Systems and methods for implementing structures for physical unclonable functions

Abstract

Disclosed herein are embodiments of PUF systems and methods that utilize photonic circuitry to generate a PUF signature based on the state of polarization of a photon. Such PUF embodiments as disclosed herein may comprise substantially the same circuitry that can be operated in the classical or quantum domain. In one embodiment, the PUF system further comprises one or more reconfigurable elements adapted to modify the birefringence of the photonic circuitry.

Description

[Technical Field]

[0001] (Related Applications) This application claims the benefit of priority under 35 U.S.C. Section 119 of U.S. Provisional Patent Application No. 63 / 395,736, entitled "Systems and Methods For Implementing A Photonic PUF Structure," filed August 5, 2022, by Duncan MacFarlane et al., which is hereby incorporated by reference in its entirety.

[0002] (Technical field) The present disclosure relates generally to security of computing devices. Specifically, the present disclosure relates to authentication of electronic devices and systems. More specifically, the present disclosure relates to Physical Unclonable Functions (PUFs). Even more specifically, the present disclosure relates to structures adapted for use in PUFs. [Background technology]

[0003] A Physically Unclonable Function (PUF) is a structure that can serve as a unique, unforgeable identifier (ID) for purposes of verifying the authenticity of a device or object. PUFs may thus function similarly to, for example, a serial number for a given device, but with the added requirement that the value of the PUF can never be forged, even if the value is likely correct. With respect to a PUF, then, this unique identification thus has two main properties: 1) it is nearly impossible to duplicate due to the details of its construction, and 2) it can be queried in a way that can reliably and securely establish the identity of the object that bears the ID.

[0004] The recent massive proliferation of connected devices (the "Internet of Things," or "IoT") has placed increasing emphasis on the ability to robustly distinguish between many otherwise identical units. At the same time, this proliferation of devices has also placed significant downward pressure on their production costs and deployment overhead. These overhead factors include not only raw distribution costs, but also the interpolation network required to implement them, the operational cycle time required to reliably establish a secure, unique identity, and finally, the overall production time (including any required per-device provisioning steps and raw device manufacturing). These time and cost pressures increase the already difficult task of providing for robust security. In addition, because all of these devices are interconnected, there is the added requirement that devices that are to be uniquely and securely identified may not always be available for direct physical inspection. These requirements are nearly all in conflict with each other, but addressing all of them simultaneously is highly desirable.

[0005] Therefore, a need exists for systems and methods for improved PUFs. Summary of the Invention [Means for solving the problem]

[0006] Some additional context regarding PUFs and their uses may be useful. PUFs can be used to securely and uniquely identify electronic devices through the generation of a (PUF) signature. Thus, perhaps the most important attribute of a PUF (e.g., the root of the host device's signature) is its uniqueness. At the same time, such a unique ID should be protected from discovery by an adversary (typically through the use of a secure verification protocol). The basic procedure for verifying a PUF value (and thus verifying the unique identity of the device hosting that PUF) is therefore typically embedded in a two-way transaction mechanism referred to as a "challenge-response" protocol (CRP).

[0007] It is often desirable for a truly secure PUF system to have certain properties, including that the device exhibits a PUF value probability distribution function (PDF) that is approximately uniform within a community of all such devices, that the challenge (for a CRP) employs an unpredictable nonce value or other means to prevent response reproducibility, that the mapping from the challenge domain to the corresponding response codomain is accomplished by a sufficiently strong one-way function, that there is a clear way to verify the authenticity of the responder, and that the PUF value (i.e., the root value from which the signature can be derived) must be safe from discovery, even under direct physical inspection (including, for example, full disassembly).

[0008] However, the ability to implement a PUF that meets such criteria can be very challenging. One particular obstacle to implementing such a PUF is the variation between the type of circuitry used to implement a computing device and the way such circuitry is operated. For example, a computing device may include electronic or photonic (also called optical) circuitry (or some combination of electronic and optical circuitry). Electronic PUF circuitry may be susceptible to side-channel or eavesdropping attacks due to electromagnetic energy emitted during PUF circuit operation. This may allow an adversary to accumulate a set of partial knowledge of the PUF value itself that can be mapped to a table of challenge / response pairs. In particular, timing-based PUFs are susceptible to “modeling attacks,” in which a digital replica is constructed based on a table of challenge / response pairs obtained during an eavesdropping attack. Information-theoretic approaches can be applied to characterize the strength of state-based PUFs, which allow exploitable information to be obtained by an adversary and facilitate characterization of specific instances of the internal PUF function. More recently, PUF attacks based on machine learning (ML) approaches such as "Generative Adversarial Networks" (GANs) have emerged and become of interest. A key vulnerability that can be exploited to defeat PUF-based security is the ability to characterize the supporting circuitry through eavesdropping or through invasive physical attacks.

[0009] Another consideration in implementing PUFs is that increasingly, circuits that include or use such PUFs can be operated in the classical domain (e.g., according to principles of classical operation, also referred to as classical mode) or in the quantum domain (e.g., according to principles of quantum mechanical operation, also referred to as quantum mode). The response of devices operating in the quantum domain is often significantly different from devices operating in the classical domain. These differences can be exploited if the same device can be operated in both domains. Both photonic and electronic circuits can exhibit this dual-domain behavior, but electronic devices are much more difficult to shield from the environment than photonic devices. Therefore, electronic PUFs are more susceptible to active external influences, i.e., electromagnetic interference, or EMI, attacks. They are also more difficult to shield from passive external (eavesdropping) attacks than photonic devices. Therefore, it is highly desirable to develop PUF systems that can potentially be used in circuits composed either wholly or partially of photonic circuitry, and the same PUF system can be operated in either the classical or quantum domain.

[0010] Additionally, if the portion of a device used to generate a PUF signature is functionally independent from portions of the circuitry used for other purposes, the device is more easily attacked by physical disassembly or other invasive attacks. Therefore, it is also desirable to develop a PUF that uses substantially the same circuitry and implements PUF functionality and “normal” operation in either the classical or quantum domain. If that “normal” mode of operation also provides a method for generating an embedded PUF signature, such a device can be used to produce “authenticated” results. In other words, results from the device’s normal operation can be verified as being produced by a particular device.

[0011] These various considerations may be addressed by embodiments as disclosed herein that utilize photonic or photonic (integrated) circuits (PCs or PICs) in implementations of PUF systems, including hybrid PUF systems, among others. The term “hybrid” is used herein to indicate that the same PUF system can be operated in either the quantum domain or the classical domain (or some mixture of both). To explain in more detail, circuits of the same design (whether electronic or optical) comprising (e.g., one or more) chains of components (e.g., hardware or physical implementations of functionality, including photonic or electrical circuits) may exhibit variations. These variations may be introduced intentionally or unintentionally (or both), either intentionally through the design of the components (e.g., a design that introduces variations in the components while keeping the intended functionality the same) or unintentionally as variations introduced, for example, through the manufacturing process or due to associated tolerances in the component circuitry. One of these variations between photonic circuits (e.g., of the same design) may be related to the state of polarization (SOP) of an optical signal (e.g., one or more photons) propagating through that photonic circuit. Because the polarization state of an optical signal can be measured independently from other properties of that same signal (e.g., frequency, phase, or amplitude), the polarization of the photon stream can be used as an orthogonal basis (to these other properties) according to which photonic circuit identification can be prepared and measured. This polarization-related behavior can thus be measured independently (e.g., in the classical domain), while other attributes can be simultaneously operated on and measured in the quantum domain.

[0012] To elaborate on these differences in more detail, it should be understood that as the frequency of an electromagnetic wave increases, the wave enters the region of the spectrum typically considered light or optical waves. This increase in frequency increases the optical wave's sensitivity to phase perturbations. Because the geometric dimensions of PC components are on the order of wavelengths, these phase perturbations translate into the SOP sensitivity desired for PC-based PUFs. An example of this sensitivity to phase manifests as a change in the optical wave's SOP as it propagates through such a waveguide, fabricated with local imperfections within the boundary conditions that define the waveguide modes. In such optical components and systems, including optical fiber communication systems, this sensitivity to impairments can be characterized as "polarization mode dispersion" (PMD) and "polarization-dependent loss" (PDL). This shift in SOP through optical circuits can be used to realize PUF systems. In particular, the inherent impairments of the optical path caused by stress and strain and component fabrication variability cause the output SOP to vary in a random but consistent manner in response to an associated input SOP. Multiple sequentially launched input wave SOPs result in corresponding multiple output SOPs with highly reproducible SOP-to-SOP variation between a set of unperturbed, fabricated photonic circuits of the same design.

[0013] As can be seen, each instance of a photonic circuit of the same design may alter the SOP of the optical signal in a different manner based on variations in the birefringence of the components that make up each instance of the photonic circuit. This variation may be due, for example, to geometric perturbations between (the components of) those photonic circuit instances or other causes. Thus, each PC of the same design may exhibit relatively large differences in the effect the PC has on the SOP of the optical signal.

[0014] Thus, the SOP can serve as an effective basis for a photonic-circuit-based PUF circuit. That is, according to one embodiment, a PUF system can include a photon source coupled to a photonic circuit comprising one or more photonic components, the photonic circuit having at least two outputs. A polarization controller is positioned between the photon source and the PC. The polarization controller is adapted to affect the polarization of an optical signal in an input waveguide. Thus, a polarization input to the polarization controller (e.g., a polarized input signal) represents the input polarization of the optical signal input to the photonic circuit.

[0015] For example, in one embodiment, the polarization controller may include a chain of one or more components responsive to an input signal, such as one or more heaters responsive to an input voltage or current. These heaters may impart stress or strain directly or indirectly (e.g., through a surrounding substrate) on the input waveguide in a reproducible manner so that the polarization of an optical signal input to the photonic circuit of the PUF system corresponds to the input voltage (i.e., the same input voltage will result in substantially the same SOP of the optical signal input to the photonic circuit). As another example, the polarization controller may include one or more polarization paddles that may be configured in different orientations (e.g., vertically or horizontally).

[0016] As mentioned, the photonic circuit of the PUF system may have at least two outputs. The signals at these outputs may be the basis for the PUF signature generated by the PUF system. Specifically, the photonic circuit may include one or more polarizing beam splitters for generating the at least two outputs of the photonic circuit.

[0017] The use of one or more polarizing beam splitters within the photonic circuit of a PUF system results in output power components on two outputs of the photonic circuit, the ratio of which (e.g., of an input signal and a polarized signal held at a particular level) provides a PUF signature for the PUF system. Thus, during operation of an embodiment of a PUF system, the input signal to the polarization controller is controlled (e.g., held at a particular level) and one or more photons can be provided from a photon source through an input waveguide to the photonic circuit. A ratio based on the signals at the output of the photonic circuit of the PUF system can therefore constitute the PUF signature of the PUF system.

[0018] The PUF system may therefore include a detector at each output of the photonic circuit, the detector adapted to detect the presence of a photon at the output or the intensity of an optical signal at that output. When operating the PUF system in the classical domain, the polarization input signal to the polarization controller may be controlled (e.g., held at a particular level), and one or more input photons may be provided to the photonic circuit from a photon source through an input waveguide. The ratio of the intensity of the signal detected by a first detector on a first output of the photonic circuit to the intensity of the signal detected by a second detector on a second output of the photonic circuit may therefore serve as a PUF signature of the PUF system.

[0019] When such a PUF system is operated in the quantum domain, it can be observed that for each input photon provided from a photon source through an input waveguide to the photonic circuit, there can be a photon output at only one of two (or more) outputs of the photonic circuit of the PUF system. Thus, when operating a PUF system in the quantum domain, multiple photons can be provided from a photon source through an input waveguide to the photonic circuit (e.g., with a polarized input signal held at a particular level). The ratio to be used for the PUF signature can then be determined by using a first detector on a first output of the photonic circuit and accumulating a first number of photons appearing on the first output, and using a second detector on a second output and accumulating a second number of photons appearing on the second output. The ratio of the first number of photons to the second number of photons (or vice versa) can then be utilized as a PUF signature for the PUF system when operated in the quantum domain.

[0020] Embodiments may therefore provide several advantages. Optical processes are advantageous for security applications such as these because they are less susceptible to eavesdropping and side-channel monitoring through the difficulty of observing the electromagnetic radiation emitted by the photonic circuits during operation. Additionally, one major advantage is that the use of SOPs and photonic circuits within a PUF system may be desirable in terms of resistance to tampering or destructive reverse engineering approaches to determine the PUF signature. This resistance arises because any attempt to tamper with a fabricated photonic circuit, such as engaging in a scraping attack, would necessarily alter the very small stresses and strains originally present in the fabricated PUF system components. Thus, photonic circuit-based PUF systems may provide an enhanced degree of security against scraping and similar reverse engineering approaches that may be employed by adversaries.

[0021] In one specific embodiment, to enhance such security benefits, among other reasons, the PUF system may be included on an integrated circuit, i.e., a "chip," and the photon source and photon circuitry may be in different or disparate locations on the chip. For example, the photon source and photon circuitry may be arranged in different layers of the chip, or arranged distal from each other relative to one or more axes of the chip. The input waveguide may thus be positioned such that it traverses a significant portion of the chip within which the PUF system is located. By configuring the input waveguide (and polarization controller) in this manner, the security of the PUF system is enhanced, as virtually any tampering with the chip on which the PUF system resides can result in changes to the stress strains that were present in the originally fabricated PUF system components due to the increased area covered by the wavy nature of the input waveguide.

[0022] In some cases, it may be desirable to reprovision a PUF system in various circumstances so that the PUF system is modified to generate different PUF signatures (e.g., based on the same set of inputs or challenges). Thus, embodiments of a PUF system as disclosed may include one or more reprovisioning mechanisms. Such reprovisioning mechanisms may serve to affect the birefringence of a photonic circuit of the PUF system to modify the effect of the photonic circuit on the SOP of a propagated optical signal (e.g., one or more photons).

[0023] These reprovisioning mechanisms can be either volatile or nonvolatile. Nonvolatile reprovisioning mechanisms can have a permanent (or semi-permanent) effect on the birefringence of the photonic circuit of a PUF system. For example, one or more reconfigurable elements can be placed within the photonic circuit (or elsewhere in the PUF system), and those reconfigurable elements can be physically altered based on a stimulus. Such reconfigurable elements can include, for example, simple fusible links that can be blown, which will affect the waveguides or other components of the photonic circuit to change the birefringence of the photonic circuit. As another example, a nonvolatile reconfigurable element can include a polysilicon area, or “tub,” through which the waveguides of the photonic circuit pass or adjacent to the waveguides in the photonic circuit. When such a polysilicon area is placed under heat, and the heat is subsequently removed, the polysilicon can refreeze with a physically different configuration. Thus, the stress and strain on the waveguides of the photonic circuit are altered, and accordingly, the birefringence of the photonic circuit of the PUF system is altered as well.

[0024] Similarly, volatile reconfigurable elements may affect the birefringence of a photonic circuit of a PUF system in a transient manner, which may be controlled to differentially affect the birefringence of the photonic circuit. For example, these volatile reconfigurable elements may include one or more heaters along one or more portions of a waveguide internal to the photonic circuit, which may be controlled to affect the birefringence of the photonic circuit. As another example of a volatile reconfigurable element, one or more variable phase shifters may be internally coupled to a waveguide internal to the photonic circuit, which may be controlled to affect the birefringence of the photonic circuit and thus (e.g., temporarily) change the polarization transfer function of the photonic circuit used to generate the PUF signature.

[0025] Specifically, with regard to the use of a variable phase shifter as a volatile reconfigurable element, as discussed in one embodiment, a photonic circuit may include one or more Hadamard gates equipped with a beam splitter. Two Hadamard gates may form a Mach-Zehnder interferometer (MZI), such that a variable phase shift gate may be coupled between two Hadamard gates of a photonic circuit of a PUF system. This variable phase shift can serve as a variable "steering" gate that can be controlled to affect the path a photon (or photon stream) will take through the photonic circuit. Because different optical paths will exhibit different polarization effects, the birefringence of the photonic circuit, and therefore the PUF signature generated by the PUF system, can then be influenced by this MZI-based steering. Note that this MZI "steering" effect acts on individual photons (thus at the quantum level), as opposed to affecting only groups of photons (i.e., in the classical domain).

[0026] In one embodiment, a PUF system may include a photon source and a photonic circuit coupled to the photon source via an input waveguide. The photonic circuit may have a first output and a second output. The PUF system may also include a polarization controller responsive to a polarization input, where operation of the polarization controller responsive to the polarization input is adapted to affect the polarization of photons in the input waveguide, a first detector coupled to the first output and adapted to detect a first signal at the first output, and a second detector coupled to the second output and adapted to detect a second signal at the second output. The PUF system may be adapted to determine a PUF signature based on the first signal and the second signal.

[0027] Thus, embodiments may determine a PUF signature at two different times. For example, a PUF system may be adapted to determine a PUF signature at a first time by providing a first polarization input to a polarization controller at a first time, detecting a first signal at the first time, detecting a second signal at the first time, and determining a PUF signature based on the first signal at the first time and the second signal at the first time, and to determine a PUF signature at a second time by providing a first polarization input to a polarization controller at a second time, detecting the first signal at the second time, detecting the second signal at the second time, and determining a PUF signature based on the first signal at the second time and the second signal at the second time.

[0028] In an embodiment, the first signal is a presence of photons in the first output and the second signal is a presence of photons in the second output, and determining the PUF signature includes accumulating a first number of photons in the first output based on the first signal, accumulating a second number of photons in the first output based on the first signal, and determining a ratio between the first number of photons and the second number of photons.

[0029] In other embodiments, the first signal is a first intensity of the optical signal at the first output, the second signal is a second intensity of the optical signal at the second output, and determining the PUF signature includes determining a ratio between the first intensity and the second intensity.

[0030] In some embodiments, a method for determining a PUF signature may include providing one or more photons from a photon source to a photonic circuit coupled to the photon source via an input waveguide, the photonic circuit having a first output and a second output; controlling a polarization controller using the polarization input to affect polarization of the photons in the input waveguide; detecting a first signal at the first output of the photonic circuit; detecting a second signal at the second output of the photonic circuit; and determining a PUF signature based on the first signal and the second signal. Controlling the polarization controller may include holding the polarization input at the same level.

[0031] These and other aspects of the present disclosure will be better appreciated and understood when considered in conjunction with the following description and the accompanying drawings. It should be understood, however, that the following description, while indicating various embodiments of the present disclosure and numerous specific details thereof, is given by way of illustration and not limitation. Many substitutions, modifications, additions, and / or rearrangements may be made within the scope of the present disclosure without departing from the spirit thereof, and the present disclosure includes all such substitutions, modifications, additions, and / or rearrangements. [Brief explanation of the drawings]

[0032] The drawings accompanying and forming a part of this specification are included to depict certain aspects of the present disclosure. It should be noted that the features illustrated in the drawings are not necessarily drawn to scale. A more complete understanding of the present disclosure and its advantages may be obtained by reference to the following description considered in conjunction with the accompanying drawings, in which like reference numerals indicate like features.

[0033] [Figure 1] FIG. 1 is a block diagram of one embodiment of a PUF system.

[0034] [Figure 2] FIG. 2 is a block diagram of one embodiment of a PUF system.

[0035] [Figure 3] FIG. 3 is a block diagram of one embodiment of a PUF system.

[0036] [Figure 4] FIG. 4 is a block diagram of one embodiment of a photonic circuit for use in an embodiment of a PUF system.

[0037] [Figure 5] FIG. 5 is a block diagram of one embodiment of a photonic circuit for use in an embodiment of a PUF system. [Figure 6] No explanation provided.

[0038] [Figure 7] FIG. 7 is a block diagram of one embodiment of a photonic circuit.

[0039] [Figure 8] FIG. 8 is a depiction of one embodiment of a trench coupler. DETAILED DESCRIPTION OF THE INVENTION

[0040] The present disclosure and various features and advantageous details thereof will be more fully described with reference to non-limiting embodiments illustrated in the accompanying drawings and detailed in the following description. Descriptions of well-known starting materials, processing techniques, components, and equipment are omitted so as not to unnecessarily obscure the invention in detail. It should be understood, however, that the detailed description and specific examples, while indicating some embodiments of the present invention, are given by way of illustration only and not by way of limitation. Various substitutions, modifications, additions, and / or rearrangements within the spirit and / or scope of the underlying inventive concept will become apparent to those skilled in the art from this disclosure.

[0041] Before discussing embodiments in detail, it may be helpful to provide a general overview of certain aspects related to the embodiments. The description contained in U.S. Application No. 17 / 729,416, filed April 26, 2022, by Thornton et al., entitled "Systems and Methods for Hybrid Physical Unclonable Functions," which is incorporated herein by reference, may also be useful for understanding the embodiments. As can be recalled from the above discussion, it is increasingly desirable to be able to securely and uniquely identify electronic devices. PUFs are one way to address this desire. Thus, perhaps the most important attribute of a PUF is its uniqueness. In other words, many different items with the same basic structure (e.g., circuitry) can be reliably distinguished from one another. Establishing a unique identity for one object that is functionally identical to many others but can nevertheless be distinguished from these other devices is a challenging task. At the same time, such a unique ID should be protected from discovery by an adversary. This ultimate task has been made much more difficult in recent years due to the proliferation of machine learning (ML)-based adversaries that are able to use the power of statistics across very large data sets to unearth patterns not easily discernible to humans. For this reason, the basic procedure for verifying a PUF value (and thus verifying the unique identity of the device hosting that PUF) must, by necessity, in many instances be built into a two-way transaction mechanism.

[0042] This transaction process is accomplished through two-way communication in a "Challenge-Response Protocol" (CRP). The challenger (who wishes to verify the device's identity) issues a query to the responder (the device), which then replies with a response message that can be uniquely verified to "prove" its identity in some way. Typically, this CRP protocol starts with a message containing a random number (called a "nonce"). This nonce is necessary to prevent replay attacks. If the nonce is not perfectly random (i.e., if it is predictable, even if only to a low degree), an attacker can precompute a set of potential response messages in advance. This ability to generate a set of potential responses reduces the attacker's search space, which can yield a statistically meaningful amount of information about the PUF value that can be gleaned from any observed message traffic to (and from) the device. After several legitimate challenge-response message pairs, an ML-based adversary may be able to successfully masquerade as a legitimate device to some other challenger. In some cases, it has been shown that as few as a dozen or so genuine CRP transactions are sufficient to allow an ML-based adversary to successfully masquerade as a genuine device.

[0043] The ability to discern statistically relevant information from an authentic device's CRP message (e.g., to defeat the security conferred by a PUF or a CRP using a PUF) depends not only on the nature of the nonce used in the challenge message, but also on the statistical distribution of the authentic device's PUF value itself (on which the device's response message is based). If the PUF signature (value) has a statistical distribution that exhibits "clustering," the same statistical inference can be made, as already mentioned. In other words, if the PUF signature probability distribution function (PDF) is not approximately uniform across the entire set of potential PUF signatures generated by a PUF or a response using a PUF, its probability value can be predicted given sufficiently legitimate message data.

[0044] Another aspect of a PUF-based CRP that is important from a security perspective is the nature of the function used to map from the PUF challenge domain to the response final domain (or image). This function mapping should be inherently non-invertible. If this is not the case, an attacker can observe only a single legitimate CRP exchange and use that information to determine the PUF signature by reversing the mapping function from the image to the PUF value domain. This type of function is typically referred to as a "one-way function." Another use of such a one-way function may be for the purpose of output "whitening." If the PDF of the PUF is not clustered but is nevertheless not uniform (e.g., a binomial PDF), the final output can be made approximately uniform by using a one-way function such as a simple hash function.

[0045] One final aspect of viable PUF technology is undiscoverability, even under direct physical inspection. In other words, if an adversary is able to disassemble a device containing a PUF, the adversary should not be able to determine the true value of the PUF, even if they are able to disassemble the device (down to the lowest level).

[0046] A PUF is a set of functions that can be implemented in terms of a system or a set of devices, {d1, d2, d3, , d k}, but for the purposes of this application, a more general definition of a PUF may also be adopted. A PUF may therefore be thought of as a physical (e.g., information storage) system that is protected by a security mechanism with the objective of making it very difficult to copy or reverse engineer the system, which means that it remains effective against an active attacker who may have temporary or permanent physical access to the module that hosts the security mechanism in its original form.

[0047] Because PUFs are typically physically implemented as circuits rather than programmed, user-defined functions, in the ideal case they are instances of one-way functions implemented through the exploitation of physical properties. This class of one-way functions is based on some property or state of a physical system, with the key concept that the resulting signature is reproducible and unique for a given device. A similar idea is the unique patterns found in individual snow crystals. While all snow crystals form through a common set of atmospheric circumstances that create the conditions for snowfall, close inspection of each snow crystal reveals that they appear to be made of ice crystals with different patterns. Furthermore, the probability that any two snow crystals have the exact same structure is very low. Therefore, a snow crystal's structure can be used as a representation of its signature. A snow crystal's signature is reproducible because each subsequent inspection of the same snow crystal (given that it has not melted) results in observing the same pattern. Two or more snow crystals can be distinguished from each other based on their unique signatures. That is, the probability of a signature collision between any two snowflakes is very low. "Unique" will therefore be interpreted for purposes of this disclosure to mean that the probability of finding another (e.g., the same signature produced by another device) is very low, rather than that it is the only one.

[0048] As can be seen, therefore, it is desirable for a secure PUF system to exhibit the following five necessary properties: 1) The set of devices must exhibit a nearly uniform PUF value PDF; 2) All challenges must employ completely unpredictable nonce values. 3) The mapping from the task domain to the corresponding response domain must be accomplished by a sufficiently powerful one-way function; 4) There must be a clear method for verifying the authenticity of the respondent; and 5) The PUF value must be safe from discovery even under direct physical inspection (including full disassembly).

[0049] Finally, to aid in the feasibility of an entity to implement such a successful PUF technology, it may also be desirable (in addition to the five characteristics listed above) for the PUF device to be low cost, low overhead, reproducible / stable, and robust.

[0050] However, the ability to implement a PUF that meets such criteria can be very challenging. One particular obstacle to implementing such a PUF is the variation between the type of circuitry used to implement a computing device and, in addition, how such circuitry is operated. For example, a computing device may include electronic or photonic (also called optical) circuitry (or some combination of electronic and optical circuitry). Electronic PUF circuitry may be susceptible to eavesdropping attacks due to electromagnetic energy emitted during PUF circuit operation, which may allow an adversary to accumulate a partial table of challenge / response pairs. In particular, timing-based PUFs are susceptible to “modeling attacks,” in which a digital replica is constructed based on a table of challenge / response pairs obtained during an eavesdropping attack. Information-theoretic approaches can be applied to characterize the strength of state-based PUFs, allowing exploitable information to be obtained by an adversary, facilitating characterization of specific instances of the internal PUF function. More recently, PUF attacks based on machine learning (ML) approaches such as "Generative Adversarial Networks" (GANs) have emerged and become of interest. A key vulnerability that can be exploited to defeat PUF-based security is the ability to characterize the supporting circuitry through eavesdropping or through invasive physical attacks.

[0051] Another consideration in implementing PUFs is that, increasingly, circuits that include (or use) such PUFs can be operated in the classical domain (e.g., according to classical principles of operation, also referred to as classical mode) or in the quantum domain (e.g., according to quantum mechanical principles of operation, also referred to as quantum mode). Thus, it is highly desirable to use PUF systems that can potentially be used in circuits that are composed either wholly or partially of photonic circuitry, and that the same PUF system can be operated in either the classical or quantum domain, and further, can operate with substantially similar properties when comprising substantially the same circuitry and operating in the classical or quantum domain.

[0052] These various considerations may be addressed by embodiments as disclosed herein that utilize photonic or photonic (integrated) circuits (PCs or PICs) in implementations of PUF systems, including hybrid PUF systems, among others. The term "hybrid" is used herein to indicate that the same PUF system can be operated in either the quantum domain or the classical domain (or some mixture of both). To explain in more detail, identical circuits in a design (whether electronic or optical) comprising a chain (e.g., one or more) of components (e.g., hardware or physical implementations of functionality, including photonic or electrical circuits) may exhibit variations. These variations may be introduced intentionally or unintentionally (or both): intentionally through the design of the components (e.g., a design that introduces variations in the components while keeping the intended functionality the same) or unintentionally as variations introduced, for example, through the manufacturing process or due to associated tolerances in the component circuitry. One of these variations between photonic circuits (eg, of the same design) may be related to the state of polarization (SOP) of the optical signal (eg, one or more photons) propagating through the photonic circuit.

[0053] To elaborate on these differences in more detail, it should be understood that as the frequency of an electromagnetic wave increases, its wavelength decreases, and this smaller wavelength makes the electromagnetic wave increasingly sensitive to phase perturbations caused by microscopic variations in photonic circuits. When the geometric dimensions of PC components are on the order of a single wavelength, these phase perturbations translate into the SOP sensitivity desired for PC-based PUFs. An example of this sensitivity to phase is clearly expressed as the change in lightwave SOP when the electromagnetic wave propagates through such a waveguide fabricated with local imperfections in the boundary conditions that define the waveguide modes. In such optical components and systems, including optical fiber communication systems, this sensitivity to impairments can be characterized as "polarization mode dispersion" (PMD) and "polarization-dependent loss" (PDL). This shift in SOP through optical circuits can be used to realize PUF systems. In particular, optical path-specific impairments caused by stress and strain and component fabrication variability cause the output SOP to vary in a random but consistent manner in response to the associated input SOP. Multiple sequentially launched input wave SOPs result in corresponding multiple output SOPs with highly reproducible SOP-to-SOP variation between a set of unperturbed fabricated photonic circuits of the same design.

[0054] As can be seen, each instance of a photonic circuit of the same design may alter the SOP of the optical signal in a different manner based on variations in the birefringence of the components that make up each instance of the photonic circuit. This variation may be due, for example, to geometric perturbations between the (components of) those photonic circuit instances or other causes. Thus, each PC of the same design may exhibit a relatively large degree of variation in the effect the PC has on the SOP of the optical signal. Therefore, the SOP may serve as an effective basis for a photonic-circuit-based PUF circuit.

[0055] Turning initially to FIG. 1 , therefore, one embodiment of the PUF system 100 includes a photonic circuit 108 coupled to a photon source 102. The photonic circuit 108 comprises one or more photonic components and has at least two outputs 130. A polarization controller 106 is mounted between the photon source 102 and the photonic circuit 108. For example, the polarization controller 106 may be on or adjacent to an input waveguide adapted to conduct an optical signal (e.g., one or more photons) from the photon source 102 to the photonic circuit 108. The polarization controller 106 is adapted to affect the polarization of the optical signal in the input waveguide. Thus, the polarization controller 106 is responsive to a polarization input 104, and operation of the polarization controller 106 in response to the polarization input 104 is adapted to affect the polarization of the photons in the input waveguide. Specifically, the polarization controller 106 is adapted to affect the polarization of the optical signal from the photon source 102 in the input waveguide in a reproducible manner based on the polarization input 104, and the effect of the polarization controller 106 on the optical signal can vary based on variations in the polarization input 104. Thus, the polarization input 104 (polarization input signal) to the polarization controller 106 represents the input polarization of the optical signal input to the photonic circuit 108. Expressed another way, the input polarization of the optical signal is programmable based on the polarization input signal 104 to the polarization controller 106. Thus, by holding the polarization input signal 104 at a particular level, a similar or the same SOP of the photons of the optical signal input to the photonic circuit 108 can be obtained.

[0056] 2 , in certain embodiments, polarization controller 206 may include a chain of one or more components 212 responsive to a polarized input signal 204, such as one or more heaters responsive to input signal 204 including an input voltage or current (collectively referred to herein, without loss of generality, as a voltage). These components 212 (e.g., heaters) may exert stress or strain directly or indirectly (e.g., through a surrounding substrate) on input waveguide 214 in a reproducible manner, such that the polarization of an optical signal input to photonic circuit 208 of the PUF system corresponds to input signal 204 (e.g., the same input voltage on input signal 204 will result in substantially the same SOP of the optical signal input to photonic circuit 208). As another example, components 212 of polarization controller 206 may include one or more polarizing paddles that may be configured in different orientations (e.g., vertically or horizontally).

[0057] 1 , as noted, the photonic circuit 108 of the PUF system 100 may include at least two outputs 130 a, 130 b. The signals on these outputs 130 may be the basis for the PUF signature 148 generated by the PUF system 100. Specifically, the photonic circuit 108 may include one or more polarizing beam splitters for generating the at least two outputs 130 of the photonic circuit 108. For example, in one instance, the photonic circuit 108 may include a chain of one or more Hadamard gates (e.g., three Hadamard gates), which are implemented as such polarizing beam splitters.

[0058] The use of one or more polarizing beam splitters within the photonic circuit 108 of the PUF system 100 results in output power components on the two outputs 130 of the photonic circuit 108, and the output power component ratio (e.g., the input signal and the polarization signal held at a particular level) may provide the basis for a PUF signature 148 for the PUF system 100. Thus, during operation of an embodiment of the PUF system 100, the polarization input signal 104 to the polarization controller 106 is controlled (e.g., held at a particular level), and one or more photons may be provided from the photon source 102 through the input waveguide to the photonic circuit 108. The ratio of the signals on the output 130 of the photonic circuit 108 of the PUF system 100 may therefore comprise the PUF signature 148 of the PUF system 100. In particular, the unique polarization transfer function of the photonic circuit 108 is the ratio of the powers that can be measured, and the ratio of the powers is highly dependent on the particular circuit instance. Furthermore, the measured PUF response signal is highly reproducible because the same birefringence perturbation is encountered by the input optical signal (eg, when the polarization input 104 is held at the same level).

[0059] The PUF system 100 may thus include a detector 110a, 110b on each of the outputs 130a, 130b of the photonic circuit 108, with each detector 110a, 110b adapted to detect the presence of a photon on the output 130a, 130b or the intensity of an optical signal on its respective output 130a, 130b. When operating the PUF system 100 in the classical domain, the polarization input signal 104 to the polarization controller 106 is controlled (e.g., held at a particular level), and one or more input photons may be provided from the photon source 102 through the input waveguide to the photonic circuit 108. The ratio of the intensity of the signal detected by the first detector 110a on the first output 130a of the photonic circuit 108 to the intensity of the signal detected by the second detector 110b on the second output 130b of the photonic circuit 108 may thus serve as a PUF signature 148 of the PUF system. Therefore, it should be understood that the same PUF signature 148 can be generated at different times by controlling the polarized input signal 104 in the same manner (e.g., holding it at the same level) when determining the PUF signature 148.

[0060] When such a PUF system is operated in the quantum domain, it can be observed that for each input photon provided from the photon source 102 through the input waveguide to the photonic circuit 108, there can only be a photon output on one of the two (or more) outputs 130 of the photonic circuit 108 of the PUF system 100. Thus, when operating the PUF system 100 in the quantum domain, multiple photons can be provided from the photon source 102 through the input waveguide to the photonic circuit 108 (e.g., with the polarized input signal 104 held at a particular level). The ratio to be used for the PUF signature 148 can then be determined on the first output 130a of the photonic circuit 108 by accumulating a first number of photons appearing on the first output 130a using the first detector 110a, and on the second output 130b using the second detector 110b. The ratio of the first number of photons to the second number of photons (or vice versa) may then be utilized as the PUF signature 148 for the PUF system when operated in the quantum domain. In certain instances, when the number of accumulated photons increases during a quantum mode of operation, it may be observed that the ratio determined during the quantum mode of operation may be substantially similar to the ratio determined during a classical mode of operation of the PUF system 100 (e.g., with the polarization input held at the same level).

[0061] Embodiments may therefore provide several advantages. Optical processes are advantageous for security applications such as these because they are less susceptible to eavesdropping and side-channel monitoring through the difficulty of observing the electromagnetic radiation emitted by the photonic circuits during operation. Additionally, one major advantage is that the use of SOPs and photonic circuits in PUF systems may be desirable in terms of resistance to tampering or destructive reverse engineering approaches to determine the PUF signature. This resistance also arises because any attempt to tamper with a fabricated photonic circuit, such as engaging in a scraping attack, will necessarily alter the very small stresses and strains originally present in the fabricated PUF system components. Thus, photonic circuit-based PUF systems may provide an enhanced degree of security against scraping and similar reverse engineering approaches that may be employed by adversaries.

[0062] In one specific embodiment, to enhance such security benefits, among other reasons, the PUF system may be included on an integrated circuit, i.e., a "chip," and the photon source and photon circuitry may be in different or disparate locations on the chip. For example, the photon source and photon circuitry may be arranged in different layers of the chip, or may be arranged distal from each other relative to one or more axes of the chip. The input waveguide may thus be arranged such that it traverses a substantial portion of the chip on which the PUF system is located. By way of example only, the input waveguide between the photon source and photon circuitry of the PUF system may be routed in a wavy or serpentine manner (e.g., across or through the layers of the chip). Components of the polarization controller may likewise be arranged along this wavy input waveguide. For example, if heaters are utilized as polarization controllers for the PUF system, one or more of such heaters may be arranged along the input waveguide of the PUF system. By configuring the input waveguide (and polarization controller) in this manner, the security of the PUF system is enhanced, as virtually any tampering with the chip on which the PUF system resides can result in changes to the stress strains originally present in the fabricated PUF system components due to the increased area covered by the wavy nature of the input waveguide.

[0063] Note that embodiments of the PUF system disclosed herein may take advantage of the fact that each photonic circuit has a unique polarization transfer function, which is a ratio of power that can be measured and is highly dependent on the particular circuit instance. Thus, the PUF response signal measured for an embodiment of a PUF system is highly reproducible because the same birefringence perturbation is encountered by the same optical input signal. However, it may be desirable to reprovision the PUF system in different situations so that the PUF system can be modified to generate different PUF signatures (e.g., based on the same set of inputs or challenges).

[0064] Thus, embodiments of a PUF system as disclosed may include one or more reprovisioning mechanisms. Figure 3 is a block diagram of one embodiment of such a PUF system 300. Such reprovisioning mechanisms may affect the birefringence of the photonic circuit 308 of the PUF system 300 and serve to modify the effect of the photonic circuit on the SOP of a propagated optical signal (e.g., one or more photons). More specifically, these reprovisioning mechanisms may affect the polarization transfer function of the photonic circuit of the PUF system such that the ratio generated at the output 330 of the photonic circuit 308 in response to a given optical input signal may be modified.

[0065] These reprovisioning mechanisms can be either volatile or nonvolatile. Nonvolatile reprovisioning mechanisms can have a permanent (or semi-permanent) effect on the birefringence of the photonic circuit of the PUF system. For example, one or more reconfigurable elements 322 can be disposed within the photonic circuit 308 (or elsewhere in the PUF system), and those reconfigurable elements 322 can be physically altered based on a stimulus. Such reconfigurable elements 322 can include, for example, a simple fusible link that can be blown and moved, which will affect the waveguide 370 (or other components of the photonic circuit 308) internal to the photonic circuit 308 to change the birefringence of the photonic circuit 308. As another example, the nonvolatile reconfigurable element 322 can include a polysilicon area, or “tub,” through which the waveguide 370 of the photonic circuit 308 passes or adjacent to the waveguide 308 of the photonic circuit. When such a polysilicon area is placed under heat and the heat is subsequently removed, the polysilicon may refrozen with a different physical configuration. Thus, the stress and strain on the waveguide 370 of the photonic circuit 308 is altered by the refrozen polysilicon tab, and the birefringence of the photonic circuit 308 of the PUF system 300 is altered accordingly.

[0066] Similarly, the volatile reconfigurable elements 322 may affect the birefringence of the photonic circuit 308 of the PUF system in a transient manner, which in some cases may be controlled (e.g., based on control signals to the reconfigurable elements 322) to differentially affect the birefringence of the photonic circuit 308. For example, these volatile reconfigurable elements 322 may include one or more heaters along one or more portions of the waveguide 370 internal to the photonic circuit 308, which may be controlled to affect the birefringence of the photonic circuit 308. As another example of a volatile reconfigurable element 322, one or more variable phase shifters may be internally coupled to the waveguide 370 internal to the photonic circuit 380, which may be controlled to affect the birefringence of the photonic circuit 308 and thus change (e.g., linearly) the polarization transfer function of the photonic circuit 308 used to generate the PUF signature 348.

[0067] Specifically, with regard to the use of a variable phase shifter as a volatile reconfigurable element, as discussed in one embodiment, the photonic circuit may include one or more Hadamard gates, each of which may include a beam splitter. FIG. 4 depicts an example of an embodiment of a photonic circuit 408 that may be utilized in embodiments of a PUF system as disclosed. Here, the photonic circuit 408 includes three cascaded Hadamard gates 402, each of which may include a beam splitter. When used within a PUF system, an input signal (e.g., from a photon source through an input waveguide, as discussed) may be provided to the input (i.e., first) Hadamard gate 402a of the photonic circuit 408, and outputs 430a and 430b of the output (i.e., last) Hadamard gate 402c serve as outputs of the photonic circuit 408 and may be provided to a detector of the PUF system in which it is utilized.

[0068] Because two (e.g., cascaded) Hadamard gates can form a Mach-Zehnder interferometer, a variable phase-shift gate can be coupled between two Hadamard gates of a photonic circuit of a PUF system, and this variable phase-shift gate can be controlled to affect the birefringence of the photonic circuit and therefore the PUF signature generated by the PUF system. Figure 5 depicts one embodiment of a photonic circuit 508 including three cascaded Hadamard gates 502, each of which can include a beam splitter. Here, one or more reconfigurable elements including variable phase shifters 522 can be interconnected to a waveguide 570 between a pair of Hadamard gates 502 of the photonic circuit 508. Thus, phase shifter 522a may be internally coupled to a portion of waveguide 570a between input Hadamard gate 502a and intermediate Hadamard gate 502b, or phase shifter 522b may be internally coupled to a portion of waveguide 570b between intermediate Hadamard gate 502b and output Hadamard gate 502c (or both phase shifters 522a, 522b may be included). These variable phase shifters 522 may therefore affect the birefringence of photonic circuit 508 and thus be controlled to (e.g., temporarily) change the polarization transfer function of photonic circuit 508 used to generate a PUF signature when photonic circuit 508 is utilized in a PUF system.

[0069] 6, one embodiment of a PUF system 600 is depicted that includes a photonic circuit 608 with configurable elements. Again, the photonic circuit 608 is coupled to a photonic source 602. The photonic circuit 608 comprises one or more photonic components and has at least two outputs 630. A polarization controller comprising a heater 612 is disposed between the photonic source 602 and the photonic circuit 608, which is on or adjacent to an input waveguide 614 that is adapted to conduct an optical signal (e.g., one or more photons) from the photon source 602 to the photonic circuit 608.

[0070] Here, photonic circuit 608 includes three cascaded Hadamard gates 602 a, 602 b, and 602 c, each of which may include a beam splitter. A variable phase shifter 624 a, such as a polarization-based beam splitter, may be internally coupled to a portion 670 a 1 of waveguide 670 between input Hadamard gate 602 a and intermediate Hadamard gate 602 b, and phase shifter 624 b may be internally coupled to a portion 670 b 1 of waveguide 670 between intermediate Hadamard gate 602 b and output Hadamard gate 602 c. Similarly, a heater 626a, such as a thermal phase modulator, may be internally coupled to a portion 670a2 of the waveguide 670 between the input Hadamard gate 602a and the intermediate Hadamard gate 602b, while a heater 626b may be internally coupled to a portion 670b2 of the waveguide 670 between the intermediate Hadamard gate 602b and the output Hadamard gate 602c. These variable phase shifters 624 and heaters 626 may thus be controlled to affect the birefringence of the photonic circuit 608 and thus change (e.g., temporarily) the polarization transfer function of the photonic circuit 608 used to generate the PUF signature 648 in the PUF system 600.

[0071] While nearly any type of desired photonic circuit may be utilized to implement embodiments of the PUF system as disclosed, as detailed elsewhere herein, it should be noted that in certain embodiments, the photonic circuit of the PUF system may comprise one or more polarizing beam splitters to generate at least two outputs for the photonic circuit. For example, in one instance, the photonic circuit may comprise a chain of one or more Hadamard gates (e.g., three Hadamard gates), which are implemented as such polarizing beam splitters.

[0072] 7 is a block diagram depicting one embodiment of a photonic circuit 708 comprising three such Hadamard gates; the photonic circuit 700 may comprise three coupled trench circuits. Specifically, light may be coupled into and out of the photonic circuit 708 using edge couplers, which collect and focus the light into the photonic circuit's internal waveguide. One extra branch 704 of the photonic circuit 708 may be terminated internally within the photonic circuit. An internal waveguide 714 connects three cascades of trench-based couplers 702.

[0073] During operation, an input signal is coupled into the photonic circuit 708 through an edge coupler, which serves as the "input coupler" 712a. The wave propagates into the first trench divider 702a, where it is split into a reflected and a transmitted component. These two signal components propagate into the second trench divider 702b, where recombination, reflection, and transmission occur. This process is repeated within the third trench divider 702c, where the two outputs of that component 702c propagate to two separate edge couplers 712b, 712c, referred to as the "output couplers." Throughout this photonic circuit 708, the propagating wave interacts with fixed, repeatable perturbations caused by local stresses, strains, and geometric variations in the waveguide and divider dimensions, which are implemented within random ranges of values ​​prior to fabrication but remain fixed during fabrication. The recombination of the waves in the trench splitter 702 is coherent, thus giving rise to a new SOP resulting from the perturbation. The relative power directed to each of the two output edge couplers 712b, 712c will be different (e.g., when operating in the classical domain) due to polarization-manufacturing variations in the trench splitter 712 in the photonic circuit 708 and the particular SOP of the input signal provided as an input to the photonic circuit 708. Importantly, input signals with different SOPs will result in different relative powers on the two output couplers 712b, 712c.

[0074] Furthermore, in certain embodiments, certain embodiments of beam splitter cells may be utilized in trench-based couplers, which add even more variation in the SOP than other common splitter cells, such as those based on Y-splitters. FIG. 8 is a depiction of such a trench-based coupler 800. Here, the beam splitter 800 may comprise a relatively narrow “trench” 802. The fact that the trench 802 is very narrow causes the ratio of very small geometric imperfections to the narrowness of the trench to have larger mode variations than would be present if a larger geometric shape were used in a beam splitter comprising a Y-splitter. This larger ratio manifests as a larger variation in the optical response signal SOP, resulting in a higher quality PUF response for certain embodiments of a PUF system, since the SOP variation between different photonic circuits (e.g., of the same design) is increased. Such a trench-based beam splitter or coupler can be fabricated, for example, in a 65 nm Si process, where at the intersection of the two waveguides, a narrow trench with a width of 100 nm is etched at a 45° angle, which For each input port, the coupler provides reflection and transmission of the incident light wave. A thin, but very deep trench causes "frustrated total internal reflection" (FTIR) and transmission to occur within the coupler. This nanoscale coupler structure replicates the operation of a macroscopic beam-splitting cube, but it requires a much smaller area than a typical splitter cell.

[0075] Although the present invention has been described with reference to specific embodiments thereof, these embodiments are illustrative only and are not limiting of the present invention. The description herein of illustrated embodiments of the present invention, including the description in the Summary, is not intended to be exhaustive or to limit the present invention to the precise form disclosed herein (in particular, the inclusion of any particular embodiment, feature, or function is not intended to limit the scope of the present invention to such embodiment, feature, or function). Rather, the description is intended to describe illustrative embodiments, features, and functions to provide those skilled in the art with a context for understanding the present invention, including any such embodiment, feature, or function described in the Summary, without limiting the present invention to any specifically described embodiment, feature, or function. Specific embodiments of the present invention and examples thereof are described herein for illustrative purposes only, and various equivalent modifications are possible within the spirit and scope of the present invention, as those skilled in the art will recognize and appreciate. As indicated, these modifications can be made to the present invention in light of the foregoing description of illustrated embodiments of the present invention and are intended to be included within the spirit and scope of the present invention. Thus, while the invention has been described herein with reference to specific embodiments thereof, it should be understood that a certain degree of modification, changes, and substitutions are contemplated within the foregoing disclosure, and that in some instances, some features of the embodiments of the invention may be employed without a corresponding use of other features without departing from the scope and spirit of the invention as described. Accordingly, many modifications may be made to adapt a particular situation or material to the essential scope and spirit of the invention.

[0076] References throughout this specification to “one embodiment,” “an embodiment,” or “a specific embodiment,” or similar terminology mean that a particular feature, structure, or characteristic described in connection with an embodiment is included in at least one embodiment, and may not necessarily be present in all embodiments. Thus, each appearance of the phrases “in one embodiment,” “in an embodiment,” or “in a specific embodiment,” or similar terminology in various places throughout this specification is not necessarily referring to the same embodiment. Furthermore, the particular features, structures, or characteristics of any particular embodiment may be combined in any suitable manner with one or more other embodiments. It should be understood that other variations and modifications of the embodiments described and illustrated herein are possible in light of the teachings herein and are considered to be part of the spirit and scope of the invention.

[0077] In the description herein, numerous specific details, such as example components and / or methods, are provided to provide a thorough understanding of embodiments of the present invention. However, those skilled in the art will recognize that an embodiment may be practiced without one or more of the specific details, or with other devices, systems, assemblies, methods, components, materials, parts, and / or equivalents. In other instances, well-known structures, components, systems, materials, or operations are not specifically shown or described in detail to avoid obscuring aspects of embodiments of the present invention. While the present invention may be illustrated using specific embodiments, this does not and does not limit the present invention to any particular embodiment, and those skilled in the art will recognize that additional embodiments are readily apparent and are part of the present invention.

[0078] It should also be understood that one or more of the elements depicted in the drawings / diagrams may also be implemented in a more separate or integrated manner, or in some cases removed or rendered inoperable, as may be useful according to a particular application. Additionally, any signal arrows in the drawings / diagrams should be considered illustrative only and not limiting, unless specifically stated otherwise.

[0079] As used herein, the terms "comprises," "comprising," "includes," "including," "has," "having," or any other variation thereof, are intended to cover non-exclusive inclusions. For example, a process, product, article, or apparatus that includes a list of elements is not necessarily limited to only those elements and may include other elements not expressly listed or inherent to such process, product, article, or apparatus.

[0080] Furthermore, the term "or," as used herein, is generally intended to mean "and / or" unless otherwise indicated. For example, a condition A or B is satisfied by any one of the following: A being true (or present) and B being false (or not present); A being false (or not present) and B being true (or present); and A and B being both true (or present). As used herein, a term preceded by "a" or "an" (or "the" when the antecedent is "a" or "an") includes both the singular and plural forms of such term (i.e., the reference "a" or "an" clearly indicates only the singular or only the plural). Also, as used in the description herein and throughout the claims that follow, the meaning of "in" includes "in" and "on," unless the context clearly dictates otherwise.

Claims

1. 1. A PUF system, comprising: a photon source; a photonic circuit coupled to the photon source via an input waveguide, the photonic circuit having a first output and a second output; a polarization controller responsive to a polarization input, operation of the polarization controller responsive to the polarization input adapted to affect the polarization of the photons in the input waveguide; a first detector coupled to the first output and adapted to detect a first signal at the first output; a second detector coupled to the second output and adapted to detect a second signal at the second output; Equipped with The PUF system is adapted to determine a PUF signature based on the first signal and the second signal.

2. 2. The PUF system of claim 1, wherein the first signal is a presence of a photon in the first output, the second signal is a presence of the photon in the second output, and determining the PUF signature comprises accumulating a first number of photons in the first output based on the first signal, accumulating a second number of photons in the first output based on the first signal, and determining a ratio between the first number of photons and the second number of photons.

3. 2. The PUF system of claim 1, wherein the first signal is a first intensity of an optical signal at the first output, the second signal is a second intensity of an optical signal at the second output, and determining the PUF signature comprises determining a ratio between the first intensity and the second intensity.

4. The PUF system of claim 1 , further comprising one or more reconfigurable elements adapted to modify birefringence of the photonic circuit.

5. The PUF system of claim 4 , wherein the reconfigurable element comprises a polysilicon tub.

6. The PUF system of claim 4 , wherein the reconfigurable element comprises a variable phase shifter.

7. 7. The PUF system of claim 6, wherein the photonic circuit comprises a first Hadamard gate and a second Hadamard gate, and the variable phase shifter is coupled between the first Hadamard gate and the second Hadamard gate.

8. The PUF system of claim 1 , wherein the polarization controller comprises one or more heaters.

9. 1. A method for determining a PUF signature, comprising: a PUF system, the method comprising: providing one or more photons from a photon source to a photonic circuit, the photonic circuit coupled to the photon source via an input waveguide, the photonic circuit having a first output and a second output; affecting the polarization of the photons in the input waveguide by controlling a polarization controller using a polarization input; Detecting a first signal at a first output of the photonic circuit; detecting a second signal at a second output of the photonic circuit; determining a PUF signature based on the first signal and the second signal; A method comprising:

10. The method of claim 9 , wherein controlling the polarization controller comprises maintaining the polarization input at the same level.

11. 10. The method of claim 9, wherein the first signal is a presence of a photon in the first output and the second signal is the presence of the photon in the second output, and determining a PUF signature comprises accumulating a first number of photons in the first output based on the first signal, accumulating a second number of photons in the first output based on the first signal, and determining a ratio between the first number of photons and the second number of photons.

12. 10. The method of claim 9, wherein the first signal is a first intensity of an optical signal at the first output, the second signal is a second intensity of an optical signal at the second output, and determining the PUF signature comprises determining a ratio between the first intensity and the second intensity.

13. The method of claim 9 further comprising modifying the birefringence of the photonic circuit.

14. The method of claim 13 , wherein modifying the birefringence comprises heating a polysilicon tub in the photonic circuit.

15. The method of claim 13 , wherein modifying the birefringence comprises controlling a variable phase shifter in the photonic circuit.

16. 10. The method of claim 9, wherein the photonic circuit comprises a first Hadamard gate and a second Hadamard gate, and the variable phase shifter is coupled between the first Hadamard gate and the second Hadamard gate.

17. The method of claim 9 , wherein the polarization controller comprises one or more heaters.

18. The method of claim 17 , wherein the polarization input is a voltage.

19. 1. A PUF system, comprising: a photon source; a photonic circuit coupled to the photon source via an input waveguide, the photonic circuit having a first output and a second output; a polarization controller responsive to a polarization input, operation of the polarization controller responsive to the polarization input adapted to affect the polarization of the photons in the input waveguide; a first detector coupled to the first output and adapted to detect a first signal at the first output; a second detector coupled to the second output and adapted to detect a second signal at the second output; The PUF system comprises: determining the PUF signature at the first time by providing a first polarization input to the polarization controller at a first time, detecting the first signal at the first time, detecting the second signal at the first time, and determining the PUF signature based on the first signal at the first time and the second signal at the first time; determining the PUF signature at the second time by providing the first polarization input to the polarization controller at a second time, detecting the first signal at the second time, detecting the second signal at the second time, and determining the PUF signature based on the first signal at the second time and the second signal at the second time; A PUF system adapted to perform the following:

Images