resonant physical component so as to form a chaotic physical generator of true random numbers as hereinafter introduced.

[0026] Optionally, the excitation system according to the first aspect of the invention may further have at least one of the following characteristics: For example, the excitation system is intended to be integrated into a microelectromechanical system comprising a resonant physical component for its use in generating a sequence of true random numbers from said analog signal;

[0027] For example, the excitation system also includes: An analog-to-digital converter configured to convert the analog signal from the resonant physical component into a digital signal representative of the analog signal; A digital processing device configured to generate a sequence of true random numbers from said digital signal;

[0028] For example, the excitation system also includes: a demodulation device configured to implement one of the following steps: i. before the conversion of the analog signal, a demodulation of the analog signal at the frequency f of the excitation signal, and ii. after the conversion of the analog signal, a demodulation of the digital signal at the frequency f of the excitation signal;

[0029] Optionally, the chaotic physical generator according to the second aspect of the invention may also have at least one of the following characteristics: For example, the analog signal to be converted is representative of the changes in amplitude and / or phase of vibration of the resonant physical component excited by the modulated excitation signal; The generator is preferably free of any type of excitation devices configured to cause the resonant physical component to overheat; For example, said multi-stability dynamic regime is a non-linear bi-stability dynamic regime known as Duffing's; For example, said excitation signal has a peak voltage between 0.01 and 10V, preferably between 0.1 and 5V, and a frequency f equal to the resonance frequency f0 of the resonant physical component to within ±20%, preferably to within ±10%;For example, said modulated excitation signal has a modulation frequency δf preferably greater than, but potentially substantially equal to, the ratio f0 / Q of the resonant frequency f0 of the physical component resonating with its quality factor Q; For example, the physical component resonating includes a micro / nano-resonator, such as a doubly embedded micro / nano-beam; For example, the generator further includes a demodulation device configured to implement one of the following steps: before the conversion of the analog signal, demodulation of the analog signal at the frequency f of the excitation signal, and after the conversion of the analog signal, demodulation of the digital signal at the frequency f of the excitation signal.

[0030] Optionally, the generation process according to the third aspect of the invention may also have at least one of the following characteristics: For example, the process may further include, after the analog signal acquisition step and before the analog signal conversion step, an amplification step of the acquired analog signal; For example, the excitation signal is parameterized to bring, or even to maintain at least temporarily, the resonant physical component into a nonlinear dynamic bi-stability regime known as Duffing's regime; For example, the dynamic multi-stability regime of the resonant physical component being associated with a continuous and limited frequency domain, the frequency f of the excitation signal is determined to bring the resonant physical component into a sub-regime of the dynamic multi-stability regime, said sub-regime being associated with a first half, or even a first third, of the frequency domain associated with the dynamic multi-stability regime of the resonant physical component;For example, the excitation of the resonant physical component includes the application across its terminals, as an excitation signal, of a peak voltage between 0.01 and 10V, and preferably between 0.1 and 5V, and of a frequency f equal to the resonance frequency f 0 of the resonant physical component to within ±20%, preferably to within ±10%;For example, the potential of the resonant physical component in its dynamic multi-stability regime has two distinct wells: The frequency modulation of the excitation signal is of a determined amplitude δf to induce changes of state of the resonant physical component in its dynamic multi-stability regime from one of the two potential wells to the other, and vice versa, and / or The amplitude modulation of the excitation signal is of a determined amplitude δf to induce changes of state of the resonant physical component from its monostable regime to its dynamic multi-stability regime, and vice versa; For example, the excitation signal is modulated with a modulation frequency δf preferably greater than, but potentially substantially equal to, the ratio f 0 / Q of the resonant frequency f 0 of the resonant physical component by its quality factor Q;For example, the process further includes one or the other of the following steps: before the conversion of the analog signal, a demodulation of the analog signal at the frequency f of the excitation signal, and after the conversion of the analog signal, a demodulation of the digital signal at the frequency f of the excitation signal;For example, the analog signal being a first analog signal directly representative of the changes in amplitude and / or phase of vibration of the resonant physical component, the demodulation of the analog signal before the conversion of the analog signal includes a comparison of the first analog signal with the excitation signal to deduce, as an analog signal indirectly representative of the changes in amplitude and / or phase of vibration of the resonant physical component, a second analog signal representative of a change in amplitude of the first analog signal and / or a change in phase between the first analog signal and the excitation signal;For example, analog signal conversion includes sampling the analog signal at a sampling frequency or in steps chosen according to the voltage of the excitation signal and a modulation frequency δf with which the excitation signal is modulated. The sampling frequency is preferably at least 10 times higher than the modulation frequency δf; For example, an analog signal representing the changes in vibration amplitude of the resonant physical component and an analog signal representing the changes in phase of the resonant physical component being acquired during the acquisition step, the conversion step includes converting each of these two analog signals into a digital signal;For example, the analog signal being converted into a succession of values ​​each coded on a number N of bits, for example strictly greater than three, typically equal to eight, the generation of the binary sequence of true random numbers includes the generation of a series of bits that can be illustrated as a square wave, and then cutting this series into a sequence of bit blocks on the basis of each of which a true random number of the sequence is generated; For example, said bit series is generated on the basis of only the n-least significant bits of each coded value of the succession;For example, the generation of the binary sequence of random numbers includes the generation of a series of bits that can be illustrated as a square wave for each of the two acquired analog signals, then a logical operation, for example by the "exclusive OR" operator, between the two generated series of bits, to obtain the series of bit blocks to be sliced.

[0031] A parameter is understood to be "approximately equal to" a given value when that parameter is equal to the given value, to within 10% or even 5% of that value. BRIEF DESCRIPTION OF THE FIGURES

[0032] The aims, objects, features and advantages of the invention will become clearer from the detailed description of an embodiment thereof, which is illustrated by the following accompanying drawings in which: There figure 1represents an electronic diagram of an embodiment of the second and fifth aspects of the invention and includes an electronic diagram of an embodiment of the first aspect of the invention. figure 2 graphically represents the transition from a monostable regime (bottom curve) to a dynamic bistability regime known as Duffing's regime (top curves). Figures 3A and 3B These figures represent: A) the Duffing dynamic bistability regime, represented by a graph of the vibration amplitude of the resonant physical component as a function of the applied excitation frequency, and B) the two-well potential of the resonant physical component as a function of its vibration amplitude. In both figures, the arrow represents a schematic guide describing the transition from a high amplitude to a low amplitude within the hysteresis. figure 4graphically illustrates possible behaviors of the resonant physical component when it is excited by the modulated excitation signal. figure 5 This graphically illustrates a method for converting each of two analog signals, representing the amplitude and phase of the resonant physical component under consideration, into a digital signal from which a sequence of true random numbers is to be generated. figure 6 is a flowchart of an embodiment of the generation process according to the third aspect of the invention.

[0033] The drawings are given by way of example and are not limiting of the invention. They constitute schematic representations of principle intended to facilitate understanding of the invention and are not necessarily to scale with practical applications. In particular, the Figures 1 , 4 And 5are not necessarily representative of reality. DETAILED DESCRIPTION

[0034] The generation of true random numbers is essential to modern cryptography. In particular, it allows the generation of keys that secure communications. To obtain a sequence of true random numbers, the present invention proposes to rely on an intrinsically random physical process. Various aspects of the invention are described below, with reference to the accompanying figures, which include an excitation system 10 for a resonant physical component 2, a chaotic physical generator 1 of true random numbers that can constitute at least part of a microelectromechanical system, and a method for generating true random numbers 100 associated with the generator 1.

[0035] Hereafter, we will sometimes use the term "resonator" to refer to the aforementioned resonant physical component 2.

[0036] The invention proposes, more specifically, to exploit the ability of most resonant physical components to exhibit chaotic behavior when excited in an ad hoc manner. Such resonant physical components are already present in numerous technologies; and the invention's first technical advantage is to demonstrate how it is possible to use the aforementioned ability of resonators, already implemented in many devices, particularly electronic ones, to generate true random numbers by repurposing these components from their original uses.Thus, those skilled in the art will appreciate upon reading the following that the invention, in certain aspects, provides for the possibility of adding to an existing device, particularly an electronic one, which includes a resonator 2, some embedded components, and in particular an excitation device 11 for the resonator 2, in order to divert the latter from its primary use, so as to use it for the generation 150 of a sequence of true random numbers. The proposed solution therefore makes it possible to give most existing devices, particularly electronic ones, an additional function directly usable by these same devices, and / or by others connected to them, in particular to allow these devices to communicate securely. Those skilled in the art will note, upon reading the following, that this additional functionality is also made possible without inducing: . significant space constraints, especially for devices that are increasingly miniaturized, and / or a significant additional manufacturing cost.

[0037] Furthermore, it is entirely possible that devices, particularly electronic ones, already manufactured can be modified at a lower cost to incorporate the device(s) enabling them to perform the additional function of generating true random numbers. figure 1can be seen as illustrating an electronic diagram comprising an excitation system 10 added to the terminals of a resonator 2 equipping an existing microelectromechanical system. Switching means, here represented in the form of switches, can then be provided which are configured to functionally connect the excitation system 10 to the terminals of the resonator 2, and to disconnect the terminals of the resonator 2 from these generic inputs and outputs. The excitation system 10 as illustrated in the figure 1includes the excitation device 11, whose input data includes the excitation parameters of the resonator 2 and the modulation of this excitation, a demodulation device 14, an analog-to-digital converter 12, and a digital processing device 13, as described below. However, as will become clear from the following description, the excitation system 10, in its most generic form, comprises only the excitation device 11; the other components of the excitation system 10 are as illustrated in the figure 1 that may belong to an existing electromechanical microsystem 1.

[0038] It should be noted that, among the existing technologies compatible with the implementation of the invention, CMOS technologies are in particular directly compatible with this implementation.

[0039] Micro / nano-electromechanical systems can be defined as micro / nanometric devices that convert a mechanical process into an electrical one, and vice versa. Micro / nano-electromechanical systems comprising at least one resonant physical component 2 are characterized by having, through their resonant physical component(s), a vibrating mass that allows the transfer of mechanical energy into electrical energy, or vice versa, to obtain, for example, an energy harvester or a force sensor, depending on the chosen geometry.

[0040] Resonant micro / nano-electromechanical systems are primarily characterized by their resonance frequency f0 and their quality factor Q.

[0041] One of the geometries usable within the framework of the present invention consists, for example, of a doubly fixed micro / nano-beam. The equilibrium position of the beam, acting as a resonator 2, can indeed alternate between different notable states, particularly when the beam is brought into a regime of dynamic multi-stability. Reaching such a regime is possible by applying a sufficiently high alternating force to the beam. The application of such a force can, in all cases, be considered as consisting of the application of an excitation signal to the resonator 2. This is the first role that the excitation device 11 can play according to the present invention. In the example considered, the position of the beam subjected to such an excitation signal can then resonate between states close to said notable states and / or around these notable states.

[0042] The excitation signal may consist, depending on the nature of resonator 2, of an alternating voltage applied to its terminals. In this case, the excitation signal can be characterized in terms of parameters of said alternating voltage, such as its peak voltage, also referred to hereafter as the "excitation voltage," and its frequency f, also referred to hereafter as the "excitation frequency." For example, the excitation signal has a peak voltage between 0.01 and 10 V, preferably between 0.1 and 5 V, and a frequency f equal to the resonance frequency f₀ of resonator 2 to within ±20%, preferably to within ±10%. It should be noted that the excitation signal is not limited to an electrical signal, but also extends, for example, to a mechanical signal to which resonator 2 would be sensitive by its nature.

[0043] More generally, any resonant physical component 2 can be excited 110 with a specific excitation signal to bring, or even to maintain at least temporarily, the resonant physical component 2 in a state of dynamic multistability. With reference to the figure 2The graph, comprising several curves from numerical simulations, shows that the amplitude response R(mV) of a resonator 2 as a function of the frequency of a weak excitation signal (lower curve) takes the form of a Lorentzian, illustrating the linear behavior of resonator 2 when subjected to a weak excitation force. As the excitation force applied to resonator 2 increases, its response gradually transforms and becomes asymmetric (see upper curves); the response of resonator 2 becomes nonlinear, which has the effect of modifying its resonance frequency f0. A frequency hysteresis is then observed, which, in the illustrated case, is representative of a dynamic bi-stability regime, and more specifically here of a nonlinear dynamic bi-stability regime known as Duffing's regime.

[0044] The upper curve illustrated on the graph of the figure 2is reproduced on the graph of the figure 3A On the latter, references "1" and "2" have been added, roughly pointing to distinct, noteworthy states in which resonator 2 can be found for a given excitation frequency. References "1" and "2" are reproduced correspondingly on the figure 3B which shows, for said given excitation frequency, the evolution of the potential of resonator 2 as a function of the amplitude R(mV) of its variations. Thus, the curve illustrated on the graph of the figure 3B shows that each of the notable states referenced "1" and "2" corresponds to a state of least potential, that is, a potential well. The aforementioned notable states therefore correspond to preferred stable states around each of which resonator 2 will have a greater probability of being found for the given excitation frequency. The graphs of Figures 3A and 3BThis illustrates a bifurcation between the two stable states of hysteresis. Thus, at high amplitudes of the excitation signal, hysteresis opens in the frequency domain, favoring either the high-amplitude variation state "1" or the low-amplitude variation state "2". These two states are directly comparable to the case of a buckled resonator, except that the latter's states are static (for example, they correspond to the high and low positions of a buckled beam), whereas the two states of resonator 2 brought into a dynamic multi-stability regime according to the invention are dynamic (they correspond to high or low vibration amplitudes of resonator 2). As with the case of a buckled resonator, it is possible to impose chaotic behavior on resonator 2 brought into a dynamic multi-stability regime according to the invention by modulating the excitation force applied to it.

[0045] It should be noted here that the excitation signal according to the invention is in no way intended to cause the resonator 2 to ignite. Preferably, the excitation system 10 according to the first aspect of the invention and / or the chaotic physical generator 1 according to the second aspect of the invention are free from any type of excitation device configured to cause the resonator 2 to ignite. Thus, the implementation of the invention is not contingent upon the creation of a ignited structure, such a structure being complex to manufacture and generally requiring high energy consumption to operate. On the contrary, the implementation of the invention benefits from the fact that almost any micro / nano-resonator 2 exhibits non-linear behavior at high excitation amplitudes, without any particular conditions on its geometry, the material used, or the transduction techniques employed.In particular, the implementation of the invention can be carried out on most micro / nano-resonators 2 as they exist, and therefore without the need for an alteration of their manufacturing process.

[0046] If the excitation signal is further modulated 120, in frequency 121 and / or in amplitude 122, as illustrated in the figure 4Resonator 2 can adopt a complex, non-periodic, chaotic dynamic. The resulting chaotic behavior is characterized in particular by its non-reproducibility and the impossibility of predicting the state of resonator 2 in the medium and long term. Indeed, although any chaotic regime is deterministic—that is, although the response of resonator 2 can be predicted if the equations governing its behavior are perfectly known—a very small variation in the initial conditions, for example, of temperature or ambient pressure, in which resonator 2 is located, quickly leads to significant changes in behavior, similar to the butterfly effect.Thus, since the behavior of any resonator 2 is always affected by the presence of noise, however weak, a drastic change in its response to a modulated excitation signal 101 such as the one mentioned above can be observed, particularly with each new application of the same modulated excitation signal 101, making it impossible to predict its dynamic behavior in the medium and long term. Therefore, a micro / nano-electromechanical system 1, in which at least one resonator 2 is brought into a dynamic multi-stability regime and is further perturbed so that the resonator adopts chaotic behavior, allows for the generation, at the output of resonator 2, of a random and high-amplitude analog signal 102.Note here that the aforementioned change in behavior of resonator 2 can be observed on the phase alone of the analog signal, on the amplitude alone of the analog signal 102, on each of the phase and amplitude of the analog signal 102, or on any combination of these two parameters of the analog signal 102; these different possibilities are embraced by the expression "changes in amplitude and / or phase of vibration of resonator 2" used below.

[0047] It should be noted here that the emergence of chaotic behavior in resonator 2 may, as already implicitly introduced above, require some time from the start of the application of the modulated excitation signal 101. More specifically, this time may be necessary to observe the change in the response of resonator 2 to the modulated excitation signal 101 as a function of the initial conditions it experiences. Those skilled in the art will be able to estimate this time a priori or heuristically, for example by verifying the randomness of the generated number sequence 150, notably by implementing the reference tests known as NIST 800-22 or AIS 31. The at least temporary maintenance of resonator 2 in the dynamic multi-stability regime can be considered, in particular, in light of this time required for the chaotic behavior of resonator 2 to be expressed by the resulting analog signal 102.

[0048] Whatever the initial application of the resonator 2, for example an application as an accelerometer or energy harvester, the latter can, according to the invention, also be used to generate an analog signal 102 directly or indirectly representative of the chaotic behavior of the resonator 2 brought into a regime of dynamic multi-stability, thus giving it a second function without additional manufacturing cost, without significant additional bulk and / or for relatively low energy consumption.

[0049] As illustrated on the figure 4The excitation signal can be modulated in many ways, including classic frequency modulation and / or amplitude modulation. More specifically, frequency modulation of the excitation signal can be performed at a specific modulation frequency δf to induce changes in the state of the resonator in its dynamic multi-stability regime from one of the two potential wells to the other, and vice versa, as illustrated by the potential curves surmounted on the... figure 4 the initials FM for "frequency modulation". Alternatively or in addition, the amplitude modulation 120 of the excitation signal can be performed at a modulation frequency δf determined to induce changes of state of the resonator 2 from its monostable regime to its dynamic multi-stability regime, and vice versa, as illustrated by the potential curves 112 surmounted on the figure 4the initials AM for "amplitude modulation". Note here that the at least temporary maintenance of resonator 2 in the dynamic multi-stability regime can be considered in particular in light of this possibility that the resonator has to visit its monostable regime, especially when the modulation 120 includes an amplitude modulation 122.

[0050] To express the above in an alternative and / or complementary way, it is possible to consider that the excitation device 11 of the resonator 2 is configured to: modulate 120 in frequency 121 the excitation signal with a modulation frequency δf determined to bring the resonant physical component alternately from one state to another among two states close to the two states of least potential of the resonator 2 when it is in said dynamic bistability regime, and / or modulate 120 in amplitude 122 the excitation signal with a modulation frequency δf determined to bring the resonator 2 alternately from a state close to its monostable state to one or the other among two states close to the two states of least potential of the resonator 2 when it is in said dynamic bistability regime.

[0051] Preferably, these transitions of resonator 2 between the aforementioned states are sufficiently rapid so that resonator 2 does not remain for a significant time in a state close to the same lower potential state. This significant time depends on the excitation signal, for example, its voltage and / or its frequency. Sufficiently rapid transitions of resonator 2 between the aforementioned states are ensured by applying to resonator 2 a modulated excitation signal 101 having a modulation frequency δf preferably greater than, but potentially substantially equal to, the ratio f0 / Q of the resonance frequency f0 of resonator 2 by its quality factor Q. The parameterization of this significant time may also need to be adapted according to the sampling parameters of the analog signal 102.Sampling parameters include sampling frequency or sampling levels, depending on the sampling method used, which is known to a person skilled in the art.

[0052] We can see, in particular on the figure 4 that the dynamic multi-stability regime, or dynamic bi-stability as illustrated in the example, of resonator 2 is associated with a continuous and limited frequency range 111. In this example, note that the frequency f of the excitation signal is preferably determined to bring resonator 2 into a sub-regime of the dynamic bi-stability regime, this sub-regime being associated with a first half, or even a first third, of the frequency range associated with the dynamic bi-stability regime of resonator 2.

[0053] Steps 110 and 120 of the process for generating 100 true random numbers are illustrated in particular on the figure 6Although these steps are illustrated there, and described above, as successive, note that they are not necessarily so. Taken in combination, they consist of applying a modulated excitation signal 101 to the resonator 2.

[0054] It is this possible combination that is symbolized by the fact that steps 110 and 120 are represented on the figure 6 in the same box.

[0055] By exploiting the capacity of a resonator 2, such as the aforementioned beam, to generate, at its output, an analog signal 102 representing the changes in amplitude and / or phase of vibration of the resonator 2, it is then possible to transform this analog signal 102 into a sequence of true random numbers. The steps of the process 100 relating to this transformation are described below, particularly with reference to Figures 5 And 6 .

[0056] To transform the analog signal 102 from the resonator 2 into a sequence of true random numbers, an analog-to-digital converter 12 is planned to be used to convert 140 the analog signal 102 into a digital signal 104. This conversion 140 is preferably carried out so that the digital signal 104 is representative of the random and high-amplitude aspects of the analog signal 102. For this, it suffices for a person skilled in the art to choose the parameters of the conversion 140 in an ad hoc manner, and in particular the sampling parameters of the analog signal 102. The sampling of the analog signal 102 can be carried out according to a determined sampling frequency fs, or by sampling steps chosen in particular as a function of the peak voltage of the excitation signal and the modulation frequency δf with which the excitation signal is modulated 120.

[0057] Note that most micro / nano-electromechanical systems already perform the conversion, into a binary digital version, of the analog signal from their resonator, using an analog-to-digital converter. The conversion 140 according to the method of the invention can be carried out: by the converter 12 already provided in the micro / nano-electromechanical system 1 considered or by a converter 12 specific to an excitation system 10 according to the first aspect of the invention which would be added to the architecture of a micro / nano-electromechanical system 1 whether the latter already exists or is in design.

[0058] Once the analog signal 102 has been converted 140 into a digital signal 104 also representative of the chaotic behavior of the resonator 2, it is expected that a digital processing device 13, such as a processor, will be configured to generate 150, from this digital signal 104, the sequence of true random numbers.

[0059] Note that most micro / nano-electromechanical systems already include such a digital processing device 13. Thus, the digital processing 150 according to the method 100 of the invention can: be carried out by the processing device 13 already equipping the micro / nano-electromechanical system 1 considered or be a processing device 13 specific to an excitation system 10 according to the first aspect of the invention which would be added to the architecture of a micro / nano-electromechanical system 1 whether the latter already exists or is in design.

[0060] As illustrated on the figure 6The method 100 according to the third aspect of the invention may further comprise a step consisting of demodulating 135 the analog signal 102 at the frequency f of the excitation signal. This step ensures that the demodulated signal contains only the information related to the effect of the modulation 120 of the excitation signal. In other words, the signal thus demodulated carries only the information representing the changes in amplitude and / or phase of vibration of the resonator 2. It is understood that, although optional, this demodulation step is of considerable interest in that it simplifies and / or increases the efficiency of the subsequent step of generating 150 the sequence of true random numbers, the latter being carried out, in effect, on the basis of only the most useful information.

[0061] It should be noted that the demodulation device 14 allows for the implementation of step 135 of process 100, particularly according to its embodiment illustrated on the figure 6 can : consist of a device already equipping the micro / nano-electromechanical system 1 considered or be a device specific to an excitation system 10 according to the first aspect of the invention which would be added to the architecture of a micro / nano-electromechanical system 1 whether the latter already exists or is in design.

[0062] As mentioned above, the analog signal 102 from the resonator 2 excited by the modulated excitation signal 101 can be directly or indirectly representative of the chaotic behavior of the resonator 2. Therefore, the analog signal 102 can be a first analog signal directly representative of the changes in amplitude and / or phase of vibration of the resonator 2. In this case, the demodulation 135 of the analog signal 102 as introduced above includes, for example, a comparison of the first analog signal with the excitation signal to deduce, as an analog signal indirectly representative of the changes in amplitude and / or phase of vibration of the resonator 2, a second analog signal representative of a change in amplitude of the first analog signal and / or a change in phase between the first analog signal and the excitation signal.

[0063] With reference to the figure 5An analog signal 1021 representing the changes in vibration amplitude of the resonant physical component 2 and an analog signal 1022 representing the phase changes of the resonator 2 can be derived from the acquisition step 130 of the analog signal 102 from the resonator 2, and in particular from the aforementioned demodulation step 135. The conversion step 140 then comprises the conversion of each of these two analog signals into a corresponding digital signal 1041, 1042.

[0064] More specifically, each analog signal 1021, 1022 is converted 140 into a succession of values ​​141 each coded on a number N of bits, equal to eight in the example illustrated by the figure 5 , the generation 150 of the binary sequence of true random numbers can include the generation, for each analog signal 1021, 1022, of a series of bits 1041, 1042 which can be illustrated in the form of a square wave signal.

[0065] With reference to the figure 5 , each series of bits 1041, 1042 can be generated 154 based solely on the n least significant bits of each value 141. On the figure 5 , only the 3 least significant bits of each value 141 are used to generate the bit series 1041 and 1042. The process according to this latter characteristic is particularly advantageous when the chaotic behavior of resonator 2 is not sufficient to amplify the noise so significantly that all the bits of each value 141 would be representative of it.

[0066] Still referring to the figure 5, two series of bits 1041 and 1042 being obtained for the two analog signals 1021, 1022, the generation 150 of the binary sequence of true random numbers can further include a logical operation 156, for example by the "exclusive OR" operator, between the two series of bits 1041 and 1042, to obtain the series of bit blocks 1043 whose random properties may be more advantageous.

[0067] The generation of 150 of the binary sequence of true random numbers can then include the cutting (not shown) of this series of 1043 bit blocks into a sequence of bit blocks on the basis of each of which a true random number can be generated 150.

[0068] A microelectromechanical system comprising a resonator 2 in the form of a disk with a submillimeter diameter and a thickness of approximately 10 microns, and whose transduction is piezoelectric, was used to demonstrate the feasibility of the present invention in its various aspects. The microelectromechanical system was placed under vacuum, and more particularly at a pressure of less than 1 millibar. Its resonant frequency f₀ is approximately 71.5 kHz, and it has a quality factor Q of 1100 and a nonlinearity coefficient α of 40 kHz / V₂. This type of resonator 2 is generally used as a generator and detector of acoustic waves. The peak voltage V₀ of the excitation signal applied to the resonator 2 is between 0.1 V and 10 V; a peak voltage of 5 V is commonly used.The excitation frequency f of the excitation signal is approximately equal to the resonance frequency f₀ of resonator 2. Using such an excitation signal, resonator 2, considered here, is brought into a so-called Duffing regime. Hysteresis is then generated over a frequency range 111 with an extent approximately equal to αV₀². To give resonator 2 chaotic behavior, the modulation frequency δf of the excitation signal is determined both by the extent of the frequency range 111 and by the bandwidth f₀ / Q of resonator 2. The value of the modulation frequency δf can vary, particularly due to its dependence on the extent of the frequency range 111 and the bandwidth f₀ / Q of resonator 2, depending on whether the peak voltage V₀, the excitation frequency f, and / or the resonance frequency f₀ are modulated.The modulation frequency δf values ​​to be used can be determined numerically or extrapolated from a known resonator 2 by normalizing it. The resulting analog signal 102 is demodulated at the excitation frequency f. This demodulated signal is then sampled at a sampling frequency dependent on the modulation frequency δf. The sampling frequency is preferably at least 10 times higher than the modulation frequency δf. For example, the modulation frequency can vary from 50 Hz to 5 kHz, and the sampling frequency can vary from 500 samples per second to 50,000 samples per second. The conversion 140 was performed with a precision of 64 bits, reduced to a precision of 8 bits to simulate an 8-bit analog-to-digital converter at the output of resonator 2.Each value of the digital signal 104 is therefore encoded on 8 bits, of which only the n least significant bits, typically the 3 least significant bits, were retained. A random binary sequence was thus generated 150 which satisfies 13 of the 15 reference tests known under the reference NIST 800-22, with a sampling rate of approximately 10 kbits / sec.

[0069] The invention is not limited to the embodiments described above and extends to all embodiments covered by the claims.

[0070] For example, the demodulation step 135 can also be carried out after the conversion 140 of the analog signal 102, on the digital signal resulting from the conversion 140.

[0071] For example, only one of the analog signals 1021 and 1022 is sufficient to generate a sequence of true random numbers. In this case, the logical operation is not performed, and the cutting step (not shown) consists of cutting one of the two bit sets 1041 and 1042.

[0072] For example, the excitation device 11 of the excitation system 10 intended to be integrated into a microelectromechanical system 1 comprising a resonator 2 for its use in the generation 150 of a sequence of true random numbers from said analog signal 102 may only play the role of modulation 120 of the excitation signal, the latter being generated by one or more components already equipping the microelectromechanical system 1.

[0073] For example, the resonance frequency f0 and quality factor Q values ​​given above are each widely adjustable within a range of available values, approximately 200 Hz to 10 GHz for the resonance frequency f0 and approximately 10 to 106 for the quality factor Q, without affecting the feasibility of the invention. The excitation force applied to resonator 2 and the non-linearity of resonator 2's behavior induced by this excitation force can vary from the values ​​indicated above to obtain a system equivalent to that studied to demonstrate the feasibility of the invention. Similarly, the initial conditions of resonator 2 can vary; for example, resonator 2 can be placed under a pressure of 1 bar.In addition, the sampling rate depends on the parameters of the resonator 2 considered; it can easily vary between 1 bit / sec and 1 Mbits / sec depending on the resonance frequency f 0, the quality factor Q and the extent of the frequency domain 111.

Claims

1. A system (10) for exciting a resonant physical component (2), the system (10) comprising an excitation device (11) configured to: - Excite (110) the resonant physical component (2) with a determined excitation signal to set the resonant physical component (2) into a dynamic multi-stability regime, and - Modulate (120) the excitation signal, so that the resonant physical component (2) has a chaotic behaviour and that an analog signal (102) originating from the resonant physical component (2) is representative of the chaotic behaviour of the resonant physical component (2), the excitation system (10) having no feedback loop.

2. The excitation system (10) according to the preceding claim, to be integrated into a micro-electromechanical system (1) comprising a resonant physical component (2) for use thereof in generating (150) a sequence of true random numbers from said analog signal (102).

3. The excitation system (10) according to any one of the preceding claims, further comprising a demodulation device (14) configured to implement either one of the following steps of: - before converting (140) the analog signal (102), demodulating (135) the analog signal (102) at the frequency f of the excitation signal, and - after converting (140) the analog signal (102), demodulating the digital signal at the frequency f of the excitation signal.

4. A chaotic physical true random number generator (1) comprising: - A resonant physical component (2), - An analog-to-digital converter (12) configured to convert an analog signal (102) originating from the resonant physical component (2) into a digital signal (104) representative of the analog signal, - A digital processing device (13) configured to generate a sequence of true random numbers from said digital signal (104), characterised in that the generator (1) further comprises an excitation device (11) of the resonant physical component (2) configured to: - Excite (110) the resonant physical component (2) with a determined excitation signal to set the resonant physical component (2) into a dynamic multi-stability regime, and - modulate (120) the excitation signal, so that the resonant physical component (2) has a chaotic behaviour and that the analog signal (102) to be converted is representative of the chaotic behaviour of the resonant physical component (2), the excitation device (11) having no feedback loop.

5. The generator (1) according to the preceding claim, wherein the analog signal (102) to be converted is representative of the changes in amplitude and / or phase of vibration of the resonant physical component (2) excited by the excitation signal (101) modulated.

6. The generator (1) according to any one of the preceding two claims, wherein said dynamic multi-stability regime is a so-called Duffing non-linear dynamic bistability regime.

7. The generator (1) according to any one of the preceding three claims, wherein said excitation signal has a peak voltage of between 0.01 and 10V and a frequency f equal to the resonance frequency f0 of the resonant physical component (2) within 20%.

8. The generator (1) according to any one of the preceding four claims, wherein said modulated excitation signal (101) has a modulation frequency δf higher than the ratio f0 / Q of the resonance frequency f0 of the resonant physical component (2) to its quality factor Q.

9. The generator (1) according to any one of the preceding five claims, wherein the resonant physical component (2) comprises a micro / nano-resonator, such as a double-embedded micro / nano-beam.

10. A method for generating (100) true random numbers comprising the following steps of: - Exciting (110) a resonant physical component (2) with a determined excitation signal to set the resonant physical component (2) into a dynamic multi-stability regime, - Modulating (120) the excitation signal, so that the resonant physical component (2) has a chaotic behaviour, The excitation (110) and modulation (120) steps being implemented by an excitation device (11) having no feedback loop, - Acquiring (130) an analog signal (102), originating from the resonant physical component (2) and representative of the chaotic behaviour of the resonant physical component (2), - Converting (140) the analog signal (2) into a digital signal (104) representative of the analog signal (102) acquired, then - Generating (150) a sequence of true random numbers from said digital signal (104).

11. The method (100) according to the preceding claim, wherein the excitation signal is parameterised to bring the resonant physical component (2) into a so-called Duffing non-linear dynamic bistability regime.

12. The method (100) according to any one of the preceding two claims, wherein, the dynamic multi-stability regime of the resonant physical component (2) being associated with a continuous, limited frequency domain (111), the frequency f of the excitation signal is determined to bring the resonant physical component (2) into a sub-regime of the dynamic multi-stability regime, said sub-regime being associated with a first half, and possibly a first third, of the frequency domain associated with the dynamic multi-stability regime of the resonant physical component (2).

13. The method (100) according to any one of the preceding three claims, wherein the excitation signal is modulated (120) with a modulation frequency δf higher than the ratio f0 / Q of the resonance frequency f0 of the resonant physical component (2) to its quality factor Q.

14. A computer program product comprising instructions, which when performed by at least one processor, executes at least the steps of the true random number generation method (100) according to any one of claims 10 to 13.

15. A micro-electromechanical system (1) comprising a resonant physical component (2), an analog-to-digital converter (12) and a digital processing device (13), characterised in that it further comprises an excitation device (9) configured to excite the resonant physical component (2) so as to form a chaotic physical true random number generator (1) according to any one of claims 4 to 9.