Chaotic physical true random number generators and related methods

Abstract

The present invention relates in particular to a chaotic physical true random number generator and an associated generation method. The generator 1 comprises a resonator 2, an analog-to-digital converter 12 configured to convert an analog signal 102 emitted by the resonator into a digital signal 104, a digital processing device 13 configured to generate a sequence of true random numbers based on the digital signal 104, and a device 11 for exciting the resonator, the device being configured to: i. excite the resonator with a determined excitation signal to set the resonator in a dynamic multistable mode; and ii. modulate the excitation signal, whereby the resonating physical component has chaotic behavior and the analog signal represents the chaotic behavior of the resonator. Advantages in terms of simplicity of implementation, bulk, and / or manufacturing costs for producing the physical true random number generator are thus realized.

Description

[Technical Field]

[0001] The present invention relates to the field of devices and methods for generating true random numbers. More specifically, according to two of its aspects, the present invention relates to chaotic physical true random number generators and related generation methods. For example, the generation of true random numbers is essential for modern cryptography to generate keys that enable secure communications. [Background technology]

[0002] It is known to rely on inherently random physical processes to obtain sequences of truly random numbers. Because the amplitude of the associated signals can be low, amplification may be necessary before converting the signals into sequences of truly random numbers. The search for sources of amplified randomness that result in such random digital sequences remains an ongoing problem.

[0003] The physical generation of truly random numbers is based on such inherently random physical processes. In particular: - 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," IEEE Journal of Solid-State Circuits, vol. 47, no. 11, pp. 2807-2821, November 2012], or - It is known to utilize various physical phenomena, including clock frequency fluctuations [Fischer V. et al., (2003), "True Random Number Generator Embedded in Reconfigurable Hardware. In: Kaliski BS, Koc. K., Paar C. (eds) Cryptography 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 in electrical circuits, but also on resonators that make up devices belonging to other fields.

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

[0006] Micro / nanoelectromechanical systems (M / NEMS) are another example of resonant bias. Some of the resonant components of M / NEMS utilize their mechanical properties, allowing the direct conversion of mechanical motion into electrical signals. These components are ubiquitous in modern technology, and are used as sensors, particularly in the form of accelerometers, gyrometers, or magnetometers [Tanaka, M., (2007), "An industrial and applied review of new MEMS devices features", Microelectronic Engineering, 84 (5-8), pp. 1341-1344]. Some of the various intrinsic properties of these resonators are sources of randomness, - Thermomechanical noise [TB Gabrielson et al., "Mechanical-thermal noise in micromachined acoustic and vibration sensors," IEEE Transactions on Electron Devices, vol. 40, no. 5, pp. 903-909, May 1993, doi: 10.1109 / 16.210197], and - This includes noise at 1 / f of the resonant frequency of the resonator [M. Sansa et al., Frequency fluctuations in Silicon nanoresonators, Nat. Nanotechnol. 11, 552-558, (2016)].

[0007] Due to the inherent nonlinearity of these resonators, it is possible to set them into a chaotic mode [Y.C. Wang et al., "Chaos in MEMS, parameter estimation and its potential application," IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 45, no. 10, pp. 1013-1020, October 1998].

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

[0009] Furthermore, there are oscillatory devices. Such devices are described, for example, in an article by Ghosh Dia et al. entitled "Generation & control of chaos in a single loop optoelectronic oscillator" published in the journal Optik. These devices cannot be compared to the resonant devices introduced above. Indeed, oscillatory devices generally have closed loops, respond to well-defined constraints, and their physical properties are fundamentally different from those of resonant devices. In particular, oscillators "influence themselves" to the extent that their circuits form closed circuits, while resonant devices or resonators do not have feedback loops. [Prior art documents] [Non-patent literature]

[0010] [Non-Patent Document 1] 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", IEEE Journal of Solid-State Circuits, vol. 47, no. 11, pp. 2807-2821, November 2012 [Non-patent document 2] Ficher V. et al.,(2003),"True Random Number Generator Embedded in Reconfigurable Hardware. In: Kaliski BS, Koc. K., Paar C. (eds) Cryptography Hardware and Embedded Systems - CHES 2002.",Lecture Notes in Computer Science,vol 2523,Springer, Berlin, Heidelberg [Non-patent document 3] Uchida, A., Amano, K., Inoue, M., Hirano, K., Naito, S., Someya, H., … and Yoshimura, K., (2008), "Fast physical random bit generation with chaotic semiconductor lasers", Nature Photonics, 2(12), 728 [Non-patent document 4] Tanaka, M., (2007), "An industrial and applied review of new MEMS devices features", Microelectronic engineering, 84(5-8), pp. 1341-1344. [Non-Patent Document 5] TB Gabrielson et al., "Mechanical-thermal noise in micromachined acoustic and vibration sensors", IEEE Transactions on Electron Devices, vol. 40, no. 5, pp. 903-909, May 1993, doi: 10.1109 / 16.210197 [Non-patent document 6] M. Sansa et al.,Frequency fluctuations in Silicon nanoresonators,Nat. Nanotechnol. 11,552-558,(2016) [Non-Patent Document 7] YC Wang et al., "Chaos in MEMS, parameter estimation and its potential application", IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 45, no. 10, pp. 1013-1020, October 1998. [Non-patent document 8] ME Yalcin et al., "True random bit generation from a double-scroll attractor", IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 51, no. 7, pp. 1395-1404, July 2004 [Non-Patent Document 9] Ghosh Dia et al.,"Generation & control of chaos in a single loop optoelectronic oscillator",Optik Summary of the Invention [Problem to be solved by the invention]

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

[0012] More specifically, it is an object of the present invention to provide a chaotic physical true random number generator that enables advantages in terms of simplicity of implementation, size, and / or manufacturing costs compared to existing chaotic physical true random number generators.

[0013] Another object of the present invention is to provide a physical true random number generator that is compatible with many existing technologies, particularly CMOS technology (an abbreviation for "Complementary Metal Oxide Semiconductor"), preferably without additional bulk or manufacturing costs.

[0014] Other objects, features, and advantages of the present invention will become apparent upon reading the following description and its accompanying drawings. It will be understood that other advantages may be incorporated into the present invention. [Means for solving the problem]

[0015] To this end, according to a first aspect of the present invention, there is provided an excitation system for a resonant physical component, comprising an excitation device, the excitation device comprising: - exciting the resonating physical component with the determined excitation signal to at least temporarily place and possibly maintain the resonating physical component in a dynamic multistable mode; - modulating the excitation signal, Thereby, a system is provided in which the resonant physical component has chaotic behavior and the analog signal emitted from the resonant physical component is configured to directly or indirectly represent the chaotic behavior of the resonant physical component.

[0016] Furthermore, the excitation system does not have a feedback loop.

[0017] It should be noted that modulation of the excitation signal may involve phase and / or frequency and / or amplitude modulation by the modulating signal.

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

[0019] The generator further comprises a device for exciting the resonant physical component, the device comprising: - exciting the resonating physical component with the determined excitation signal to at least temporarily place and possibly maintain the resonating physical component in a dynamic multistable mode; The excitation signal is configured to be modulated.

[0020] The excitation device does not have a feedback loop.

[0021] Thus, the resonant physical component has chaotic behavior, and the converted analog signal directly or indirectly represents the chaotic behavior of the resonant physical component.

[0022] By applying an excitation signal to the resonant physical component, the resonant physical component can be set into a dynamic multistable mode, and further modulating the excitation signal can cause the behavior of the resonant physical component to become chaotic. The noise source inherent to the resonant physical component is then amplified, e.g., exponentially, resulting in high-amplitude noise. The analog signal emitted from the resonant physical component then represents the chaotic behavior of the resonant physical component. This allows for the generation of a sequence of truly random numbers using the chaotic behavior. Considering that, barring exceptions, any microelectromechanical system comprises a physical component capable of serving as a resonator for a generator according to the second aspect of the present invention, it should be appreciated that the excitation system according to the first aspect of the present invention allows for advantages in terms of simplicity of implementation, size, and / or manufacturing costs for producing a chaotic physical true random number generator, particularly compared to generators based on oscillatory devices (with feedback loops). It should further be appreciated that the excitation system according to the first aspect of the present invention is compatible with many existing technologies, particularly CMOS technology, potentially using a small size or limiting additional manufacturing costs.

[0023] According to a third aspect of the present invention, there is provided a method of true random number generation, in particular implementing the chaotic physical generator presented herein, comprising the steps of: - exciting the resonating physical component with the determined excitation signal to at least temporarily set and possibly maintain the resonating physical component in a dynamic multistable mode; - modulating the excitation signal, whereby the resonant physical component has chaotic behavior; The excitation step and the modulation step are performed by an excitation device that does not have a feedback loop, and the true random number generation method comprises: - acquiring analog signals, and more particularly electrical signals, emanating from a resonant physical component and directly or indirectly representing the chaotic behavior of the resonant physical component; - converting the analog signal into a digital signal representative of the acquired analog signal; - generating a sequence of true random numbers based on said digital signal.

[0024] According to a fourth aspect of the present invention, there is provided a computer program comprising instructions which, when executed by at least one processor, perform at least the steps of the true random number generation method as presented herein.

[0025] According to a fifth aspect of the present invention, there is provided a microelectromechanical system comprising a resonant physical component, an analog-to-digital converter, and a digital processing device, and further comprising an excitation device configured to excite the resonant physical component to form a chaotic physical true random number generator as presented herein.

[0026] In some cases, the excitation system according to the first aspect of the invention may have at least one of the following features:

[0027] For example, the excitation system is adapted to be incorporated into a micro-electromechanical system comprising a resonant physical component for use in generating a sequence of truly random numbers based on said analog signal.

[0028] For example, the excitation system - an analog-to-digital converter configured to convert an analog signal emitted from the resonating physical component into a digital signal representative of the analog signal; a digital processing device configured to generate a sequence of truly random numbers based on the digital signal.

[0029] For example, the excitation system - further comprising a demodulation device, i. demodulating the analog signal at the frequency f of the excitation signal before converting the analog signal; ii. converting the analog signal and then demodulating it to a digital signal at the frequency f of the excitation signal.

[0030] Optionally, the chaotic physical generator according to the second aspect of the present invention may further comprise at least one of the following features:

[0031] For example, the converted analog signal represents the change in amplitude and / or phase of vibration of a resonant physical component excited by a modulated excitation signal.

[0032] Preferably, the generator does not have any type of excitation device configured to buckle a resonating physical component.

[0033] For example, the dynamic multistable mode is a nonlinear dynamic bistable mode called a Duffing mode.

[0034] For example, the excitation signal has a peak voltage between 0.01V and 10V, preferably between 0.1V and 5V, and a frequency f equal to the resonant frequency f0 of the resonating physical component within 20%, preferably within 10%.

[0035] For example, said modulated excitation signal has a modulation frequency δf that is preferably higher than, and possibly substantially equal to, the ratio f0 / Q of the resonant frequency f0 of the resonant physical component to the quality factor Q.

[0036] For example, the resonant physical component comprises a micro / nano resonator, such as a double embedded micro / nano beam.

[0037] For example, the generator Further comprising a demodulation device, the demodulation device comprising: demodulating the analog signal at a frequency f of the excitation signal before converting the analog signal; The method is configured to perform either one of the steps of converting the analog signal and then demodulating the digital signal at the frequency f of the excitation signal.

[0038] Optionally, the production method according to the third aspect of the invention may further comprise at least one of the following features:

[0039] For example, the method may further include, after the step of obtaining the analog signal and before the step of converting the analog signal, amplifying the obtained analog signal.

[0040] For example, the excitation signal is parameterized to set, and possibly at least temporarily maintain, a resonant physical component in a nonlinear dynamic bistable mode known as a Duffing mode.

[0041] For example, a dynamic multistable mode of a resonant physical component is associated with a continuous and limited frequency range, and the frequency f of the excitation signal is determined to set the resonant physical component into a sub-mode of the dynamic multistable mode, said sub-mode being associated with the first half, or possibly the first third, of the frequency range associated with the dynamic multistable mode of the resonant physical component.

[0042] For example, exciting the resonant physical component includes applying, as an excitation signal, at the terminals of the resonant physical component, a peak voltage between 0.01 V and 10 V, preferably between 0.1 V and 5 V, and a frequency f equal to within 20%, preferably within 10%, the resonant frequency f of the resonant physical component.

[0043] For example, the potential of a resonant physical component that is a dynamic multistable mode has two distinct wells. - the frequency modulation of the excitation signal has a determined amplitude δf for causing a change from one of the two potential wells to the other and from the other to the one in the state of the resonant physical component, which is a dynamic multistable mode; and / or - the amplitude modulation of the excitation signal has a determined amplitude δf for causing a change in the state of the resonant physical component from a monostable mode to a dynamic multistable mode of the resonant physical component, and for causing a change in the state of the resonant physical component from a dynamic multistable mode to a monostable mode of the resonant physical component.

[0044] For example, the excitation signal is modulated with a modulation frequency δf that is preferably higher than, and possibly substantially equal to, the ratio f0 / Q of the resonant frequency f0 of the resonating physical component to the quality factor Q.

[0045] For example, this method: - demodulating the analog signal at the frequency f of the excitation signal before converting the analog signal; and - after converting the analog signal, demodulating the digital signal at the frequency f of the excitation signal.

[0046] For example, the analog signal may be a first analog signal that directly represents a change in amplitude and / or phase of vibration of the resonant physical component, and demodulating the analog signal prior to converting the analog signal may include comparing the first analog signal with an excitation signal to infer a second analog signal that represents a change in amplitude of the first analog signal and / or a change in phase between the first analog signal and the excitation signal as an analog signal that indirectly represents a change in amplitude and / or phase of vibration of the resonant physical component.

[0047] For example, converting the analog signal includes sampling the analog signal at a sampling frequency or step selected according to the voltage of the excitation signal and the modulation frequency δf for modulating the excitation signal. Preferably, the sampling frequency is at least 10 times higher than the modulation frequency δf.

[0048] For example, an analog signal representing a change in amplitude of vibration of the resonating physical component and an analog signal representing a change in phase of the resonating physical component are acquired during the acquiring step, and the converting step includes converting each of the two analog signals into a digital signal.

[0049] For example, an analog signal is converted into a series of values, each value coded over N bits, for example strictly greater than 3 and generally equal to 8, and the generation of a binary sequence of truly random numbers involves generating a series of bits that can be represented in the form of a square signal, then dividing this series of bits into a sequence of bit blocks and generating a sequence of truly random numbers based on each bit block.

[0050] For example, the sequence of bits is generated according to only the n bits with the lowest weights of each encoded value of the sequence of values.

[0051] For example, generating a random binary sequence involves generating a series of bits that can be represented in the form of a square signal for each of the two acquired analog signals, and then performing a logical operation, for example using an "exclusive OR" operator, between the two generated series of bits to obtain a series of bit blocks that are divided.

[0052] By a parameter "substantially equal" to a given value, it is understood that the parameter is equal to the given value within a 10% tolerance, or even a 5% tolerance.

[0053] The aims, objects, features and advantages of the present invention will be better understood upon reading the detailed description of one embodiment of the present invention, one embodiment of which is illustrated by the accompanying drawings, in which: [Brief explanation of the drawings]

[0054] [Figure 1]1 is an electronic circuit diagram of an embodiment of the second and fifth aspects of the present invention, including an electronic circuit diagram of an embodiment of the first aspect of the present invention; [Figure 2] 1 is a graph illustrating switching from a monostable mode (lower curve) in a dynamic bistable mode called Duffing mode (upper curve). [Figure 3A] 1 illustrates the so-called Duffing dynamic bistable mode by a graph of the amplitude of vibration of a resonating physical component as a function of the excitation frequency applied to the resonating physical component, with the arrows indicating a schematic guide representing switching from high amplitude to low amplitude within a hysteresis. [Figure 3B] 1 is a diagram illustrating the two-well potential of a resonating physical component according to the amplitude of its oscillation, the arrows showing a schematic guide representing the switching from high amplitude to low amplitude within the hysteresis. [Figure 4] 1 is a graph illustrating possible behavior of a resonant physical component when excited by a modulated excitation signal. [Figure 5] 10 is a graph illustrating an embodiment of converting each of two analog signals representing the amplitude and phase of a possible resonant physical component into a digital signal on which a sequence of truly random numbers is generated. [Figure 6] 4 is a flowchart of an embodiment of a generating method according to the third aspect of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0055] The drawings are provided by way of example and are not intended to limit the scope of the present invention. The drawings constitute schematic diagrams intended to facilitate understanding of the present invention and are not necessarily to scale with respect to actual applications. In particular, Figures 1, 4, and 5 do not necessarily represent actual applications.

[0056] The generation of truly random numbers is essential for modern cryptography. In particular, generating truly random numbers makes it possible to generate keys that ensure secure communications. To obtain a sequence of truly random numbers, the present invention proposes to rely on an inherently random physical process. Various aspects of the present invention will now be described with reference to the accompanying figures, which include an excitation system 10 for a resonant physical component 2, a chaotic physical true random number generator 1 that may form at least part of a microelectromechanical system, and a true random number generation method 100 associated with the generator 1.

[0057] In the following, the term "resonator" will sometimes be used to refer to the resonating physical component 2 described above.

[0058] More specifically, the present invention proposes to utilize the ability of most resonant physical components to exhibit chaotic behavior when excited ad hoc. Such resonant physical components already exist in many technologies, and the present invention, as a first technical advantage, shows how the aforementioned functionality of resonators already implemented in many devices, particularly electronic devices, can be used to generate truly random numbers by diverting such components from their primary use. Thus, upon reading the following, those skilled in the art will understand that the invention according to some aspects of the present invention provides an existing device, particularly an electronic device, equipped with a resonator 2 with the possibility of adding some on-board components, particularly a device 11 for exciting the resonator 2, thereby diverting the resonator 2 from its primary use to generate a sequence of truly random numbers (150). Thus, the proposed solution allows most existing devices, particularly electronic devices, to be endowed with additional functionality that can be directly used by such same device and / or other devices connected to it, in particular to enable these devices to communicate securely. Upon reading the following, those skilled in the art will understand that this additional functionality also provides: - significant bulk issues, especially for devices that are intended to become increasingly miniaturized, and / or It will be appreciated that this is possible without incurring significant additional manufacturing costs.

[0059] It is also possible to quickly and inexpensively modify already manufactured devices, especially electronic devices, to embed a device that allows the additional functionality of a true random number generator 1. FIG. 1 can be considered as showing an electronic circuit diagram including an excitation system 10 added to the terminals of a resonator 2 constituting an existing microelectromechanical system. Switching means, represented here in the form of a switch, can then be provided, configured to functionally connect the excitation system 10 to the terminals of the resonator 2 and to disconnect the latter from these general-purpose inputs and outputs. The excitation system 10 as shown in FIG. 1 comprises an excitation device 11, whose input data include parameters for the excitation 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 will be explained below. However, as will become clear from the following description, the excitation system 10 only comprises the excitation device 11 in its most generalized version and other components of the excitation system 10 as shown in FIG. 1 that may belong to an existing microelectromechanical system 1.

[0060] Of the existing technologies that are suitable for implementing the present invention, it is noted that CMOS technology in particular is directly suitable for this implementation.

[0061] A micro / nanoelectromechanical system can be defined as a micro / nano-sized device that converts mechanical processes into the electrical domain and vice versa. A micro / nanoelectromechanical system comprising at least one resonant physical component 2 has the particularity of having a seismic mass that allows, through its resonant physical component, to convert mechanical energy into electrical energy or vice versa, obtaining, for example, an energy recovery device or a force sensor depending on the chosen geometry.

[0062] A resonant micro / nanoelectromechanical system is primarily characterized by its resonant frequency f0 and its quality factor Q.

[0063] One of the geometries that can be used in the context of the present invention consists, for example, of a double-embedded micro / nano beam. Indeed, the equilibrium position of the beam as a resonator 2 can switch between different interesting states, especially when the beam is set in a dynamic multistable mode. Reaching such a mode is made possible by applying a sufficiently high reciprocating force to the beam. In all cases, applying such a force can be considered as applying 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 that case, according to the example under consideration, the position of the beam receiving such an excitation signal can resonate between states close to and / or around the interesting states.

[0064] Depending on the characteristics of the resonator 2, the excitation signal may consist of an alternating voltage applied to the terminals of the resonator 2. In that case, the excitation signal can be characterized according to parameters of said alternating voltage, such as its peak voltage, hereinafter also referred to as "excitation voltage", and its frequency f, hereinafter also referred to as "excitation frequency". For example, the excitation signal has a peak voltage between 0.01 V and 10 V, preferably between 0.1 V and 5 V, and a frequency f equal to the resonant frequency f0 of the resonator 2 with an error of 20%, preferably 10%. It should be noted that the excitation signal is not limited to electrical signals, but also extends to, for example, mechanical signals that the resonator 2 is inherently sensitive to.

[0065] More generally, any resonant physical component 2 can be excited (110) with a determined excitation signal to place the resonant physical component 2 in a dynamic multistable mode, and possibly maintain it at least temporarily. Referring to FIG. 2, which shows a graph including several curves derived from a digital simulation, it can be seen that the response of the amplitude R (mV) of the resonator 2's fluctuations as a function of the frequency of the low excitation signal (lower curve) takes the form of a Lorentzian function, indicating the linear behavior of the resonator 2 when subjected to low excitation power. By increasing the excitation power applied to the resonator 2, the response of the resonator 2 gradually becomes distorted and asymmetrical (see upper curve). The response of the resonator 2 becomes nonlinear, thereby modifying the resonant frequency f0 of the resonator 2. A frequency hysteresis is then observed, which in the illustrated case represents a dynamic bistable mode, and more specifically, a nonlinear dynamic bistable mode referred to as the Duffing mode.

[0066] The upper curve shown in the graph of FIG. 2 is also shown in the graph of FIG. 3A. In FIG. 3A, the reference symbols "1" and "2" have been added to roughly indicate different noteworthy states that the resonator 2 can substantially assume for a given excitation frequency. Correspondingly, the reference symbols "1" and "2" are also shown in FIG. 3B, which illustrates the change in the potential of the resonator 2 as a function of the amplitude R (mV) of the resonator 2's fluctuations for the given excitation frequency. Thus, the curves shown on the graph of FIG. 3B indicate that each of the noteworthy states, designated "1" and "2," corresponds to a state of lowest potential, i.e., a potential well. Therefore, the noteworthy states correspond to preferred stable states, and the resonator 2 has a higher probability of assuming a state around each of these stable states for the given excitation frequency. Thus, the graphs of FIGS. 3A and 3B show a bifurcation between two stable states of hysteresis. Thus, at high amplitudes of the excitation signal, the hysteresis opens in the frequency domain and tends to either state "1" with high amplitude fluctuations or state "2" with low amplitude fluctuations. These two states are directly comparable to the case of a buckled resonator, the difference being that the states of the buckled resonator are static (e.g., they correspond to high and low positions of the buckled beam), whereas the two states of the resonator 2 configured in the dynamic multistable mode according to the present invention are dynamic (these states correspond to high and low amplitudes of vibration of the resonator 2). As in the case of a buckled resonator, it is possible to impose chaotic behavior on the resonator 2 configured in the dynamic multistable mode according to the present invention by modulating the excitation force applied to the resonator 2.

[0067] It should be noted herein that the excitation signal according to the present invention is not intended to buckle the resonator 2. Preferably, the excitation system 10 according to the first aspect of the present invention and / or the chaotic physical generator 1 according to the second aspect of the present invention do not have any type of excitation device configured to buckle the resonator 2. Therefore, implementations of the present invention do not require the fabrication of buckled structures, which are complex in terms of manufacturing and generally require high energy consumption to operate. In contrast, implementations of the present invention advantageously allow almost any micro / nano resonator 2 to exhibit nonlinear behavior at high excitation amplitudes without specific requirements regarding its shape, the materials used, or the transduction technique implemented by the resonator 2. In particular, implementations of the present invention can be implemented on most micro / nano resonators 2 when they are present and therefore can be implemented without the need to modify the resonator's fabrication process.

[0068] If the excitation signal is further modulated (120) in frequency 121 and / or amplitude 122, as shown in FIG. 4, the resonator 2 can adopt complex, non-periodic, chaotic dynamics. The resulting chaotic behavior is characterized by, among other things, the unrepeatable and inability to predict the medium- and long-term state of the resonator 2. While all chaotic modes are deterministic—i.e., the resonator 2's response can be predicted if the mathematical equations governing its behavior are fully known—very slight variations in the initial conditions, such as the ambient temperature or pressure, can rapidly produce significant changes in behavior, similar to the butterfly effect. Therefore, the behavior of any resonator 2 is always subject to noise, regardless of how weak the noise. The resonator 2's response to the modulated excitation signal 101, especially with each new application of the same modulated excitation signal 101, can exhibit such rapid changes, making the medium- and long-term dynamic behavior of the resonator 2 unpredictable. Thus, a micro / nanoelectromechanical system 1 in which at least one resonator 2 is set in a dynamic multistable mode and the resonator is further inhibited to adopt chaotic behavior allows the generation of a random high amplitude analog signal 102 at the output of the resonator 2. Herein, said changes in the behavior of the resonator 2 can be observed on the phase of the analog signal only, on the amplitude of the analog signal 102 only, 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 encompassed by the expression "changes in the amplitude and / or phase of the oscillations of the resonator 2" used below.

[0069] It should be noted here that, as already implicitly introduced above, a certain time from the start of application of the modulated excitation signal 101 may be required for the chaotic behavior of the resonator 2 to emerge. More specifically, this time may be required to determine the change in the response of the resonator 2 to the modulated excitation signal 101 as a function of the initial conditions experienced by the resonator 2. Those skilled in the art can evaluate this time a priori or heuristically, for example by checking the randomness of the sequence of generated numbers 150, and in particular by implementing standard tests known under the names reference NIST 800-22 or AIS 31. Maintaining the resonator 2 in a dynamic multistable mode, at least temporarily, can be considered in particular in light of this time required for the analog signal 102 derived from the resonator 2 to express its chaotic behavior.

[0070] Notwithstanding the initial application of resonator 2, e.g., as an accelerometer or energy recovery device, in accordance with the present invention, resonator 2 may also be used to provide a second function, such as generating an analog signal 102 that directly or indirectly represents the chaotic behavior of resonator 2 configured in a dynamic multistable mode, without additional manufacturing costs, without significant additional bulk, and / or with relatively low energy consumption.

[0071] As shown in FIG. 4 , the excitation signal can be modulated in many ways, including conventional frequency 121 modulation and / or amplitude 122 modulation. More specifically, frequency 121 modulation 120 of the excitation signal can be performed at a determined modulation frequency δf to cause a change in the state of the resonator 2 from one of two potential wells to the other and vice versa, which are dynamic multistable modes of the resonator 2, as shown by the potential curve 112 labeled above in FIG. 4 with the acronym FM for “frequency modulation.” Alternatively or supplementally, amplitude 122 modulation 120 of the excitation signal can be performed at a determined modulation frequency δf to cause a change in the state of the resonator 2 from the monostable mode of the resonator 2 to the dynamic multistable mode of the resonator 2 and vice versa, as shown by the potential curve 112 labeled above in FIG. 4 with the acronym AM for “amplitude modulation.” It should be noted that maintaining the resonator 2 in a dynamic multistable mode, at least temporarily, can be considered in light of this possibility that the resonator may need to go into a monostable mode, particularly when the modulation 120 includes an amplitude modulation 122.

[0072] Alternatively and / or complementary to the above, the excitation device 11 of the resonator 2 may be - frequency modulating (120) the excitation signal 121 with the determined modulation frequency δf when the resonator 2 is in said dynamic bistable mode, to set the resonating physical component alternately from one of two states close to the two states of the lowest potential of the resonator 2 to another; and / or It is possible to consider that when the resonator 2 is in said dynamic bistable mode, an excitation signal is amplitude-modulated (120) using the determined modulation frequency δf in order to set the resonator 2 alternately from a state close to the monostable state of the resonator 2 to one of two states close to the two states of lower potential of the resonator 2.

[0073] Preferably, these transitions of the resonator 2 between the different states mentioned above are rapid enough that the resonator 2 does not remain in a state close to the same state at a lower potential for a long time. The long time depends on the excitation signal, for example its voltage and / or its frequency. A sufficiently rapid transition of the resonator 2 between the different states mentioned above is ensured by applying to the resonator 2 a modulated excitation signal 101 having a modulation frequency δf, preferably higher than, or possibly substantially equal to, the ratio f / Q of the resonant frequency f of the resonator 2 to its quality factor Q. The parameterization of the long time can also be adapted according to the sampling parameters of the analog signal 102. Among the sampling parameters, reference may be made to the sampling frequency or the sampling step, depending on the sampling method used, as known to those skilled in the art.

[0074] 4, it will be appreciated that the dynamic multistable or dynamic bistable mode of the illustrated example of resonator 2 is associated with a continuous and limited frequency range 111. Note that in this example, the frequency f of the excitation signal preferably determines a frequency that places resonator 2 in a submode of the dynamic bistable mode, with this submode being associated with the first half, or possibly the first third, of the frequency range associated with the dynamic bistable mode of resonator 2.

[0075] Steps 110 and 120 of the true random number generation method 100 are particularly shown in Figure 6. Note that although these steps are shown in Figure 6 and described above as consecutive steps, they are not necessarily consecutive. Taken in combination, these steps consist of applying a modulated excitation signal 101 onto the resonator 2.

[0076] This possible combination is symbolized by steps 110 and 120 being represented in the same box in FIG.

[0077] The ability of a resonator 2, such as the beam described above, can thus be utilized to generate an analog signal 102 at the output of the resonator 2 that represents the changes in amplitude and / or phase of the oscillations of the resonator 2, thereby converting this analog signal 102 into a sequence of truly random numbers. The steps of a method 100 relating to this conversion are described below with particular reference to Figures 5 and 6.

[0078] In order to convert the analog signal 102 emitted by the resonator 2 into a sequence of truly random numbers, the analog signal 102 is converted 140 into a digital signal 104 using an analog-to-digital converter 12. Preferably, this conversion 140 is performed in such a way that the digital signal 104 represents the random and high-amplitude aspects of the analog signal 102. For this purpose, the skilled person only has to ad hoc select the parameters of the conversion 140, and in particular the parameters of the sampling of the analog signal 102. The sampling of the analog signal 102 is performed at a determined sampling frequency f s or by a selected sampling step, in particular according to the peak voltage of the excitation signal and the modulation frequency δf for modulating 120 the excitation signal.

[0079] It should be noted that in most micro / nanoelectromechanical systems, an analog-to-digital converter already ensures the conversion of the analog signal emitted by its resonator into a digital binary version. The conversion 140 according to the method of the present invention can be performed by: - it may be performed by a converter 12 already provided in the micro / nanoelectromechanical system 1 under consideration, or - This may be done by a converter 12 specific to the excitation system 10 according to the first aspect of the invention that is added to the architecture of the micro / nano electromechanical system 1, whether the micro / nano electromechanical system 1 already exists or is being designed.

[0080] After the analog signal 102 is converted into a digital signal 104 that also represents the chaotic behavior of the resonator 2, a digital processing device 13, such as a processor, is configured to generate 150 a sequence of truly random numbers based on the digital signal 104.

[0081] It should be noted that most micro / nanoelectromechanical systems already include such a digital processing device 13. Therefore, the digital processing 150 according to the method 100 of the present invention can be implemented as follows: - may be performed by a processing device 13 that already configures the micro / nanoelectromechanical system 1 under consideration, or - may be performed by a processing device 13 specific to the excitation system 10 according to the first aspect of the invention that is added to the architecture of the micro / nanoelectromechanical system 1, whether the micro / nanoelectromechanical system 1 already exists or is being designed.

[0082] 6, the 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 makes it possible to have in the demodulated signal only information about the effect of the modulation 120 of the excitation signal. In other words, the signal thus demodulated carries only information representative of the changes in amplitude and / or phase of the oscillations of the resonator 2. It should be understood that this demodulation step, although optional, is obviously interesting in that it makes it possible to simplify and / or improve the efficiency of the subsequent step of generating (150) a sequence of truly random numbers, so that this step is in fact carried out only on the basis of the information most useful for this step.

[0083] A demodulation device 14 making it possible to carry out step 135 of the method 100 according to the embodiment shown in particular in FIG. 6, - may consist of devices that already constitute the micro / nanoelectromechanical system under consideration, or - It should be noted that the device may be specific to the excitation system 10 according to the first aspect of the invention to be added to the architecture of the micro / nano electromechanical system 1, whether the micro / nano electromechanical system 1 already exists or is being designed.

[0084] As mentioned above, the analog signal 102 emitted from the resonator 2 excited by the modulated excitation signal 101 may directly or indirectly represent the chaotic behavior of the resonator 2. Thereby, the analog signal 102 may be a first analog signal directly representing the changes in amplitude and / or phase of the oscillations of the resonator 2. In this case, the demodulation 135 of the analog signal 102 as introduced above comprises, for example, comparing the first analog signal with the excitation signal to infer a second analog signal representing the changes in amplitude of the first analog signal and / or the changes in phase between the first analog signal and the excitation signal as an analog signal indirectly representing the changes in amplitude and / or phase of the oscillations of the resonator 2.

[0085] 5, an analog signal 1021 representing the change in amplitude of the vibration of the resonating physical component 2 and an analog signal 1022 representing the change in phase of the resonator 2 can be obtained from an acquisition step 130 of the analog signal 102 emitted by the resonator 2, in particular the demodulation step 135 mentioned above. A conversion step 140 then comprises converting each of the two analog signals into a corresponding digital signal 1041, 1042.

[0086] More specifically, each analog signal 1021, 1022 is converted into a sequence of values ​​141, each value being coded over N bits, equal to 8 in the example shown by FIG. 5, and the generation 150 of a truly random binary sequence may comprise generating, for each analog signal 1021, 1022, a sequence of bits 1041, 1042 that can be represented in the form of a square signal.

[0087] 5, each series of bits 1041, 1042 can be generated 154 according to only the n bits with low weights of each value 141. In FIG. 5, the series of bits 1041 and 1042 are generated using only the 3 bits with low weights of each value 141. This method according to the above features is particularly advantageous when the chaotic behavior of the resonator 2 is not sufficient to significantly amplify the noise such that all bits of each value 141 exhibit chaotic behavior.

[0088] Still referring to FIG. 5, two runs of bits 1041 and 1042 are obtained for two analog signals 1021, 1022, and the generation 150 of the truly random binary sequence may further include obtaining a series of bit blocks whose random properties may be more prevalent, for example by a logical operation 156 using an “exclusive OR” operator between the two runs of bits.

[0089] In that case, generating 150 a binary sequence of truly random numbers may involve dividing this series of bit blocks 1043 into a sequence of bit blocks (not shown), and generating 150 a truly random number based on each bit block.

[0090] The feasibility of the invention in its different aspects has been demonstrated using a microelectromechanical system with a resonator 2 in the form of a disk with a diameter of less than a millimeter and a thickness substantially equal to 10 microns, the transduction of which is carried out piezoelectrically. The microelectromechanical system has been placed under vacuum, more particularly under a pressure of less than 1 mbar. The resonant frequency f0 of the microelectromechanical system is substantially equal to 71.5 kHz, the quality factor Q is equal to 1100 and the nonlinear coefficient α is 40 kHz / V. 2This type of resonator 2 is typically 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, with a peak voltage equal to 5 V being predominantly used. The excitation frequency f of the excitation signal is substantially equal to the resonance frequency f0 of the resonator 2. By using such an excitation signal, the resonator 2 considered here is set in the so-called Duffing mode. In that case, the range α.V0 is substantially equal to 2 Hysteresis is generated over a frequency range 111 equal to . To impart chaotic behavior to the resonator 2, the modulation frequency δf of the excitation signal is determined by both the range of the frequency range 111 and the bandwidth f / Q of the resonator 2. The value of the modulation frequency δf can vary depending on whether the peak voltage V, the excitation frequency f, and / or the resonance frequency f are modulated (120), particularly due to the dependence of the modulation frequency δf on the range of the frequency range 111 and the bandwidth f / Q of the resonator 2. The value of the modulation frequency δf used can be determined numerically or estimated from the resonator 2 by normalizing the resonator 2 to an already known value. The analog signal 102 thus obtained is demodulated at the excitation frequency f. Sampling of this demodulated signal is performed at a sampling frequency that depends on the modulation frequency δf. Preferably, the sampling frequency is at least 10 times higher than the modulation frequency δf. For example, the modulation frequency can be in the range of 50 Hz to 5 kHz, and the sampling frequency can be in the range of 500 samples per second to 50,000 samples per second. The conversion 140 was performed with 64-bit precision, which was then reduced to 8-bit precision to simulate an 8-bit analog-to-digital converter at the output of the resonator 2. Thus, each value of the digital signal 104 was coded over 8 bits, retaining only the lowest n bits, typically the lowest 3 bits. In this way, a random binary sequence was generated (150) that complied with 13 of the 15 standard tests known as "reference NIST 800-22." The sampling rate was approximately equal to 10 kbits / s.

[0091] The present invention is not limited to the above-described embodiments, but includes all embodiments covered by the claims.

[0092] For example, the demodulation step 135 may be performed after conversion 140 of the analog signal 102 on the digital signal derived from the conversion 140 .

[0093] For example, only one of analog signal 1021 and analog signal 1022 may be sufficient to generate 150 a sequence of truly random numbers. In this case, logical operation 156 is not performed, and the division step (not shown) consists of dividing corresponding ones of the two series of bits 1041 and 1042.

[0094] For example, an excitation device 11 of an excitation system 10 adapted to be incorporated into a microelectromechanical system 1 having a resonator 2 for use in generating a sequence 150 of truly random numbers based on said analog signal 102 may act only as a means for modulating 120 an excitation signal, the excitation signal being generated by one or more components already constituting the microelectromechanical system 1.

[0095] For example, each of the values ​​of the resonant frequency f0 and quality factor Q given above may be substantially within a set of available values, i.e., within about 200 Hz to 10 GHz for the resonant frequency f0 and about 10 to 10 for the quality factor Q. 6The excitation force applied to the resonator 2 and the resulting nonlinearity of the resonator 2's behavior can be varied relative to the values ​​shown above to find a system equivalent to the one considered and demonstrate the feasibility of the present invention. Similarly, the initial conditions under which the resonator 2 is placed can be varied; for example, the resonator 2 can be placed under a pressure equal to 1 bar. Furthermore, the sampling rate depends on the parameters of the resonator 2 considered and can be easily varied between 1 bit / s and 1 Mbit / s depending on the resonant frequency f0, the quality factor Q, and the range of the frequency domain 111. [Explanation of symbols]

[0096] 1 Chaotic physical true random number generator, microelectromechanical system 2. Resonant physical components, resonators, micro / nano resonators 10. Excitation System 11 Excitation Device 12 Analog-to-Digital Converter 13 Digital Processing Devices 14 Demodulation Device 100 True Random Number Generation Methods 101 modulated excitation signal 102 Random high amplitude analog signal 104 Analog Signal 110 Excitation 111 Frequency Domain 112 Potential Curve 120 modulation 121 Frequency 122 Amplitude 130 obtained 135 Demodulation 140 Conversions 141 Value 150 Digital Processing, Generation 154 generation 156 Logical Operations 1021 Analog Signal 1022 analog signal 1041,1042 digital signal, bits 1043 bit blocks

Claims

1. An excitation system (10) for a resonant physical component (2), comprising: The excitation device (11) includes: exciting (110) the resonant physical component (2) with the determined excitation signal to place the resonant physical component (2) in a dynamic multistable mode; modulating (120) the excitation signal; An excitation system (10) configured such that the resonant physical component (2) has chaotic behavior and an analog signal (102) emitted from the resonant physical component (2) represents the chaotic behavior of the resonant physical component (2), wherein the excitation system (10) does not have a feedback loop.

2. 10. The excitation system (10) of claim 1, which is incorporated into a microelectromechanical system (1) having a resonant physical component (2) for use in generating a sequence of truly random numbers (150) based on the analog signal (102).

3. an analog-to-digital converter (12) configured to convert the analog signal (102) emitted from the resonating physical component (2) into a digital signal (104) representative of the analog signal (102); a digital processing device (13) configured to generate a sequence of truly random numbers based on said digital signal (104); 3. The excitation system (10) of claim 1 or 2, further comprising:

4. Further comprising a demodulation device (14), wherein the demodulation device (14) demodulating (135) the analog signal (102) at the frequency f of the excitation signal before converting (140) the analog signal (102); After converting (140) the analog signal (102), demodulating it into a digital signal at the frequency f of the excitation signal.

4. The excitation system (10) of claim 3, configured to perform one of:

5. A chaotic physical true random number generator (1), Resonant physical components (2); an analog-to-digital converter (12) configured to convert an analog signal (102) emitted from the resonating physical component (2) into a digital signal (104) representative of the analog signal; a digital processing device (13) configured to generate a sequence of truly random numbers based on said digital signal (104); Equipped with The generator (1) further comprises an excitation device (11) for the resonant physical component (2), the excitation device (11) comprising: exciting (110) the resonant physical component (2) with the determined excitation signal to place the resonant physical component (2) in a dynamic multistable mode; modulating (120) the excitation signal; A generator (1) configured such that the resonant physical component (2) has chaotic behavior and the converted analog signal (102) represents the chaotic behavior of the resonant physical component (2), and wherein the excitation device (11) does not have a feedback loop.

6. 6. The generator (1) of claim 5, wherein the converted analog signal (102) represents a change in amplitude and / or phase of vibration of the resonant physical component (2) excited by the modulated excitation signal (101).

7. 7. The generator (1) according to claim 5 or 6, wherein the dynamic multistable mode is a nonlinear dynamic bistable mode called a Duffing mode.

8. The excitation signal has a peak voltage between 0.01 V and 10 V and a frequency f that is equal to the resonant frequency f of the resonant physical component (2). 0 8. A generator (1) according to any one of claims 5 to 7, which is equal to within 20% of

9. The modulated excitation signal (101) is modulated at the resonant frequency f of the resonant physical component (2). 0 The ratio of f to the quality factor Q 0 9. A generator (1) according to any one of claims 5 to 8, having a modulation frequency δf higher than / Q.

10. The generator (1) according to any one of claims 5 to 9, wherein the resonant physical component (2) comprises a micro / nano resonator such as a double embedded micro / nano beam.

11. Further comprising a demodulation device (14), wherein the demodulation device (14) demodulating (135) the analog signal (102) at the frequency f of the excitation signal before converting (140) the analog signal (102); After converting (140) the analog signal (102), demodulating the digital signal at the frequency f of the excitation signal.

11. A generator (1) according to any one of claims 5 to 10, configured to implement either

12. 1. A computer-implemented method for generating truly random numbers (100), comprising: exciting (110) a resonant physical component (2) with the determined excitation signal to place said resonant physical component (2) in a dynamic multistable mode; modulating (120) the excitation signal, whereby the resonant physical component (2) has chaotic behavior; Including, The excitation (110) and modulation (120) steps are performed by an excitation device (11) without a feedback loop, and the method comprises: acquiring (130) an analog signal (102) emanating from the resonant physical component (2) and representing the chaotic behavior of the resonant physical component (2); converting (140) the analog signal (102) into a digital signal (104) representative of the acquired analog signal (102); generating (150) a sequence of truly random numbers based on said digital signal (104); The method (100) further comprises:

13. 13. The method (100) of claim 12, wherein the excitation signal is parameterized to set the resonant physical component (2) in a nonlinear dynamic bistable mode called a Duffing mode.

14. 14. The method (100) of claim 12 or 13, wherein the dynamic multistable mode of the resonant physical component (2) is associated with a continuous and limited frequency range (111), and the frequency f of the excitation signal is determined to set the resonant physical component (2) into a sub-mode of the dynamic multistable mode, the sub-mode being associated with the first half, or possibly the first third, of the frequency range associated with the dynamic multistable mode of the resonant physical component (2).

15. The excitation (110) of the resonant physical component (2) is performed by providing an excitation signal at the terminals of the resonant physical component (2) with a peak voltage between 0.01 V and 10 V and a resonant frequency f of the resonant physical component (2). 0 15. The method (100) of any one of claims 12 to 14, comprising applying a frequency f equal to within 20% of

16. the potential (112) of the resonant physical component (2) of the dynamic multistable mode has two distinct wells; the frequency (121) modulation (120) of the excitation signal has an amplitude δf determined to cause a change from one of the two potential wells to the other and from the other to one in the state of the resonant physical component (2) in the dynamic multistable mode; and / or 16. The method (100) of any one of claims 12 to 15, wherein the amplitude (122) modulation (120) of the excitation signal (22) has a determined amplitude δf for causing a change in the state of the resonant physical component (2) from a monostable mode to a dynamic multistable mode of the resonant physical component and for causing a change in the state of the resonant physical component (2) from a dynamic multistable mode to a monostable mode of the resonant physical component.

17. The excitation signal is at the resonant frequency f of the resonant physical component (2). 0 The ratio of f to the quality factor Q 0 17. The method (100) according to any one of claims 12 to 16, wherein the signal is modulated (120) with a modulation frequency δf higher than / Q.

18. demodulating (135) the analog signal (102) at the frequency f of the excitation signal before converting (140) the analog signal (102); After converting (140) the analog signal (102), demodulating the digital signal at the frequency f of the excitation signal.

18. The method (100) of any one of claims 12 to 17, further comprising:

19. 20. The method of claim 18, wherein the analog signal is a first analog signal directly representative of a change in amplitude and / or phase of the vibration of the resonant physical component, and wherein the demodulation of the analog signal prior to converting comprises comparing the first analog signal with the excitation signal to infer 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 as an analog signal indirectly representative of a change in amplitude and / or phase of the vibration of the resonant physical component.

20. 20. The method (100) of any one of claims 12 to 19, wherein the converting (140) of the analog signal (102) comprises sampling the analog signal (102) at a sampling frequency or sampling step selected according to a voltage of the excitation signal and a modulation frequency δf for modulating (120) the excitation signal.

21. 21. The method (100) of any one of claims 12 to 20, wherein an analog signal (1021) representing a change in amplitude of vibration of the resonant physical component (2) and an analog signal (1022) representing a change in phase of the resonant physical component (2) are acquired during the acquiring step (130), and wherein the converting step (140) comprises converting each of the two analog signals (1021 and 1022) into a digital signal (1041, 1042).

22. 22. The method (100) of claim 20 or 21, wherein the analog signal (102) is converted into a sequence of values ​​(141) each coded over N bits, and wherein generating (150) a binary sequence of truly random numbers comprises generating a sequence of bits that can be represented in the form of a square signal (1043), then dividing the sequence of bits into a sequence of bit blocks, and generating (150) a truly random number of the sequence based on each bit block.

23. 23. The method (100) of claim 22, wherein the series of bits is generated according to only the n bits with the lowest weights of each encoded value (141) of the series of values.

24. 24. The method (100) according to claim 22 or 23, wherein the generation (150) of the binary sequence of random numbers comprises generating (154) for each of the two acquired analog signals (1021, 1022) a series of bits that can be represented in the form of a square signal (1041, 1042), thus a double series of bits, and then performing a logical operation (156) between the generated double series of bits to obtain the series of bit blocks (1043) to be divided.

25. 25. A computer program comprising instructions for performing at least the steps of the method (100) of any one of claims 12 to 24 when executed by at least one processor.

26. 12. A microelectromechanical system (1) comprising a resonant physical component (2), an analog-to-digital converter (12), and a digital processing device (13), further comprising an excitation device (11) configured to excite the resonant physical component (2) to form a generator (1) according to any one of claims 5 to 11.

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