Classifications

• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
  • G06F21/70—Protecting specific internal or peripheral components, in which the protection of a component leads to protection of the entire computer
  • G06F21/71—Protecting specific internal or peripheral components, in which the protection of a component leads to protection of the entire computer to assure secure computing or processing of information
  • G06F21/73—Protecting specific internal or peripheral components, in which the protection of a component leads to protection of the entire computer to assure secure computing or processing of information by creating or determining hardware identification, e.g. serial numbers
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
  • G01R19/0046—Arrangements for measuring currents or voltages or for indicating presence or sign thereof characterised by a specific application or detail not covered by any other subgroup of G01R19/00
  • G01R19/0053—Noise discrimination; Analog sampling; Measuring transients
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
  • G01R23/16—Spectrum analysis; Fourier analysis
• • G—PHYSICS
  • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
  • G09C—CIPHERING OR DECIPHERING APPARATUS FOR CRYPTOGRAPHIC OR OTHER PURPOSES INVOLVING THE NEED FOR SECRECY
  • G09C1/00—Apparatus or methods whereby a given sequence of signs, e.g. an intelligible text, is transformed into an unintelligible sequence of signs by transposing the signs or groups of signs or by replacing them by others according to a predetermined system
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/10—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols with particular housing, physical features or manual controls
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
  • H04L9/3271—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using challenge-response
  • H04L9/3278—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using challenge-response using physically unclonable functions [PUF]
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
  • H04L2209/12—Details relating to cryptographic hardware or logic circuitry

Definitions

• the present disclosure is generally related to techniques for implementing physically unclonable functions (PUFs) in electronic circuits.
• PEFs physically unclonable functions
• CMOS complementary metal-oxide-semiconductor
• SRAM static random-access memory
• PCM phase change memory
• Embodiments of the present disclosure provide techniques for implementing physically unclonable functions (PUFs) in electronic circuits.
• PEFs physically unclonable functions
• One such system comprises a challenge generator circuit; a transmitter circuit coupled to the challenge generator circuit; and a receiver circuit configured to receive and be stimulated by the transmitted challenge signal.
• a combination of the transmitter circuit and the receiver circuit which comprises a parity-time-symmetric structure that operates at an exceptional point, a divergent exceptional point, or a coherent perfect absorber-laser (CPAL) point of the parity time-symmetric structure.
• CPAL coherent perfect absorber-laser
• the transmitter circuit is configured to transmit a challenge signal generated by the challenge generator circuit to the receiver circuit; after transmitting the challenge signal, the transmitter circuit and the receiver circuit are configured to generate a unique transient response that is dependent on eigenfrequencies and harmonic responses of the parity-time-symmetric structure or on the eigenvalues of the scattering matrix of the parity-time-symmetric structure; the transmitter circuit or the receiver circuit is configured to measure the unique transient response and convert a value of the measured unique transient response to a bit string, or is configured to measure the spectral (frequency-domain) response near the CPAL point and convert a value of the measured unique spectral response of output coefficient to a bit string; and/or wherein the bit string comprises a physically unclonable function (PUF)-based cryptographic key.
• PAF physically unclonable function
• Embodiments of the present disclosure also present a method for implementing physically unclonable functions (PUFs) in electronic circuits.
• One such method comprises pairing a transmitter circuit and a receiver circuit through inductive coupling; transmitting a challenge signal from the transmitter circuit to the receiver circuit to stimulate the receiver circuit; measuring a unique transient response that depends on eigenfrequencies of a combined system of the transmitter circuit and the receiver circuit, wherein the eigenmodes are a function of values of physical properties of the receiver circuit; and/or converting a measured value of the unique transient response to a bit string, wherein the bit string comprises a physically unclonable function (PUF)-based cryptographic key.
• PEF physically unclonable function
• the receiver circuit and the transmitter circuit are complementary metal-oxide semiconductor integrated circuits, lll-V semiconductor integrated circuits, ll-VI semiconductor integrated circuits, and/or a combination of these techniques via the heterogeneous integration;
• the receiver circuit comprises an RLC oscillator having a positive resistance and the transmitter circuit comprises a -RLC oscillator and one or more LC oscillators that act as repeaters;
• the RLC circuit, the -RLC oscillator, and the one or more LC oscillators are based on complementary metal-oxide semiconductor integrated circuits;
• the unique transient response comprises a voltage value measured across a capacitor of the RLC oscillator of the transmitter circuit or the -RLC oscillator receiver circuit;
• the RLC oscillator and the -RLC oscillator are configured to be coupled inductively via an on-chip transformer, or are configured to be coupled capacitively via an on-chip capacitor or a negative capacitance converter, or are configured to be coupled both inductively
• such method or system may involve verifying the bit string by comparing the bit string against a stored valid identifier; and/or upon verifying the bit string, transmitting information stored in a memory of the receiver circuit to the transmitter circuit.
• a system may further comprise a first digital memory unit that is accessible by the transmitter circuit, wherein the transmitter circuit is configured to verify the bit string against a valid bit string that is stored in the first digital memory unit; and/or a second digital memory unit that is accessible by the receiver circuit, wherein the receiver circuit is configured to verify the bit string against a valid bit string that is stored in the second digital memory unit.
• Embodiments of the present disclosure also present a system comprising a challenge generator circuit; and a physically unclonable function (PUF) device that is configured to receive and be stimulated by a challenge signal transmitted by the challenge generator circuit.
• the PUF device comprises a parity-time-symmetric structure that operates at an exceptional point, divergent exceptional point, and/or coherent perfect absorber-laser (CPAL) point of the parity time-symmetric structure; after transmitting the challenge signal, the PUF device generates a unique transient response that is dependent on eigenfrequencies and output harmonics of the parity-time-symmetric structure or a unique spectral response that is dependent on the eigenvalue of the scattering matrix of the parity-time-symmetric structure; the PUF device is configured to measure the unique transient and/or spectral response and convert a value of the measured transient response to a bit string; and/or the bit string comprises a physically unclonable function (PUF)-based cryptographic key.
• PUF physically unclonable
• the PUF device comprises a pair of active and passive electromagnetic metasurfaces separated by a dielectric spacer; the PUF device can also be realized with an equivalent lumped-element circuit that comprises a negative resistance converter (NRC) and a shunt resistor separated by a transmission line or a T/7T-transformer; the NRC is implemented using a cross-coupled pair (XCP) circuit or a current-feedback operational amplifier; the challenge generator circuit generates two coherent waves with a complex amplitude ratio; and/or two pairs of incoming coherent waves having different complex-valued amplitude ratios generate different unique responses.
• NRC negative resistance converter
• XCP cross-coupled pair
• FIG. 1 (a) illustrates physically unclonable function (PUF)-enabled secure radio-frequency (RF) authentication and communication in accordance with the present disclosure.
• PAF physically unclonable function
• RF radio-frequency
• FIG. 1 (b) shows exemplary plots of radio frequency (RF) challenge, temporal responses, and bit string processing in accordance with various embodiments of the present disclosure.
• RF radio frequency
• FIG. 2(a)-2(c) shows a transmitter-receiver architecture that implements a wireless setup having a divergent excellent point (DEP), a standard excellent point (EP), and no singular points, respectively, along with corresponding pseudospectra, in accordance with the present disclosure.
• DEP divergent excellent point
• EP standard excellent point
• no singular points respectively, along with corresponding pseudospectra
• FIGS. 3(a)-3(b) show distributions of (a) real and (b) imaginary parts of eigenfrequencies for a third-order PT telemetry system in accordance with various embodiments of the present disclosure.
• FIGS. 4(a)-4(b) show a (a) bitmap and (b) entropy E x , E y ) analysis of a 256- bit PUF response from 100 PUF instances for an exemplary DEP-based RF PUF system in accordance with various embodiments of the present disclosure.
• FIG. 4(c) shows a plot of Inter-Hamming distance (inter-HD) and intra- Hamming distance (intra-HD) histograms obtained from 100 PUF instances for the exemplary DEP-based RF PUF system used in FIGS. 4(a)-4(b).
• FIG. 4(d) depicts the inter-HD histograms obtained from three different RF- PUF systems of FIGS. 2(a)-2(c).
• FIG. 4(e) shows inter-HD histograms of PUFs based on (1 ) a third-order PT system operating near DEP, (2) a third-order PT system operating away from DEP , and (3) a standard PT system operating near the exceptional point (EP); and (4) a conventional telemetry system using an NFC coil antenna.
• FIG. 5(a) shows an entropy (E x ,E y ) analysis of a 256-bit PUF response from 100 readers with discrepant RLC circuits interrogating the same receiving device in accordance with various embodiments of the present disclosure.
• FIG. 5(b) shows a plot of Inter-Hamming distance (inter-HD) and intra- Hamming distance (intra-HD) histograms obtained from the experimental setup of FIG. 5(a).
• FIG. 5(c) depicts the inter-HD histograms obtained from three different RF- PUF systems of FIGS. 2(a)-2(c) the experimental setup used in FIGS. 5(a)-5(b).
• FIG. 6 shows a block diagram for an exemplary DEP-based RF-PUF cryptographic system used in radio-frequency identification (RFID) and wireless access control in accordance with various embodiments of the present disclosure.
• RFID radio-frequency identification
• FIG. 7 shows a block diagram for an exemplary DEP-based RF-PUF cryptographic system used in near-field wireless communication (NFC) and authorization process in accordance with various embodiments of the present disclosure.
• FIG. 8(a) shows a schematic of an exemplary coherent perfect absorber-laser (CPAL) PUF system implemented using the active and passive metasurfaces, which form the PT-symmetric system, in the optical region in accordance with various embodiments of the present disclosure.
• CPAL coherent perfect absorber-laser
• FIG. 8(b) shows a transmission-line network model of the CPAL PUF system of FIG. 8(a).
• FIG. 8(c) shows a sequence of operations used in the cryptographic random number generation process of an exemplary CPAL PUF system in accordance with various embodiments of the present disclosure.
• FIG. 9(a)-9(b) provide a comparison of randomness between (a) an exemplary CPAL-enabled PUF and (b) a Fabry-Perot Interferometer (FPI)-enabled PUF.
• FPI Fabry-Perot Interferometer
• FIG. 10(a) shows a circuit diagram (top) and a photograph (bottom) of an exemplary CPAL PUF device realized using printed circuit board technology in the radiofrequency range.
• FIG. 10(c) shows measured entropies E x and E y for the bit-strings and keystrings of the CPAL PUF device of FIG. 10(a).
• FIG. 10(d) shows a pairwise map comparing the inter-HDs between two arbitrary PUF devices, showing that the fabricated PUF keys are almost uncorrelated.
• FIG. 10(e) shows measured inter-HDs and intra-HDs of an exemplary CPAL PUF by applying lasing (top) and CPA (bottom) challenges and their Gaussian-fitting results.
• FIG. 11 (a) shows a passive (top) and active (bottom) of FPI-enabled PUF devices and their onboard realizations in the radio-frequency region.
• FIG. 11 (b) shows a bitmap measured over 25 passive FPI-based PUF instances of FIG. 11 (a).
• FIG. 11 (c) shows measured entropy contents of passive FPI and active FPI PUF instances of FIG. 11 (a).
• FIG. 11 (d) shows a pairwise map of the 25 passive FPI PUF instances of FIG. 11 (a).
• FIG. 11 (e) shows inter-HDs of the active and passive FPI-based PUF instances of FIG. 11 (a).
• FIG. 12(a) shows a schematic of a Fourier regression (FR) model.
• FIGS. 12(b)-12(d) report the results of a FR modeling attack utilizing the FR model of FIG. 12(a).
• FIG. 13(a) shows a schematic of a generative adversarial network (GAN) structure having a generator and a discriminator.
• GAN generative adversarial network
• FIGS. 13(b)-13(d) shows probability mass functions (PMFs) of (b) prediction accuracies, (c) correlation coefficients (CCs), and (d) Hamming distances (HDs) between the predicted CRPs by GAN and the simulated CRPs by an exemplary CPAL PUF system of the present disclosure.
• PMFs probability mass functions
• CCs correlation coefficients
• HDs Hamming distances
• an extreme sensitivity to perturbation near exceptional points presents a solution to hardware security and authentication.
• naturally occurring fabrication errors can be used to build EP-based electronic circuits, implementing physically unclonable functions (PUFs) with excellent statistical characteristics in terms of the randomness of the generated keys and the uniqueness between different keys.
• PAFs physically unclonable functions
• PUFs are among the most promising and cost-effective hardware security primitives for key generations and authentications in the cyberspace.
• PUFs exploit unique physical variations that occur naturally during the device manufacturing process, and the encrypted key is generated by mapping a given input (i.e. , “challenge”) to an output (i.e., “response”), forming a challenge-response pair (CRP) (e.g., electrical signals in time/frequency domain, mechanical or optical signals).
• CCP challenge-response pair
• PUFs physically unclonable functions
• PUFs are a class of hardware-specific security primitives based on secret keys extracted from integrated circuits, which can protect important information against cyber-attacks and reverse engineering.
• PUFs can be categorized into two major classes: the strong PUFs capable of generating a large number of CRPs, and the weak PUFs possessing only a limited number of CRPs.
• CMOS complementary metal- oxide semiconductor
• IC complementary metal- oxide semiconductor
• arbiter PUFs arbiter PUFs
• SRAM static random-access memory
• memristor PUFs memristor PUFs
• ring oscillator PUFs ring oscillator
• CMOS digital products can have good robustness through micro- /nano-manufacturing with high precision, their applications in PUFs, on the flip side, are usually affected by the relatively low entropy and power consumption. As a result, CMOSbased PUFs are still potentially vulnerable to machine learning attacks based on predictive regression models and generative adversarial neural networks.
• Other emerging PUFs with improved randomness, such as quantum electronic PUFs, optical and photonic PUFs, and those based on features of randomly distributed nanostructures, are still subject the implementation cost and system complexity.
• EP exceptional points
• An EP is formed when two or more eigenstates (eigenvalues and corresponding eigenvectors) of a non-Hermitian Hamiltonian structure coalesce and become identical.
• the onset of this peculiar degeneracy signals the collapse of the eigenspace dimensionality, which in turn enhances the structure’s sensitivity to perturbations.
• This observation has inspired the recent proposal of building sensing devices operating at EPs. Subsequent experimental studies have confirmed that EP-based sensors enjoy enhanced responsivity.
• EP- and DEP-based circuits can be excellent candidates for producing robust, high-quality radiofrequency (RF) PUFs, which can be generalized to realize the secure wireless authentication (e.g., RFID and wireless access control) and NFC systems.
• RF radiofrequency
• CPAL coherent perfect absorber-laser
• FIG. 1 (a) depicts a generic architecture of a PUF-enabled RF wireless identification and communication system 100 having a transmitter (Tx) or reader circuit device 102 that transmits a challenge signal (e.g., RF pulse signal) (generated by a challenge generator circuit (not shown)) to a receiver (Rx) or tag circuit device 104 that is stimulated by the challenge signal and produces a response in either the Rx or Tx circuit.
• the response is converted to a cryptographic key 108 via a converter circuit (e.g., analog to digital (A/D) converter circuitry) 106.
• A/D analog to digital
• the security keys in this exemplary system are encoded in the unavoidable, irreproducible fabrication errors in the values of the electric components (resistors, capacitors and/or inductors) that are used to build the receiver circuit 104.
• These fabrication errors equip each individual circuit with a unique fingerprint that can serve as a PUF-based cryptographic key 108, which can be probed as follows: when the transmitter/reader and receiver/tag are paired for PUF encryption as secure wireless identification system, the reader (Tx) launches an RF pulse, known as a “challenge” to stimulate the Rx; the temporal response of the latter strongly depends on its eigenmodes of the combined system, which in turn are functions of the exact values of its electric components.
• tags will exhibit unique temporal responses as given by the instantaneous voltages measured across a reader’s capacitor, called for short as the “response.”
• the temporal response is digitized (e.g., via analog/digital conversion) to generate a 256-bit (or greater) string identifier (ID) for a given challenge.
• FIG. 1 (b) shows exemplary plots of radio frequency (RF) challenge, temporal responses, and bit string processing in accordance with various embodiments of the present disclosure.
• RF radio frequency
• this digitized ID passes the validation by specific loT database via the Tx (reader), the access request of the Rx (tag) will be authorized.
• this reader-tag scheme is used for secure wireless communication, the RF signals transmitted by Tx will introduce unique voltage response drop across a Rx’s capacitor in time domain. Only when such a temporal response is digitized and verified by the Rx with pre-defined verification, will the encrypted data and/or information stored in the Rx’s memory be allowed to be transmitted back to the Tx, in accordance with various embodiments. The secure wireless communication is therefore achieved, effectively avoiding the disclosure of privacy.
• an exemplary Tx-Rx architecture that can implement DEPs is shown in the left panel of FIG. 2(a).
• an exemplary transmitter circuit comprises an active transmitter (-RLC oscillator) and one or multiple neutral intermediator (LC oscillator) that act as repeaters.
• an exemplary receiver circuit comprises a passive receiver (RLC oscillator).
• the RLC oscillator and the -RLC oscillator are configured to be coupled inductively via an on-chip transformer or are configured to be coupled capacitively via an on-chip capacitor or a negative capacitance converter, or are configured to be coupled both inductively and capacitively via the aforementioned electronic components.
• L and M are self and mutual inductances of the two coil antennas.
• the system is considered in an intermediate regime where the singularity enhances the eigenfrequency splitting but without causing any divergency, and hence the system can be well defined within the context of a linear circuit, in which this DEP divides the system into exact and broken PT symmetry phases.
• An exemplary system can be designed to operate exactly at the DEP in accordance with the principles herein. Due to the strong bifurcation around this point, any small deviations in the values of the circuit’s components can lead to a substantial drift in the eigenfrequencies and, consequently, the response to external excitations. This is exactly the basis for system designs that utilize DEP systems for producing a high-quality PUF by leveraging the process variation naturally occurring in electronic components.
• FIG. 3(a) illustrates that real parts of eigenfrequencies are randomly distributed around the DEP, showing high uncertainty and a dark region that infers a low probability of detection.
• real parts of eigenfrequencies have a narrow distribution centered at the mean value, as indicated by brighter colors (i.e. , high probabilities) in FIG. 3(a).
• a transmitter/reader circuit can be used for interrogating fully-passive ID tags (i.e., RLC oscillator). It is composed of an intermediary neutral LC circuit and an active RLC oscillator connected to a challenge generator circuit (e.g., pulse generator). Together with the receiver circuit, the whole circuit forms the third-order PT-symmetric electronic system.
• RLC oscillator fully-passive ID tags
• a challenge generator circuit e.g., pulse generator
• the bitmap extracted from the transient voltage responses should have an unbiased distribution of “0” and “1” states.
• E y -[p y log 2 Py + (1 - Py) log 2 ( 1 - Py)]; (2) where p x , p y are the probabilities of obtaining digit “1”, along the x- and y-axis, respectively.
• the cryptographic key 108 of FIG. 1 (a) illustrates a bitmap (white means 1 and black means 0) generated by using the circuit in FIG. 2(a) and FIG. 4(a) depicts the entropy functions along both axes, showing that E x and E y are close to 1 and thus high randomness is obtained.
• FIGS. 4(a)-4(b) show the (a) bitmap and (b) entropy E x , E y ) analysis of a 256-bit PUF response from 100 PUF instances for an exemplary DEP-based RF PUF system in accordance with various embodiments of the present disclosure.
• the average entropy is found to be 0.93, 0.06 and 0.91 , 0.05 along the x- and y-axis.
• HD inter-device Hamming distance
• Another important metric characterizing the performance of PUF devices is their reliability, which is defined as the ability to generate identical keys after the same repeated challenges. In other words, the response associated with the same challenge should not change overtime, even though the environmental conditions are changed (e.g., temperatures in electronic components). A reliable RF-PUF system should have sufficient tolerance against the temperature variation.
• intra-HD obtained from 5 temperature conditions at 0, 5, 15, 20 and 25 Celsius can be compared.
• a pairwise map of 50 CRPs can be plotted, where the diagonal line indicates the intra-HD for the PUF instance itself and the off-diagonal points represent the inter-HD values compared to other PUF instances.
• the sharp contrast of the colormap in FIG. 4(c) shows a distinct difference between the intra-HD of a specific PUF instance (i.e., 0) and the inter-HD between two different PUF instances (i.e., small fluctuation around its average of 0.5). Accordingly, results obtained in accordance with the principles herein verify the possibility of building a lightweight, robust solution to secure wireless authorization and access control for devices and systems constructed in accordance with the principles of the present disclosure.
• the encoding capacity can be evaluated. Encoding capacity can be defined as the potential number of codes that can be generated by a PUF instance.
• c n The encoding capacity is given by c n .
• FIG. 4(e) depicts the inter-HD histograms obtained from three different RF-PUF systems considered herein.
• a standard EP i.e., without the pole singularity
• FIG. 4(e) depicts the inter-HD histograms obtained from three different RF-PUF systems considered herein.
• the traditional telemetry system can be formed by an RLC resonator coupled to a coil antenna with selfinductance L
• the input impedance of the RLC oscillator is assumed to follows a Gaussian statistical distribution similarly used in producing the simulation results of FIG. 3(a). From FIG. 4(d), it is shown that the traditional telemetry setup acts as a low entropy source with a biased distribution of “1” and “0”, causing the mean inter-HD to downshift to 0 and thus degraded key uniqueness.
• the EP-enabled bifurcation effect in the standard PT electronic system can increase the entropy, however, its performance still lags far behind that of the third-order PT electronic system operating nearby the DEP.
• HDs of DEP PUF are highly concentrated around 0.5.
• the distribution of HDs of EP-PUF is wider than that of DEP PUF.
• the PUF performance of EP PUF is not as good as the DEP one.
• This wider distribution of HDs of EP PUF also yields a smaller encoding capacity, since it has a larger standard deviation.
• the entropy decreases as the K/K DEP ratio decreases, since the system operates far away from DEP.
• the upshot of this comparison is that using DEP-based electronic circuits to implement PUF devices can significantly boost the system’s entropy and uniqueness beyond their values in standard devices.
• the exemplary PUF device set forth herein can also be exploited to secure the near-field communication (NFC) or low-power wireless sensors, as illustrated in FIG. 1 (a).
• NFC near-field communication
• a challenge signal e.g., pulse signal
• the reader circuit can generate unique transient response on each receiving circuit device’s capacitor, which can be used as the PUF-based cryptographic key.
• the PUF-based key detected by the receiving device must be verified before sending out the information stored in its digital memory, thus preventing the participation of the third entity and avoiding leakage of confidential information.
• a similar numerical experiments to that associated with FIGS. 5(a)-5(d) was used to evaluate the device merits.
• 100 readers with discrepant RLC circuits were used to interrogate the same receiving device.
• the lumped elements of the 100 readers are assumed to follow the same Gaussian distribution used before.
• FIG. 5(a) The entropy plots of FIG. 5(a) clearly indicate a nearly ideal scenario that guarantees high quality randomness.
• an exemplary security system of the present disclosure can utilize an RF PUF cryptographic system.
• the system can comprise: an NFC reader having a circuit programmed to selectively pair with at least one of tags or sensors via inductive coupling, and to generate a pulse signal output from the reader circuit containing a unique transient response for a receiving device’s capacitor.
• the unique transient response can serve as a PUF-based cryptographic key.
• the PUF-based cryptographic key can contain verifiable data preventing a response for a data non-match so that no information stored in the receiving device digital memory is sent when a non-match is received. The verification thus prevents the participation of the third entity and avoiding leakage of confidential information.
• FIG. 6 shows a block diagram of an exemplary DEP-based RF- PUF cryptographic system used in radio frequency (RF) identification (RFID) and wireless access control.
• Operations for such as system can include pairing an identification tag (receiver circuit) 604 and a wireless reader (transmitter circuit) 602 such that a DEP condition is satisfied.
• the operations can further include a launching of a challenge signal (e.g., RF pulse) by the reader 602 to interrogate the ID tag 604.
• the reader 602 acquests or acquires a transient RF response after transmitting the challenge signal and discretizes & digitizes the RF response to obtain a binary PUF cryptographic key.
• a database or memory unit of the reader 602 identifies and validates or invalidates the PUF cryptographic key by comparing the key against a stored valid identifier in the database (CRP database) or memory unit. Based on whether the PUF cryptographic key is validated, access is either denied or allowed by the reader 602. For example, access may be associated with unlocking an electrical lock to a room or compartment, as a non-limiting example, or may be associated with providing access to a computer resource, as another non-limiting example, among others.
• FIG. 7 shows a block diagram of an exemplary DEP-based RF- PUF cryptographic system used in an exemplary near-field wireless communication (NFC) and authorization process.
• Operations for such as system can include pairing a transmitter circuit 702 and a receiver circuit 704 such that a DEP condition is satisfied.
• the operations can further include a launching of a challenge signal (e.g., pulse excitation) by the transmitter 702 to the receiver circuit 704.
• the receiver circuit 704 acquests or acquires a transient RF response after receiving the challenge signal and discretizes & digitizes the RF response to obtain a binary PUF cryptographic key.
• a database or memory unit of the receiver circuit 704 identifies and validates or invalidates the PUF cryptographic key by comparing the key against a stored valid identifier in the database (CRP database) or memory unit. Based on whether the PUF cryptographic key is validated, a data transmission request is either denied or allowed by the receiver circuit 704. For example, access may be associated with a user of the transmitter circuit 702 requesting access to a computer file or directory that will be granted upon successful validation of the PUF cryptographic key, as one possible nonlimiting example, among others.
• the extreme sensitivity of PT symmetric electronic systems near EPs can be utilized for building a new type of physical system, devices and schemes (architectures), and these lightweight PUF-based cryptosystems may enable secure authentication and message exchange among the system/devices/schemes.
• the unprecedentedly large eigenvalues bifurcation arising near divergent exceptional points in higher-order (i.e., third-order and beyond) PT electronic circuits can enhance the randomness, uniqueness, encoding capacity of PUFs generated by inevitable physical differences between devices due to uncontrolled variations in the values of their electronic components.
• this new PUF paradigm can serve as a perfect entropy source or cryptographic random number generator for encryption and authentication in enormous wireless communication and identification applications.
• the extreme sensitivity of PT symmetric electronic systems near EPs can be used, in accordance with the principles herein, for building a new type of physical unclonable function (PUF) schemes and have shown that these lightweight PUF based cryptosystems may enable secure authentication and message exchange among the devices.
• PUF physical unclonable function
• the unprecedentedly large eigenvalues bifurcation observed near divergent exceptional points in higher-order (i.e., third order and beyond) PT electronic circuits can enhance the randomness, uniqueness, encoding capacity of PUFs generated by inevitable physical differences between devices due to uncontrolled variations in the values of their electronic components.
• cybersecurity devices and systems can be developed for hardware security that can avoid even machine learning assisted cyberattacks.
• such devices and systems herein can be a plugin to existing devices, and can also work as a standalone module, if desired.
• the spectral sensitivity associated with exceptional points (EPs) can be used for building optical and electronic sensors with enhanced sensitivity.
• the spectral sensitivity associated with EPs can be used as a resource for hardware security.
• the present disclosure introduces a physically unclonable function (PUF) by virtue of exotic spectral singularity of a divergent exceptional point (DEP) existing in higher-order parity-time (PT) symmetric electronic system.
• PPF physically unclonable function
• DEP divergent exceptional point
• PT parity-time
• the drastic eigenvalues bifurcation near the DEP can significantly enhance the stochastic entropy caused by inherent parameter fluctuations in electronic components, resulting in a perfect entropy source to generate encryption keys encoded in analog electrical signals (e.g., radio wave).
• analog electrical signals e.g., radio wave.
• a DEP-boosted entropy source can enable PUFs with truly random and unique inter-device variation, while achieving great robustness proven by a small intra-device variation.
• This lightweight and robust PUF structure may lead to a variety of unforeseen securities and anticounterfeiting applications in radio-frequency fingerprinting, anti-counterfeiting, wireless communications, and the like.
• PUF physically unclonable function
• PCB parity-time
• IC chipsets An exemplary electronic analogy (e.g., PCB or IC chipsets) of the PT-symmetric quantum system which has a non-Hermitian effective Hamiltonian and exceptional points is set forth.
• a wireless telemetry system e.g., RFID or NFC
• the highly uncertain output responses can be exploited for encryption and security applications (i.e., true random number generator).
• a group of RFID or NFC tags (Rx) are fabricated and wirelessly interrogated by the PT reader (Tx)
• their output RF responses can be unique, as manufacturing variations of electronic components (e.g., resistors, capacitors, and transistors etc.) could result in very different electrical output signals detected by the reader.
• Other devices and systems are contemplated as well in accordance with the principles herein. Devices/systems/schemes herein provide promising cryptosystems configured to defend against machine learning-assisted attacks to secure wireless communications.
• an exemplary PT PUF is a simple, low-cost true random number generator, which is robust against adversarial attacks.
• this hardware security technique is compatible to the existing wireless and telemetric systems, such near-field secure communication (NFC), radio frequency identification (RFID), etc.
• a security system constructed in accordance with the principles herein can comprise, in an exemplary embodiment, two or more RF-PUF’s having a first PUF one-dimensional key and a second PUF one-dimensional key.
• the first and second one dimensional keys are uncorrelated, with a normalized inter-HD approximately equal to 0.5 for a group of PUFs.
• a security system constructed in accordance with the principles herein can comprise, in an exemplary embodiment, the RF-PUF’s being further defined by divergent exceptional point (DEP)-based RF-PUFs.
• DEP divergent exceptional point
• a security system constructed in accordance with the principles herein can comprise, in an exemplary embodiment, an NFC reader having a circuit programmed to selectively pair with at least one of tags or sensors via inductive coupling, and to generate a pulse signal output from the reader circuit containing a unique transient response for a receiving device’s capacitor, wherein the unique transient response serves as a PUF- based cryptographic key.
• a security system constructed in accordance with the principles herein can also comprise, in an exemplary embodiment, the PUF-based cryptographic key containing verifiable data preventing a response for a non-match to prevent sending out the information stored in its digital memory when a non-match is received, thus preventing the participation of the third entity and avoiding leakage of confidential information.
• DEP- based circuits can also be excellent candidates for producing PUF devices among coherent perfect absorber-laser (CPAL) devices to generate unique encryption keys.
• CPAL coherent perfect absorber-laser
• emerging lightweight, low-cost PUFs with outstandingly lower predictability and, most importantly, higher resilience against machine learning-assisted attacks can be developed so as to facilitate their practice as hardware security primitives.
• PT-symmetry has been innovating the design paradigms of wave propagation and scattering by expanding the control of waves into the non-Hermitian realm.
• exceptional point EP
• the distribution of complex eigenvalues/eigenstates could be quite turbulent and noisy. This may cause pronounced sample-to-sample fluctuations that affect the reproducibility and scalability of non-Hermitian physical systems having exceptional points.
• high entropy nearby the exceptional point or the exceptional/CPAL point may be leveraged to generate high- quality PUF-based encryption keys.
• the output of the system can be switched from the lasing mode to its time-reverse counterpart, coherent perfect absorption (CPA) mode, by adjusting the complex-valued amplitude ratio of incident waves.
• CPA coherent perfect absorption
• both CPA and lasing modes are narrowband effects, and, more interestingly, both modes are susceptible to fluctuations in materials properties of gain and loss elements and their coupling rate.
• even small but inevitable process variations in manufacturing PT-symmetric structures may produce very different output responses from device to device.
• such a property may be seen as a foe for sensing purposes, on the flip side, it may find useful applications in generating high-quality PUF keys.
• the inherent device variability on an electronic or photonic microchip has been minimized, which poses a challenge to improve the randomness and uniqueness of digital circuitbased PUFs.
• the exemplary PUF keys generated from the frequencydomain electromagnetic responses may remarkably enhance the entropy inherent in fabrication flaws, in light of the extreme sensitivity at the self-dual singularity - CPAL point, thereby enabling high cryptographic randomness and uniqueness.
• FIG. 8(a) shows a schematic of an exemplary CPAL PUF system implemented using the active and passive metasurfaces in the optical region.
• manufacturing variations can cause random fluctuations among unit cells (or meta-atoms), resulting in device-to-device variations.
• FIG. 8(b) shows the two-port transmission-line network (TLN) model for the generalized PT-symmetric CPAL device of FIG. 8(a) that is composed of spatially- distributed and balanced gain and loss, of which the shunt/surface conductances —G
• the structure can be implemented using integrated circuit or printed circuit board (PCB) technology, where a negative resistance converter (NRC) and a shunt resistor are separated by a portion of a transmission line or a T/n-transformer.
• PCB printed circuit board
• NRC negative resistance converter
• the nonlinear analog output responses of CPAL-based PUF instances can be appropriately discretized and digitized into the bitstring-based authorization codes with excellent unclonability, as represented in FIG. 8(c).
• the responses are then discretized and digitized into binary bit-strings, forming digital cryptographic maps for PUF applications.
• the output responses in FIG. 8(c) are simulation results.
• the PUF keys retrieved from the output responses of the CPAL-based PUF instances can be reconfigured by adjusting the complex amplitude ratio of incident waves. Such a property may not be possible for most CMOS-based digital PUFs, in which each instance corresponds to one or multiple bits in the response, and thus, increasing the number of CRPs comes at the cost of increased size, device area and design complexity.
• the scattering parameters of the two-port TLN model in FIG. 8(b) can be computed using the transfer matrix method.
• the eigenvalues of the system’s scattering matrix approach zero and infinity, corresponding to the CPA mode and the lasing mode, respectively.
• such a complex-valued amplitude ratio of two incident light waves can be achieved with a polarizer and a voltage-controlled liquid crystal phase shifter (LCPS).
• LCPS liquid crystal phase shifter
• various analog/digital phase shifters and attenuators can be used to precisely tune the complex amplitude ratio of two input radio signals.
• FIG. 9(a) presents the theoretical results for the contour of the output response P ⁇ PAL as a function of 8x and v, plotted using Eq. (4).
• the scattered points represent the simulation results.
• FIG. 9(a) we find that, surprisingly, even with subtle fluctuations in conductance and electrical distance, the outputs of a set of devices can differ by ⁇ 60 dB.
• FIG. 9(b) plots the same contours as FIG. 9(a) but for the Fabry-Perot interferometer (FPI)-based PUF system under the same perturbation levels.
• FPI Fabry-Perot interferometer
• the active FPI exhibits only lasing properties.
• FIG. 8(b) shows a photograph of a prototype of an onboard CPAL PUF instance.
• NRC is based on a single current-feedback operational amplifier.
• the fabricated “T”-networks also have phase variation (6x) of ⁇ 3°, alongside other parasitics from the board and package. It is already known that if the system is initially designed to work at the CPAL point, any small perturbation in lumped element values may cause the output response to differ substantially. This makes possible the generation of PUF keys.
• each CPAL device as a PUF instance translates various input challenges C n (i.e. , different sets of ip ⁇ /-i *) to unique output responses R n .
• the output response was measured over a frequency range of 16.7 ⁇ 0.1 MHz.
• the output response spectrum was first normalized in the range of (0, 1 ) and then discretized into 64 points.
• the 64 points were digitized into a 4-bit binary code to form a 256 (4 x 64)-bit CRP as the device-specific unique identifier. For example, points with values smaller than 0.0625 will be given the binary code “0000” (details are schematically shown in FIG.
• the quality of PUF keys, by and large, is determined by three main metrics, namely randomness, uniqueness, and reliability. Different PUF instances should have random and unique responses when interrogated by the same challenge, while reliability represents the consistency of the response of the same PUF instance at different environmental conditions.
• We first evaluate the randomness of an exemplary CPAL- based PUF, i.e., the entropy of the cryptographic map associated with the uniformity Ideally, the number of “0”s and “1”s in the cryptographic map should occur with equal probability, which results in E x , y 1.
• FIG. 10(c) shows the entropies E x and E y extracted from the bitmap in FIG. 10(b).
• E y (0.97 ⁇ 0.02) exhibits a nearly perfect distribution and E x (0.90 ⁇ 0.11) deviates only slightly from unity, indicating excellent randomness in the generated PUF keys.
• the entropy quality is a direct measure but may not be sufficient to describe the randomness of a PUF.
• the National Institute of Standards and Technology (NIST) randomness tests suite may be used to fully assess the randomness of the CPAL-based PUF. The results show that the CPAL-based PUF can pass all 9 NIST randomness tests (the rest 6 require a bit length greater than 10 6 ) with P- values larger than 0.01 . Therefore, the exemplary PUF can be regarded as a true random number generator.
• inter-device Hamming Distance (or inter-HD) between the (digitized) response bitstrings of all PUF instances under the same challenge.
• An ideal inter-HD should be 0.5, which means that, on average, half the response bits are not repeated, thus ensuring the best quality of encryption from the statistical perspective.
• FIG. 10(d) shows the pairwise comparisons of inter-HDs among 25 PUF keys. It is seen that inter- HDs in the off-diagonal areas only fluctuate slightly around the mean value of 0.46. The result suggests that all PUF keys have great uniqueness; that is, each key is unique, highly uncorrelated, and unpredictable from history.
• PUF can be divided into strong and weak categories, which are classified according to the number of CRPs.
• a PUF is considered strong (weak) if the number of CRPs scales exponentially (linear or polynomial) with its size.
• Weak PUFs with a limited number of CRPs are often used for cryptographic key generation in identification applications, whereas strong PUFs capable of generating a large number of CRPs are utilized for authentication and secure communication applications. Since the output response of the CPAL device is very sensitive to input challenges (i.e. , it may be possible to create a large CRP space by adjusting both the amplitude and/or phase offset between two incident waves.
• FIG. 10(e) plots the histogram of average inter-HDs measured over 25 PUF instances under the two challenges.
• the CRPs on the upper (lower) panel of FIG. 10(e) are obtained by applying the lasing (CPA) challenge.
• the inter-HD histogram fitted by a Gaussian distribution is centered around the ideal value of 0.5.
• the PUF metrics may be further improved by using advanced fabrication techniques that minimize the board parasitics, allowing the devices to operate in close proximity to the exceptional/CPAL point.
• the entropy contents of the active (hollow circle) and passive (solid dot) FPI-based PUFs are plotted in FIG. 11 (c).
• FIG. 11 (d) reports the pairwise map of inter-HDs for the passive FPI CPA-based PUF. From FIG. 11 (d), we find that most FPI CPA instances are highly correlated, namely, the extracted PUF keys could be vulnerable to attacks.
• FIG. 11 (e) is similar to FIG. 10(e) but obtained with active and passive FPI-based PUF instances.
• the mean inter-HD value for the passive (active) FPI-based PUFs is found to only be 0.31 (0.12).
• the passive (active) FPI-based PUF instances are also initially locked at the CPA (lasing) mode, the resulting uniqueness or randomness is much worse than that of their CPAL counterparts.
• the results in FIG. 11 (e) are in sharp contrast to FIG. 10(e) obtained with the CPAL-based PUF. Therefore, the presence of the self-dual CPAL singularity in PT non-Hermitian systems, indeed, plays a key role in amplifying the output response deviation caused by the inter-device variation, thus providing unique and unclonable encryption keys.
• reliability refers to the consistency of CRPs under environmental variations (e.g., ambient temperature) is essential.
• PUF applications reliability can be described by intra-device HD (intra-HD), defined as the bit error rate between responses generated by the same PUF instance at different operating conditions for a given challenge.
• intra-HD intra-device HD
• each instance was measured at eleven different temperatures (from -20 °C to 80 °C with an interval of 10 °C).
• the measured intra-HD histogram of the disclosed PUF is shown in the upper panel of FIG. 10(e), which is normally distributed with a mean of 0.05 and a standard deviation of 0.05. Such values are sufficiently low to ensure good robustness against environmental variations.
• “dynamic” noises such as phase/flicker noises and thermal noises introduced by the agitation of electrical charges, may also generate temporal fluctuations in a system’s responses.
• We also studied the time dependence of reliability by measuring the output responses of 6 CPAL PUF instances every 30 s (for a total of 3 minutes) and calculating the intra-HDs of the generated CRPs.
• the intra-HD histogram associated with the temporal stability is plotted in the lower panel of FIG. 10(e), which shows a near-zero mean, implying that the CPAL PUF can be robust against “dynamic” noises.
• the FR model extracts the features of randomness from the training data set (estimator CRPs) to predict PUF responses.
• the GAN-based modeling attack comprising two deep neural networks - a generator and a discriminator, as illustrated in FIG. 13(a), is another strong passwordguessing tool.
• the discriminator is a binary classifier used to distinguish whether an input CRP belongs to the training dataset or is produced by the generator.
• the generator on the flip side, strives to generate fake CRPs that resemble the training data to fool the discriminator.
• the well-trained GAN can generate new data instances that resemble the training data.
• 13(a) includes a generator network with 4 layers and a discriminator network with 3 layers; here, 4/3 linear layers were adopted because too many hidden layers could lead to convergence failure, which reduces the prediction accuracy of the model.
• the GAN structure requires a large amount of training data, we simulated 1000 PUF instances with the fabrication tolerance extracted from experimental results and applied 10 input challenges (10 phase differences between two input signals) to generate 10000 CRPs, where 2000 CRPs were used for testing, and the rest were kept for training. The GAN was trained with 3000 epochs. Without the loss of generality, all “0”s of the CRPs for training the GAN were replaced with “-1”s.
• the distributions of ACC, CC, and HD between the GAN-predicted and simulated CRPs are shown in FIGS. 13(b)-13(d), respectively; here, the probability mass function (PMF) of a normal distribution is adopted.
• PMF probability mass function
• the maximum (minimum) prediction accuracy is 73% (35%), corresponding to a success possibility of only 0.0001 (0.0003).
• the mean CC and HDs are 0.07 and 0.46, which further confirms an exemplary PUF is resilient to machine learning-assisted attacks.
• the present disclosure presents a robust, high-quality PUF primitive based on the CPAL effect enabled by PT-symmetric non-Hermitian electromagnetic structures. It has been theoretically demonstrated that the self-dual singularity may make output responses of CPAL-based PUF instances highly sensitive to inevitable device-to- device variations. Besides, experimental studies conducted for the CPAL-based PUF keys implemented using the RF circuits have shown that the performance metrics, including randomness, uniqueness, correlation level, encoding capacity, and thermal/temporal stability, can outperform PUF instances based on traditional passive and active FPIs. Furthermore, the CPAL-based PUF is highly robust against state-of-the- art machine learning-assisted attacks, such as FR and GAN modeling attacks.
• the disclosed PUF techniques may pave a promising avenue toward next-generation identification, authentication, encryption, and security systems, which may find widespread applications in modem society.
• the disclosed hardware security paradigm may also be extended to other wave systems, such as photonics, acoustics, elastics, and optomechanics.
• the present disclosure puts forward an emerging type of PUF in the electromagnetic domain by virtue of the self-dual emitter-absorber singularity that uniquely exists in the parity-time (PT)-symmetric structures.
• the reconfigurable emissive and absorptive properties with order-of-magnitude differences in scattered power can respond sensitively to admittance or phase perturbations caused by, for example, manufacturing imperfectness. Consequently, the entropy sourced from inevitable manufacturing variations can be amplified, yielding excellent PUF security metrics in terms of randomness and uniqueness. It is shown that this electromagnetic PUF can be robust against machine learning-assisted attacks based on the Fourier regression and generative adversarial network.
• the disclosed PUF concept is wavelength-scalable and transformative in radio-frequency, terahertz, infrared, and optical systems, paving a promising avenue toward applications of cryptography and encryption, including using stochastic and fluctuating properties among CPAL devices to generate unique encryption keys.

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