Method and system for authenticating an object by using a physically unclonable function

Abstract

The invention relates to a method for authenticating an object (12) by a physically unclonable function, carried out using a transducer implanted on the object, which includes: recording (302) a measurement, using the transducer, of a spectrum (SP) of a physical quantity characteristic of the object (12) in response to excitations produced in a predetermined frequency band; generating (300, 304, 306, 308, 310) a digital signature (SIG) to identify the object (12) on the basis of this measurement; and authenticating (312) the object (12) by comparing this signature (SIG) with a reference signature (SIGREF). The step of generating (300, 304, 306, 308, 310) the signature (SIG) includes previously obtaining (300) at least one resonant frequency mode (F1, … FN) of the object (12), transforming (304) the measured spectrum (SP) by processing that is dependent on this resonant frequency mode, and generating (306, 308, 310) the signature (SIG) from the transformed spectrum (SP').

Description

Method and system for authenticating an object using a physically unclonable function

[0001] The present invention relates to a method for authenticating an object using a physically non-clonable function implemented with a transducer implanted on the object. It also relates to a corresponding computer system and program.

[0002] The invention applies more particularly to an authentication method comprising the following steps: recording a measurement, obtained using the transducer, of a spectrum of a physical quantity characteristic of the object in response to a plurality of excitations produced in a predetermined frequency band; generating a digital signature for identifying the object from this measurement; authenticating the object by comparing the digital identification signature generated from the measurement with a reference digital identification signature.

[0003] Such a method for authenticating an object using a physically non-clonable function is described, for example, in the article by Sandborn et al., entitled "Towards secure cyber-physical information association for parts," published in the Journal of Manufacturing Systems 59 (2021), pages 27-41. In this paper, an electromechanical impedance frequency spectrum is obtained by implanting a piezoelectric transducer on a manufactured industrial part and by electromechanically exciting the part in a predetermined frequency band. It is demonstrated that this spectrum can indeed be considered the result of a physically non-clonable function due to its strong correlation with the specific physical characteristics of the manufactured part, in terms of material, dimensions, and density, and of the piezoelectric transducer, in terms of material, dimensions, and positioning on the part.It can therefore theoretically be used to generate a digital signature for identifying and authenticating the manufactured part.

[0004] However, every electromechanical impedance measurement is subject to noise, related to the part itself, the transducer, and the environment in which the measurement is performed. This results in noise such that, even when exploiting tolerance parameters of a fuzzy extractor, the authentication generally does not produce truly satisfactory results. Therefore, it is ultimately not robust.

[0005] It may therefore be desirable to provide a method of authenticating an object, by using a physically non-clonable function implemented with a transducer implanted on the object, which makes it possible to overcome at least some of the aforementioned problems and constraints.

[0006] A method for authenticating an object is therefore proposed using a physically non-clonable function implemented with a transducer implanted on the object, comprising the following steps: recording a measurement, obtained with the transducer, of a spectrum of a physical quantity characteristic of the object in response to a plurality of excitations produced in a predetermined frequency band; generating a digital signature for identifying the object from this measurement; authenticating the object by comparing the digital signature generated from the measurement with a reference digital signature; in which the generation of the digital signature for identifying the object includes the following steps: prior acquisition of at least one frequency mode of resonance of the object in the predetermined frequency band;transformation of the measured spectrum by a processing dependent on said at least one resonance frequency mode obtained; and generation of the digital identification signature from the transformed spectrum.

[0007] Thus, by exploiting prior knowledge of one or more frequency mode(s) of resonance of the object to be identified in the measured spectrum to transform this spectrum accordingly, it becomes possible to generate a digital identification signature that is much more relevant and much less sensitive to measurement noise, so that the authentication of the object is significantly improved.

[0008] Optionally, the processing performed on the measured spectrum includes filtering adapted to at least one previously obtained resonance frequency mode, so as to obtain smoothing of the spectrum out of a neighborhood of said at least one obtained resonance frequency mode and an accentuation of each peak of the spectrum present in said neighborhood of each obtained resonance frequency mode, in particular using an averaging filter or a Butterworth filter of order N, N being an integer greater than or equal to 1.

[0009] Optionally, said at least one frequency mode of resonance of the object in the predetermined frequency band is obtained beforehand by: simulation carried out, using finite element method simulation software on a model of the object on which the transducer is implanted, in the predetermined frequency band; or measurement carried out on at least one reference object on which a reference transducer is implanted, in the predetermined frequency band.

[0010] Optionally, the comparison of the digital identification signature generated from the measurement with the reference digital identification signature is carried out by applying a fuzzy extractor with tolerance parameters.

[0011] Optionally also: tolerance values ​​for variations around each frequency mode of resonance of the object in the predetermined frequency band are obtained beforehand: by simulation carried out, using the finite element method simulation software on several models of the object on which the transducer is implanted, in the predetermined frequency band, by varying physical properties of the object relating to manufacturing or aging tolerances, or by measurements carried out on several reference objects on each of which a reference transducer is implanted, in the predetermined frequency band, by varying the said physical properties of the object relating to the said manufacturing or aging tolerances; and the previously obtained tolerance values ​​for variations are integrated into the tolerance parameters of the fuzzy extractor.

[0012] Optionally, the generation of the digital identification signature from the transformed spectrum also includes: frequency sampling of the transformed spectrum to select a predetermined number of identifying frequency values; quantification, for example hexadecimal, of each selected identifying frequency value; generation of the digital identification signature by combining the quantified identifying frequency values.

[0013] Optionally, a piezoelectric transducer is also implanted on the object to obtain an electromechanical impedance spectrum as a result of the physically non-clonable function.

[0014] Optionally, an object authentication method according to the present invention may also include a step of providing the reference identification digital signature, generated for the same object assumed to be under identical conditions of measurement and spectrum transformation, in the form of a token stored, transmitted and authenticated using a blockchain.

[0015] A system for authenticating an object is also proposed, using a physically non-clonable function implemented with a transducer implanted on the object, comprising: means for recording a measurement, obtained with the transducer, of a spectrum of a physical quantity characteristic of the object in response to a plurality of excitations produced in a predetermined frequency band; a computing unit for: generating a digital signature for identifying the object from this measurement, and authenticating the object by comparing the digital signature generated from the measurement with a reference digital signature for identifying the object; characterized in that: the recording means are adapted for recording at least one frequency mode of resonance of the object obtained previously in the predetermined frequency band;and the processing unit is programmed to: transform the measured spectrum by a processing dependent on said at least one previously obtained resonance frequency mode, and generate the digital identification signature from the transformed spectrum.

[0016] Also proposed is a computer program downloadable from a communication network and / or recorded on a computer-readable medium and / or executable by a processor, comprising instructions for executing the steps of a method for authenticating an object according to the present invention, when said program is executed by a computing unit of an object authentication system according to the present invention.

[0017] The invention will be better understood with the aid of the following description, given solely by way of example and made with reference to the accompanying drawings in which: 1 schematically represents the general structure of an object authentication system using a physically non-clonable function, according to one embodiment of the invention; 2 schematically represents the general structure of an object tracking installation comprising the authentication system; 3 illustrates the successive steps of an object tracking method, including, among other things, the steps of a method for authenticating this object using a physically non-clonable function, according to one embodiment of the invention; 4 illustrates an example of the effect of performing a spectrum transformation step of the method; 5 illustrates the effect of performing a sampling step on the processed spectrum, according to a first embodiment of this sampling.This illustrates the effect of performing the sampling step on the processed spectrum, according to a second embodiment of this sampling.

[0018] The authentication system 10 of an object 12 by the use of a physically non-clonable function carried out using a transducer 14 implanted on the object 12, as illustrated in the figure, mainly comprises a computer 16 and secondarily a device 18 for measuring the SP spectrum of a physical quantity characteristic of the object 12, as well as a simulator 20 of the object 12 with its implanted transducer 14.

[0019] The measuring device 18 is an electronic device capable of exciting the transducer 14 with electrical signals generated at multiple frequencies within a predetermined frequency band, thereby obtaining respective amplitude responses to form the SP spectrum of the physical quantity considered as a physically non-clonable function. As a non-limiting example, the transducer 14 may consist of a piezoelectric pellet fixed to the surface of the object 12, excitable by means of electrodes electrically connected to the measuring device 18 for measuring an electromechanical impedance spectrum characteristic of the object 12 within a predetermined frequency band, such as [100 Hz; 10,000 Hz], explored in 10 Hz steps.Alternatively, the transducer 14 could consist of an interdigitated capacitance sensor fixed to the surface of the object 12, excitable by means of electrodes electrically connected to the measuring device 18 for the measurement of an electromagnetic spectrum characteristic of the object 12. Other variants can be envisaged depending on the applications intended, using other transducers, for the measurement of spectra of other physical quantities characteristic of the object 12 as physically non-clonable functions.

[0020] The simulator 20 is, for example, a finite element method simulation software tool, in which a model 22 of the object 12 on which the transducer 14 is mounted can be stored. A simulation engine 24 takes this model 22 as input to provide, by simulation, at least one resonance frequency mode, in the form of at least one resonance frequency denoted F1, … F N, in the predetermined frequency band of the SP spectrum to be measured. Optionally, but advantageously, several models 22 of the object 12 on which the transducer 14 is mounted are stored in memory in the simulator 20, varying physical properties of the object 12, and possibly of the transducer 14, related to manufacturing or aging tolerances. All these models are provided as input to the simulation engine 24 to obtain values ​​ΔF1, … ΔF N tolerances for variations around each resonance frequency mode F1, … F N of object 12 in the predetermined frequency band.

[0021] Alternatively, the use of simulator 20 could be replaced by measurements performed on at least one reference object on which a reference transducer is implanted, in the predetermined frequency band, of said at least one resonance frequency mode F1, … F NAlternatively, several measurements can be performed on several reference objects, each equipped with a reference transducer, within the predetermined frequency band, by varying the physical properties of the object, and possibly of the transducer 14, related to the manufacturing or aging tolerances, to obtain the values ​​ΔF1, … ΔF N tolerances for variations around each resonance frequency mode F1, … F N of object 12 in the predetermined frequency band. This can be done using an electronic device similar to measuring device 18.

[0022] The computer 16 includes an interface 26 for receiving data necessary for its authentication of the object 12. Among this data, the interface 26 receives, in particular, the SP spectrum, provided by the measuring device 18, the resonance frequencies F1, … F Nof object 12 with transducer 14 in the predetermined frequency band, provided by simulator 20 or by reference measurements, as well as the values ​​ΔF1, … ΔF N tolerances for variations around these resonance frequencies F1, … F N taking into account the aforementioned manufacturing or aging tolerances, also provided by simulator 20 or by reference measurements. Interface 26 is further intended to receive a digital signature for GIS reference identification. REF specific to the assembly consisting of object 12 and its transducer 14. According to an optional but preferred variant of the present invention, this reference signature is received by interface 26 in the form of a storable, transmissible, and authenticable token (TOK). REF in a way known in itself by a blockchain.

[0023] The computer 16 can also have a completely conventional architecture with a processing unit 28 (for example, a processor) associated with at least one memory 30 (for example, RAM or other memory), possibly including a memory area 32 dedicated to storing data received via the interface 26 at the command of the processing unit 28. It can, for example, be implemented in a computing device such as a conventional computer comprising a processor associated with one or more memories for storing data files and computer programs whose instructions are intended to be executed by the processor. As illustrated in Figure 1, the computer 16 thus functionally comprises six computer programs 34, 36, 38, 40, 42, 44 or six functions of the same computer program.It should be noted that computer programs 34, 36, 38, 40, 42, and 44 are presented as distinct, but this distinction is purely functional. They could just as easily be grouped in any possible combination into one or more software programs. Their functions could also be at least partially microprogrammed or micro-wired into dedicated integrated circuits. Thus, as an alternative, the computer system implementing calculator 16 could be replaced by an electronic device composed solely of digital circuits (without a computer program) to perform the same functions. Also as an alternative, at least some of the aforementioned computer programs could be remote and accessible to calculator 16 via the Internet.In general, even if all the aforementioned software and memory components are presented as being gathered in the same computer 16, they could just as well be dispersed in separate hardware elements, or even far from each other, but interconnected in a network (data transmission bus, local network, wide area network, Internet, etc.).

[0024] The computer program 34 contains instructions which, when executed by the processing unit 28, perform a transformation of the measured spectrum SP by a process dependent on each resonance frequency F1, … F N stored in memory area 32. This processing includes, for example, filtering adapted to each resonance frequency F1, … F N , so as to obtain a smoothing of the SP spectrum outside a neighborhood of each resonance frequency F1, … F Nand an accentuation of each peak of the SP spectrum when it is present in this neighborhood, notably using an averaging filter adapted to each resonance frequency F1, … F N or a Butterworth filter of order N, where N is an integer greater than or equal to 1. The neighborhood of each resonance frequency F1, … F N can be defined as being directly correlated, or even equal, to each value ΔF1, … ΔF N of tolerances for variations. A transformed spectrum SP' is thus obtained.

[0025] As a non-limiting example, the following illustrates the result that such a transformation can give on an SP spectrum like the one shown on the left. Based on five resonance frequencies previously obtained independently of the SP spectrum measurement, ordered according to their expected amplitudes, the filtering transformation gives the transformed spectrum SP' shown on the right. It is noted that, while the SP spectrum exhibits a significant number of amplitude peaks, probably resulting from measurement noise, only five peaks remain after applying an averaging or low-pass filter adapted to the five resonance frequencies F1, … F5, denoted I1, I2, I3, I4, and I5 in the respective neighborhoods of the five resonance frequencies F1, … F5. That said, the five peaks I1, I2, I3, I4, and I5 are located at frequencies that are not necessarily equal to F1, F2, F3, F4, and F5.

[0026] Computer program 36 includes instructions which, when executed by processing unit 28, perform frequency sampling of the transformed spectrum SP' for the selection of a predetermined number of identifying frequency values.

[0027] According to a first embodiment of this sampling, Figure 1 illustrates sampling by regular frequency steps of the transformed spectrum SP'. In this case, only the sampled amplitudes need to be recorded as identifying frequency values, the corresponding frequencies being known. According to a second embodiment of this sampling, Figure 1 illustrates sampling by preserving only the peaks I1, I2, I3, I4, and I5 measurable in the transformed spectrum SP'. In this case, the sampled amplitudes I1, I2, I3, I4, and I5 must be recorded with their respective frequencies f1, f2, f3, f4, and f5, as identifying frequency values.

[0028] The computer program 38 contains instructions which, when executed by the processing unit 28, perform a quantization, for example hexadecimal, of each identifying frequency value selected by the sampling described above. Hexadecimal quantization consists of encoding each identifying frequency value as a sequence of hexadecimal values. Thus, in the first sampling embodiment, only the sampled amplitudes are quantized, while in the second sampling embodiment, the amplitudes of peaks I1, I2, I3, I4, and I5 are quantized along with their respective frequencies f1, f2, f3, f4, and f5.

[0029] Computer program 40 contains instructions which, when executed by processing unit 28, generate a digital GIS identification signature by combining quantified identifying frequency values. In a particularly simple but not limiting embodiment, the digital GIS identification signature can result from a concatenation of the quantified identifying frequency values. Other signature generation methods, more or less simple and within the grasp of a person skilled in the art, can also be considered.

[0030] Computer program 42 contains instructions which, when executed by processing unit 28, perform a comparison of the SIG digital identification signature with the SIG reference digital identification signature REFas mentioned above, it being understood that the latter was generated for the same assumed object 12, with the same assumed transducer 14, under comparable conditions of measurement and spectrum transformation. Optionally, but advantageously, the comparison of the SIG and SIG signatures REF is performed by applying a fuzzy extractor with the values ​​ΔF1, … ΔF N of variation tolerances as a basis for calculating its tolerance parameters, knowing that in the simplest terms these values ​​ΔF1, … ΔF N can constitute the tolerance parameters themselves. The operation of such a fuzzy extractor is known to those skilled in the art, so it will not be detailed. The originality of using this fuzzy extractor in the context of the present invention lies essentially in integrating the values ​​ΔF1, … ΔF N of tolerances of variations previously obtained in the tolerance parameters of the fuzzy extractor.

[0031] Finally, computer program 44 contains instructions which, when executed by processing unit 28, provide a result for the authentication of object 12 based on the comparison of the two signatures SIG and SIG REF : authentication is validated if the two signatures are deemed sufficiently similar by the fuzzy extractor, or authentication is not validated otherwise.

[0032] Such authentication by the use of a physically non-clonable function carried out using the transducer 14 implanted on the object 12 can more generally be part of a secure tracking of the object 12 implemented by an installation such as that of the.

[0033] At a controlled stage of its manufacture and / or distribution, the object 12 is subjected to measurement by a server 46, for example similar to the assembly consisting of the computer 16 and the measuring device 18, for the generation of the reference SIG identification digital signature REF This reference signature is generated using the same processing chain as that described previously for the SIG digital identification signature.

[0034] In addition to server 46 for generating the digital signature of reference identification GIS REF The installation of the provision includes a 48-block chain capable of making this SIG reference signature REF available in the form of a storable, transferable and authenticable token (TOK) REF in a way known in itself using the 48 blockchain.

[0035] The installation therefore also includes the authentication system 10, capable of extracting the reference SIG digital identification signature REF of the authenticable TOK token REF in a totally secure and authenticated manner thanks to the blockchain 48 to authenticate (by certificate 50) or not the object 12 at any time of its uncontrolled life course.

[0036] A method for tracking object 12, including among other things the steps of a method for authenticating this object by the use of a physically non-clonable function, will now be described with reference to the according to an embodiment of the invention implementing the installation of the and the authentication system 10 of the.

[0037] In a preliminary step 100, the simulator 20 determines, using the model 22, at least one frequency resonance mode of the object 12 with transducer 14, in the form of at least one resonance frequency denoted F1, … F N , in the predetermined frequency band for measuring the SP spectrum. It also optionally, but advantageously, determines the values ​​ΔF1, … ΔF by modeling manufacturing and / or aging tolerances. N tolerances for variations around each resonance frequency mode F1, … F N for object 12. As previously stated, simulator 20 can be replaced by measurements taken on at least one reference object for the execution of step 100.

[0038] In a step 200 independent of step 100, object 12 is subjected to a measurement by server 46 for the generation of the SIG reference identification digital signature REFAs previously stated, this generation of reference signature is carried out at a controlled stage of the manufacture and / or distribution of object 12 since it must then allow its authentication regardless of its subsequent path.

[0039] In a subsequent step 202, the GIS reference identification digital signature REF is processed by the 48 blockchain to obtain the storable, transferable and authenticable token (TOK). REF .

[0040] During a subsequent step 204, executed by the computer 16 at any point in the lifecycle of object 12 for its authentication, the reference SIG identification digital signature REF is extracted from the TOK token REF using blockchain 48.

[0041] The actual authentication process of object 12, which can be implemented by the authentication system 10 at any time during its lifecycle, will now be detailed.

[0042] During step 300, the interface 26 of the computer 16 receives the resonance frequency values ​​F1, … F N of object 12 with transducer 14 in the predetermined frequency band, provided by simulator 20 or by reference measurements, as well as the values ​​ΔF1, … ΔF N tolerances for variations around these resonance frequencies F1, … F N taking into account the manufacturing or aging tolerances of object 12, also provided by simulator 20 or by reference measurements. These values ​​are stored in memory area 32.

[0043] During a step 302, the measuring device 18 produces the SP spectrum in the predetermined frequency band and transmits it to the computer 16 which receives it via its interface 26 and stores it in memory area 32.

[0044] Then, during a step 304 carried out by the execution of the computer program 34 by the processing unit 28, the spectrum SP is transformed, as described previously and as illustrated by way of simple example by the, into the transformed spectrum SP'.

[0045] In a subsequent step 306 carried out by the execution of the computer program 36 by the processing unit 28, the transformed spectrum SP' is sampled for the selection of identifying frequency values, whether for example those of the or those of the.

[0046] In a subsequent step 308 carried out by the execution of the computer program 38 by the processing unit 28, the identifying frequency values ​​are quantized, for example each in the form of a sequence of hexadecimal values.

[0047] In a subsequent step 310 carried out by the execution of the computer program 40 by the processing unit 28, the digital identification SIG signature is generated by combining the quantified identifying frequency values.

[0048] In a subsequent step 312 carried out by the execution of the computer program 42 by the processing unit 28, the SIG digital identification signature is compared to the SIG reference digital identification signature REF As previously mentioned, this comparison is advantageously performed by applying a fuzzy extractor with values ​​ΔF1, … ΔF Nof tolerances of variations as tolerance parameters, or at least integrated in some way into these tolerance parameters.

[0049] Finally, by executing computer program 44 by processing unit 28, and based on the comparison of the two signatures SIG and SIG REF using the fuzzy extractor, object 12 is authenticated or not.

[0050] It is clear that an authentication system such as the one described above optimizes the use of a physically unclonable function, i.e., the spectrum of a physical quantity characteristic of the object within a predetermined frequency band. This is achieved by leveraging prior knowledge of one or more frequency modes of resonance of the object to be authenticated within that frequency band to construct its digital identification signature. Furthermore, when integrated into an object tracking system that uses a blockchain to authenticate the reference signature, the authentication is both robust and highly secure.

[0051] It should also be noted that the invention is not limited to the embodiments described above.

[0052] Thus, for example, even though a particularly simple SP to SP' spectrum transformation has been detailed, a person skilled in the art is capable of considering any well-known more complex processing that optimizes spectrum smoothing while accentuating its identifying peaks.

[0053] It will be more generally apparent to a person skilled in the art that various modifications can be made to the embodiments described above, in light of the instruction just disclosed to them. In the detailed presentation of the invention given previously, the terms used should not be interpreted as limiting the invention to the embodiments set forth in this description, but should be interpreted to include all equivalents that a person skilled in the art can foresee by applying their general knowledge to the implementation of the instruction just disclosed to them.

Claims

A method for authenticating an object (12) by using a physically non-clonable function implemented with a transducer (14) implanted on the object (12), comprising the following steps: prior acquisition (300) of at least one frequency mode (F1, … F N ) resonance of the object (12) in a predetermined frequency band; recording (302) of a measurement, obtained using the transducer (14), of a spectrum (SP) of a physical quantity characteristic of the object (12) in response to a plurality of excitations produced in the predetermined frequency band; generation (300, 304, 306, 308, 310) of a digital identification signature (GIS) of the object (12) from this measurement; authentication (312) of the object (12) by comparing the digital identification signature (GIS) generated from the measurement with a reference digital identification signature (GIS) REF); characterized in that the generation (300, 304, 306, 308, 310) of the digital identification signature (GIS) comprises the following steps: transformation (304) of the measured spectrum (SP) by a processing dependent on said at least one frequency resonance mode obtained (F1, … F N ); and generation (306, 308, 310) of the digital identification signature (GIS) from the transformed spectrum (SP'). A method for authenticating an object (12) according to claim 1, wherein the processing performed on the measured spectrum (SP) comprises filtering adapted to at least one previously obtained resonance frequency mode (F1, … F N ), so as to obtain a smoothing of the spectrum outside a neighborhood of said at least one resonance frequency mode obtained (F1, … F N ) and an accentuation of each peak of the spectrum present in said neighborhood of each frequency resonance mode obtained (F1, … F N), in particular using an averaging filter or a Butterworth filter of order N, where N is an integer greater than or equal to 1. Method for authenticating an object (12) according to claim 1 or 2, wherein said at least one frequency mode (F1, … F N ) of resonance of the object (12) in the predetermined frequency band is obtained beforehand by: simulation (100) carried out, using a finite element method simulation software (24) on a model (22) of the object (12) on which the transducer (14) is implanted, in the predetermined frequency band; or measurement carried out on at least one reference object on which a reference transducer is implanted, in the predetermined frequency band. A method for authenticating an object (12) according to any one of claims 1 to 3, wherein the comparison of the digital identification signature (GIS) generated from the measurement with the reference digital identification signature (GIS) REF ) is achieved by applying a fuzzy extractor with tolerance parameters. Method for authenticating an object (12) according to claims 3 and 4, wherein: tolerance values ​​for variations (ΔF1, … ΔF N ) around each frequency mode (F1, … F NThe resonance values ​​of the object (12) in the predetermined frequency band are obtained beforehand: by simulation (100) carried out using finite element method simulation software (24) on several models (22) of the object (12) on which the transducer (14) is implanted, in the predetermined frequency band, by varying physical properties of the object (12) related to manufacturing or aging tolerances; or by measurements carried out on several reference objects, each of which is implanted with a reference transducer, in the predetermined frequency band, by varying said physical properties of the object related to said manufacturing or aging tolerances; and the previously obtained variation tolerance values ​​(ΔF1, … ΔF N ) are integrated into the fuzzy extractor's tolerance parameters. A method for authenticating an object (12) according to any one of claims 1 to 5, wherein the generation (306, 308, 310) of the digital identification signature (GIS) from the transformed spectrum (SP') comprises: frequency sampling (306) of the transformed spectrum (SP') for the selection of a predetermined number of identifying frequency values; quantification (308), for example hexadecimal, of each selected identifying frequency value; generation of the digital identification signature (GIS) by combination (310) of the quantified identifying frequency values. Method for authenticating an object (12) according to any one of claims 1 to 6, wherein a piezoelectric transducer (14) is implanted on the object (12) for obtaining an electromechanical impedance spectrum (SP) as a result of the physically non-clonable function. A method for authenticating an object (12) according to any one of claims 1 to 7, comprising a step (202) of providing the reference identification digital signature (GIS) REF ), generated for the same object assumed to be under identical conditions of measurement and spectrum transformation, in the form of a token (TOK REF ) stored, transmitted and authenticated using a blockchain (48). System (10) for authenticating an object (12) by using a physically non-clonable function implemented with a transducer (14) implanted on the object (12), comprising: means (26, 28, 32) for recording a measurement, obtained with the transducer (14), of a spectrum (SP) of a physical quantity characteristic of the object (12) in response to a plurality of excitations produced in a predetermined frequency band, these recording means (26, 28, 32) being adapted for recording at least one frequency mode (F1, … F N) of resonance of the object (12) obtained previously in the predetermined frequency band; a computing unit (28, 30) for: the generation of a digital identification signature (GIS) of the object (12) from this measurement, and the authentication of the object (12) by comparison (42) of the digital identification signature (GIS) generated from the measurement with a reference digital identification signature (GIS) REF ); characterized in that the calculation unit (28, 30) is programmed (34, 36, 38, 40) to: transform (34) the measured spectrum (SP) by a processing dependent on said at least one previously obtained resonance frequency mode (F1, … F N ), and generate (36, 38, 40) the digital identification signature (GIS) from the transformed spectrum (SP'). A computer program downloadable from a communication network and / or stored on a computer-readable medium and / or executable by a processor, characterized in that it includes instructions for executing the steps of a method for authenticating an object (12) according to any one of claims 1 to 8, when said program is executed by a computing unit (28, 30) of an authentication system (10) for an object (12) according to claim 9.

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