Methods, protocols, and apparatuses for quantum physical unclonable functions

Abstract

A method for authentication between a plurality of communication parties is disclosed. The authentication can be performed by means of each communication party possessing a device with a physically unclonable function. To achieve this, the devices have a known quantum correlation which can be used in combination with entangled photons to verify the identity of the devices.

Description

[0001] Statement regarding federally funded research:

[0002] none

[0003] Cross-references to related applications

[0004] This application claims priority to U.S. Provisional Patent Application No. 63 / 224,820, filed July 22, 2021, the entire disclosure of which is incorporated herein by reference. Technical Field

[0005] This invention relates to information security, and more particularly to a quantum physics-based no-cloning function (QPUF) protocol for device authentication, identification, verification, secure communication, and proof of existence. Background Technology

[0006] The methods of storing secret information using digital memory in modern communications cannot be proven unconditionally secure, as these devices can be altered, forged, or stolen. Therefore, security is not guaranteed when communication nodes identify themselves by providing "secret knowledge" rather than "physically presenting their irreplaceable uniqueness." An emerging technique for verifying device integrity and authenticity is to embed physically unclonable functions (PUFs) into hardware to act as "fingerprints." PUFs derive their inherent randomness from micrometer- or nanometer-scale sensitive manufacturing processes, such as threshold voltage mismatches in transistors (i.e., SRAM PUFs), the physical orientation of accelerometers to different electrostatic pulses (MEMS PUFs), or optical interactions in chaotic silicon microcavities. This approach means that, given different inputs to a PUF device, different outputs will not only be unique and repeatable but also non-absolute. In other words, PUFs provide inexpensive, easily evaluated, but unpredictable one-way functions. Furthermore, due to uncontrollable errors in the manufacturing process, even for the creator of the PUF, the task of reproducing the same PUF is considered impractical.

[0007] The conventional approach used for PUF protocols employs challenge-response pairs (CRPs), where the response of each PUF device is measured given different input challenges to generate one or more CRPs at the manufacturer. A list of CRPs is securely stored, treated as a "codebook" for each device. During the authentication process, if the challenge is repeated and its corresponding response matches a response in the "codebook," the device is successfully authenticated. However, if an adversary gains access to the CRP information, PUF device authentication is no longer secure, as the adversary can respond to queries without applying a challenge to the PUF. Therefore, protecting the CRP database from this type of digital emulation attack is a challenge for this approach. Another type of attack occurs when an adversary has physical access to a PUF device; even if they cannot replicate it, they can still study the device and gather some CRP information for further attacks. Furthermore, the conventional PUF protocol is vulnerable to machine learning attacks. Even for strong PUF devices that generate a large number of CRPs (where each CRP is used only once), access to the device still gives an adversary the opportunity to use machine learning to predict unknown responses from the known set of CRPs they have acquired.

[0008] There is a known method for implementing device verification that is remote and independent of the confidentiality of a database known as a quantum readout (PUF). However, this protocol is vulnerable to quantum simulation attacks. Furthermore, the quantum readout PUF requires a large amount of CRP memory, which is inconvenient for devices with limited memory. Another drawback of this protocol is its reliance on trusted devices. Summary of the Invention

[0009] The method disclosed in this paper aims to provide a PUF protocol that is immune to digital simulation attacks, machine learning attacks, quantum computer attacks, and CRP database attacks.

[0010] The disclosed embodiments take different approaches and provide unconditionally secure methods based on quantum physics, including quantum entanglement and quantum superposition. This invention can be used as a next-generation authentication technology for credit card use, banking systems, telecommunications, and more.

[0011] Traditionally, during the authentication process, the prover must demonstrate the uniqueness of a device that matches information in the verifier's known CRP codebook. However, this protocol redefines the meaning of successful verification / authentication by assembling a unique signature from the correlations obtained from the outputs of physical one-way functions from all communicating parties.

[0012] For example, during manufacturing, measurements are performed on PUF A, PUF B, and PUF C to extract correlation information between them based on quantum entanglement, thereby creating measurement results in the form of signatures AB, AC, and BC. These signatures are stored in a public database and are known to all parties, thus eliminating the need for a secure database. By completely eliminating the need for any private codebook, this invention eliminates security vulnerabilities in conventional PUF protocols.

[0013] The three PUF devices (PUF A, PUF B, and PUF C) are then distributed to users Alice, Bob, and Charles, respectively. To perform the mutual authentication process, Alice and Bob publicly perform a correlation measurement to construct a unique signature between them. If this signature matches signature AB in the database, authentication is successful. Similarly, when Alice wants to authenticate herself to Charles or vice versa, they again perform a correlation measurement to construct a unique, publicly known signature between them, and then compare it to AC. Therefore, this method allows each party to authenticate itself simultaneously to each other and to the public. Figure 1 An example of a QPUF database is shown, which is essentially a storage of different QPUF schemas corresponding to its specified QPUF. In this embodiment, the database may be publicly stored and accessed.

[0014] The disclosed invention provides a method for unconditionally ensuring QPUF security, wherein the device signature is based on a correlation measurement of quantum complementary variables (e.g., photon arrival time and carrier frequency) following the interaction of entangled photons with optical chaos. In one embodiment, utilizing energy-time degrees of freedom, the uniqueness of a device pair is defined as the intensity correlation of entangled photons in frequency and / or arrival time. The protocol of this disclosed invention does not rely on a trusted device to complete a successful authentication.

[0015] One embodiment of the present invention relates to a laser source, an entangled photon source, a single-photon detector, a photon chaotic chip that provides a physical one-way function, a photon arrival time measurement device, a photon frequency measurement device, and a publicly available database of related measurement results.

[0016] In this embodiment, authentication can be performed through the following steps: generating a set of entangled photons; transmitting each entangled photon to a corresponding device within the device, wherein each device embodies a corresponding physically unclonable function, and together they have a known quantum correlation signature; recording responses from each device based on its corresponding physically unclonable function; repeating the above steps to establish a verification pattern from the recorded responses; comparing the verification pattern with the known quantum correlation signature; and verifying whether authentication has achieved a similarity threshold between the verification pattern and the known quantum correlation signature. In this embodiment, the entanglement of entangled photons is performed by periodically turning the entangled photons away from the device for verification purposes.

[0017] In this embodiment, the quantum correlation signature is public knowledge and can be set, for example, by the device manufacturer.

[0018] In this embodiment, the authentication method is performed in a public channel.

[0019] In one embodiment, the quantum correlation signature can be based on quantum complementary variables resulting from the interaction of entangled photons with optical chaos. For example, optical chaos can be provided by a physically non-cloning function nanostructure for each device. In another embodiment, the physically non-cloning function nanostructure can include a chaotic optical transmission medium. In yet another embodiment, the quantum complementary variables can be based on photon arrival time and / or carrier frequency. In yet another embodiment, the quantum correlation signature is defined based on the intensity correlation of entangled photons at frequency and / or arrival time.

[0020] In an embodiment, the authentication method may utilize reference signals continuously transmitted to each device.

[0021] In another embodiment, it is known that quantum correlation signatures are based on one or more of joint spectral intensity, joint temporal intensity, or joint spectral-temporal intensity.

[0022] In yet another embodiment, security can be enhanced by selectively maintaining the confidentiality of at least some of the recorded responses.

[0023] In this embodiment, the recorded response is publicly announced to establish an authentication pattern. Furthermore, by having the sender encode a confidential message into the recorded response and the receiver decode the confidential message from the recorded response, secure communication can be performed simultaneously with authentication. For example, the decoding step can be performed on the recorded response by maximizing the similarity to the authentication pattern when calculating it. Simultaneously, the encoding step can be performed according to a publicly agreed-upon protocol. For this purpose, the publicly agreed-upon protocol may include a finite number of swapping actions. This allows the decoding step to be performed by exhaustively trying all finite number of swapping actions. Attached Figure Description

[0024] To gain a more complete understanding of the invention, reference is made to the following detailed description of embodiments considered in conjunction with the accompanying drawings, wherein:

[0025] Figure 1 This is an example of a QPUF database containing two QPUF schemas;

[0026] Figure 2 This is an example of a joint spectral strength verification mode;

[0027] Figure 3 This is another example of a joint spectrum strength verification mode;

[0028] Figure 4 This is another example of a joint spectral strength verification mode;

[0029] Figure 5 This is yet another example of a joint spectral strength verification mode;

[0030] Figure 6 This is an example of a joint time-intensity verification pattern;

[0031] Figure 7 This is another example of a joint time-intensity verification pattern;

[0032] Figure 8 This is another example of the joint time-intensity verification pattern;

[0033] Figure 9 This is yet another example of the joint time-intensity verification pattern;

[0034] Figure 10 This is a schematic diagram illustrating an example of a two-party QPUF system;

[0035] Figure 11 An example of how a QPUF system can be implemented is shown; and

[0036] Figure 12 Another example of how a two-party QPUF system can be implemented is shown. Detailed Implementation

[0037] The following disclosure is provided to illustrate the general principles of the invention and is not intended to limit the inventive concept contained herein in any way. Furthermore, specific features described in this section may be used in combination with other features described in each of the many possible permutations and combinations contained herein.

[0038] All terms defined herein shall be provided with their broadest possible interpretation, including any implied meanings as indicated by reading the specification and any words assigned to them by those skilled in the art and / or dictionaries, papers or similar authorities.

[0039] Furthermore, it should be noted that, as described herein, the singular forms “a,” “an,” “the,” and “an” include plural indicators unless otherwise stated. Additionally, when used herein, the terms “comprising” and “including” specify the presence of certain features in the embodiment; however, this phrase should not be construed as excluding the presence or addition of additional steps, operations, features, components, and / or groups thereof.

[0040] All examples and conditional language described herein are intended for pedagogical purposes to aid the reader in understanding the principles of the invention and the ideas contributed by the inventors to advance the field, and should be interpreted as not being limited to such specific examples and conditions. Furthermore, all statements herein describing the principles, aspects, and embodiments of the invention, as well as specific examples thereof, are intended to cover their structural and functional equivalents. Additionally, it is intended that such equivalents include both currently known equivalents and those developed in the future, i.e., any elements developed that perform the same function, regardless of their structure.

[0041] To better illustrate the exemplary QPUF protocol according to embodiments of the present invention, the following definitions will be given: Joint Spectral Intensity (JSI), Joint Temporal Intensity (JTI), Joint Spectral Temporal Intensity (JSTI), Challenge-Response Pair (CRP), Quantum Entanglement Process, PUF Nanostructure, Measurement Synchronization, and Threshold Verification.

[0042] JSI refers to the correlation function of two photons measured in their respective spectral states (i.e., the correlation of their carrier frequencies). JTI refers to the correlation function of two photons measured in their respective temporal states (i.e., the correlation of their arrival times). JSTI refers to the correlation function of two photons measured in one spectral state and another temporal state (i.e., the correlation between the arrival time of one and the carrier frequency of the other). CRP refers to the input state that matches the PUF and the expected output state. For the purposes of this disclosure, a quantum entanglement process is any process in which two or more objects undergo inherent quantum nonlocal correlation. The PUF device comprises a PUF nanostructure having inherent defects and / or uncontrollable random characteristics that cannot be replicated by any manufacturing means. Measurement synchronization is the process of synchronizing the timestamps of remote communicators so that JTI, JST, and / or JSTI can be successfully performed. Threshold verification is a test that returns a positive verification result if the number of measurements exceeds a certain threshold.

[0043] Figure 10The diagram illustrates the QPUF protocol. At the manufacturer's location, after entangled photons are sent through different PUF nanostructures to allow for chaotic responses, QPUF CRPs are collected by measuring the JSI, JTI, or hybrid JSTI of the entangled photons. Given a combination of consistent components among the PUF devices (e.g., filters, single-photon detectors, arrival time converters, etc.), the conservation of energy and momentum in the entangled photon generation process ensures invariant correlated patterns of JSI, JTI, and JSTI. During each authentication attempt, these patterns are constructed by collecting different sets of sequences of truly random and uncontrollable data points, based on the local measurements of photons by each communicating party after interacting with the individual's PUF, due to quantum superposition. As a result, the JSI / JTI / JSTI created after the entangled photons pass through the PUF form unique joint patterns, and all measurement data is one-off. This feature allows a CRP database generated at the manufacturing point to be stored in a publicly accessible manner without compromising security. Therefore, unlike conventional PUFs where measurements are taken at the manufacturing point to generate many CRPs, the QPUF protocol requires only one pattern.

[0044] The proposed protocol can be used regardless of the nanostructure or physical basis of the PUF. PUF devices can have any type of structure that provides highly complex and unpredictable photonic chaotic responses, yet are reproducible given the same input. Such nanostructures have been designed and have shown to satisfy the necessary PUF properties. In some embodiments, a chaotic optical transmission medium can act as a PUF for security authentication purposes.

[0045] To align synchronous measurements, the communicating / verifying parties can use REF IDs. For the purposes of this disclosure, a REF ID is a reference identifier and / or pulse index representing the time slot number of a detected photon, whether detected in time or frequency. To enable a common REF ID, all participants in the communication pool are synchronized to a common reference signal to identify the time slot of their detected photons. Such a reference signal can be provided through the same optical communication channel (i.e., a quantum optical communication channel) used for allocating entangled photons. Such a channel can utilize the same existing telecommunications fiber optic infrastructure. Furthermore, communication channels are expected to become widespread in the future due to the anticipated adoption of quantum information technology. In some embodiments, the reference can be in the form of a train of optical pulses separated and distributed via optical fiber or free-space communication. The system should be configured such that at most one entangled photon pair can be created within each cycle of the reference pulse. Therefore, if a communicating party receives photons entangled with photons of others, they will have a high probability of being detected in the same time slot. Verification modes are formed by a number of quantum states given in terms of frequency or time. For this purpose, REF IDs serve as a synchronization mechanism, enabling the identification of which photons belong to which entangled states.

[0046] The source of entangled photons can be a verifier, a third party, a service provider, or the public. The entanglement of photons should be verified before and during their use in the QPUF. This can be done between user A and user B in a manner similar to entanglement verification during typical quantum key distribution protocols. It can also be done by a publicly disclosed verifier. In an exemplary embodiment, entanglement verification is performed by bypassing the PUF and having user A and user B each construct JSI and JTI. This verification leverages the fact that only truly entangled photons can simultaneously produce inseparable JSI and JTI. Such JSI and JTI can be publicly known knowledge. JSI and JTI are independent of transmission loss but depend on the characteristics of the source and the resolution of the measurement device employed.

[0047] To prevent dishonest parties from cheating during entanglement verification, each party can choose to share only about half of its photon count results with the other party, reserving the other half for verification purposes. For security reasons, in some embodiments, QPUF continues only if both parties agree to entanglement verification. In an exemplary embodiment, such verification is performed during the QPUF process by bypassing the PUF using passive or active switches. To this end, user A and user B can randomly select some pulses to bypass the PUF and use them solely for entanglement verification purposes.

[0048] Assuming entanglement verification is successful, users A and B can publicly announce their reference IDs. They will first compare IDs and select those that match (i.e., IDs that appear in both users A's and users B's lists). They will then divide the matching IDs into two roughly equal subgroups. User A will publicly report his / her measurements (e.g., time or frequency) for all reference IDs within one subgroup, and user B will report the other subgroup. This reporting arrangement can be performed on a public channel. Once these results are published, users can examine the published measurements with their own secret, unpublished results by comparing the published measurements to a public schema (i.e., a database signature).

[0049] To complete the final verification, the similarity between the publicly available database signature and the measured (i.e., calculated) signature is calculated. Verification succeeds if the similarity is above a set threshold, and fails if it is below the threshold. The threshold is determined by the properties of the PUF device being used, ensuring that no alternative PUF device can be used to create signatures above the threshold. The threshold requires a certain amount of photon count statistics to suppress inherent photon count noise and possible detector dark counts.

[0050] Losses during transmission can affect the length of the verification process. Entangled photons must be sent continuously until photon count statistics are obtained, allowing sufficient information to be compared with unique identifiers / responses in a public database.

[0051] Example 1:

[0052] For simplicity, the following discussion will assume that the authentication process involves only two parties; however, it should be noted that the method of the present invention can also be applied to perform authentication simultaneously with more than two parties. This can be achieved by using higher-order nonlinearities, for example, by creating three entangled photons for three parties, four entangled photons for four parties, and so on. Figure 10 An example of a QPUF protocol between Party A and Party B is shown. The following are the steps of a QPUF protocol where Party A and Party B want to authenticate each other, or when A or B wants to prove their identity to the public. In other embodiments, Party A can prove its identity to Party B, and vice versa.

[0053] Step 1: A and B publicly announce that they want to perform certification on each other.

[0054] Step 2: Send entangled photons to parties A and B.

[0055] In this step, the entangled photons on both sides are randomly switched to bypass the PUF and directly enter the JSI, JTI, or JSTI measurements. The event of entangled photons bypassing the PUF will be publicly announced, and JSI, JTI, and JSTI results will be constructed to verify their entanglement. As a security feature, authentication can be aborted if verification fails.

[0056] Step 3: A and B measure their entangled photons in terms of time or frequency, respectively. Figure 10 This is an example of a two-party QPUF protocol system setup. As mentioned earlier, photon properties can be measured in time or frequency. The measurement resolution affects the number of pixels that must be agreed upon by all communicating parties in the authentication mode for successful authentication.

[0057] Step 4: Both Party A and Party B announce the REF ID of their photons, followed by their measurement results.

[0058] Step 5: Construct a verification pattern in the public channel using the response of each PUF device. In some embodiments, the information from the laser and entanglement sources can be described by the following equation:

[0059]

[0060] in, It is an entangled photon state, which can be the product of the spectral profile of the pump photon, the phase matching of the nonlinear medium, filters, etc. This information is publicly announced, stored, and kept consistent during the database signature creation and authentication process. From the database, p_1(ω_s) and p_2(ω_i) are the PUF responses of each communication end. Therefore, the joint spectral intensity verification mode... It is exported and used as a unique "fingerprint" between party A and party B. Similarly, it can be constructed... Using the time domain or by constructing or Use a combination of time and frequency domains to form other verification patterns. Figure 1 An example of a verification mode is shown, where grayscale coloring represents intensity (e.g., temporal intensity, spectral intensity, etc.).

[0061] Step 6: The public channel collects measurement results from both A and B to establish a verification pattern. Due to the superposition property of quantum mechanics, photons are simultaneously in all states before measurement, and the results are inherently random, as they can also collapse into any possible state. Even if each successful authentication returns the same verification pattern, the measurement results from each series from A and B are random each time. Therefore, knowledge of the verification pattern does not provide any useful information for an adversary to attack, deceive, or execute any brute-force search methods.

[0062] Step 7: Compare the authentication pattern with the authentication pattern stored in the public database to obtain the difference. If this difference is below the error threshold, authentication is successful.

[0063] The system prerequisites for guaranteeing unconditionally secure authentication protocols will now be discussed. First, the PUF device must meet all PUF requirements: physically uncopyable, providing reproducible responses, and providing unique responses. However, it need not be unpredictable. For example, machine learning or quantum computer attacks can only predict the responses of a PUF device. Simultaneously, successful authentication or verification depends on joint measurements, which are truly random through quantum mechanics. Second, the pump photons must be kept at low power levels to avoid generating multiple pairs of entangled photons. Third, witnesses to entanglement must be verified during the process. Finally, the number of possible photon states in time or frequency must be large enough to create a large number of potentially unique identifiers to prevent different PUF devices from returning the same jointly unique identifier. Given n possible states for A, m possible states for B, and k possible joint intensity levels that can be explicitly resolved (given sufficient statistics on the number of detected photons), the total number of potentially unique identifiers is P = k^((n x m)). If k = 100, as is the case with the typical coincidence ratio (CAR) used in quantum key distribution systems, and n = m = 5, then P = 10^50, which is approximately equal to the total number of particles on Earth.

[0064] Example 2:

[0065] In some applications, the same QPUF authentication system can be used for both authentication and secure communication. In one embodiment, user A will shuffle / swap / modify the index of his / her measurement results before announcing them. User B will attempt to deshuffle / deswap / demodify the results to maximize the similarity between the measured signature and the database signature. If the maximum similarity is above a threshold, user A's identity is verified. Simultaneously, user B will know how user A shuffled / swap the measurement results, thus allowing user A and user B to securely transmit certain information.

[0066] As a simplified example, according to a publicly agreed-upon indexing protocol, User A's original measurement results are (1,3,4,3,2,4), each representing time or frequency. User A wants to prove his / her identity to User B by sending the message "11" or "00". To do this, if the message is "11", User A will publicly announce that he / she will swap indexes 1 and 3, and if the message is "00", he / she will swap 1 and 4. According to this protocol, User A will announce the measurement results as (3,1,4,1,2,4). After receiving User A's measurement results, User B will try both swap actions and combine them with User B's own measurement results to see if any actions give a similar pattern and pass a similarity threshold test. If the test passes, User B will not only verify User A's identity but also obtain the correct message.

[0067] There are many other ways to encode information. However, such information needs to be well-defined and not overly complex, so that user B can exhaustively try all possible encoding protocols.

[0068] It will be understood that the embodiments described herein are merely exemplary, and many variations and modifications can be made by those skilled in the art without departing from the spirit and scope of the invention. All such variations and modifications are included within the scope of the invention.

Claims

1. A method for security authentication, comprising the following steps: i) Generate multiple entangled photons; ii) Transmit each of the plurality of photons to a corresponding device in at least one of a pair of devices, each of the pair of devices embodying a corresponding physically unclonable function, the physically unclonable function of the pair of devices having a known quantum correlation signature, the quantum correlation signature being defined based on the intensity correlation of entangled photons in frequency and / or arrival time; iii) Record the response from one of the devices based on the corresponding physical non-clonable function of the device; iv) Record the response from the other device based on the corresponding physically unclonable function of the other device; v) Repeat steps i) - iv); vi) Establish a verification pattern from the recorded response, the verification pattern being formed by a number of quantum states given in terms of frequency or time; vii) Compare the verification pattern with the known quantum correlation signature; as well as viii) Based on the comparison step, verify whether the similarity threshold between the verification mode and the known quantum correlation signature has been achieved.

2. The method of claim 1, further comprising the step of verifying the entanglement of the plurality of said entangled photons.

3. The method as described in claim 2, wherein, The verification step is performed by periodically redirecting entangled photons away from the pair of devices for verification purposes.

4. The method of claim 1, wherein, The quantum correlation signature is known public knowledge.

5. The method of claim 4, wherein, The known quantum correlation signature was established by the manufacturer of the pair of devices.

6. The method of claim 1, wherein, Perform step v) in the public channel.

7. The method of claim 1, wherein, The quantum correlation signature is based on quantum complementary variables resulting from the interaction of entangled photons with optical chaos.

8. The method of claim 7, wherein, The optical chaos is provided by the physically unclonable function nanostructure of each of the pair of devices.

9. The method of claim 8, wherein, The physically unclonable function nanostructures include chaotic optical transmission media.

10. The method of claim 7, wherein, The quantum complementary variables are based on photon arrival time and / or carrier frequency.

11. The method of claim 7, wherein, The quantum correlation signature is defined based on the intensity correlation of entangled photons in frequency and / or arrival time.

12. The method of claim 1, further comprising the step of continuously transmitting a reference signal to each of the pair of devices.

13. The method of claim 1, wherein, The known quantum correlation signature is based on one or more of joint spectral intensity, joint temporal intensity, or joint spectral-temporal intensity.

14. The method of claim 1, further comprising the step of selectively maintaining the confidentiality of at least some of the responses from step iii) and / or step iv) for security purposes.

15. The method of claim 1, wherein, The recorded response is publicly announced in order to complete step vi).

16. The method of claim 15, further comprising the steps of encoding a confidential message into the recorded response and decoding the confidential message from the recorded response.

17. The method of claim 16, wherein, The decoding step is performed on the recorded response by maximizing the similarity to the verification pattern when calculating the verification pattern.

18. The method of claim 17, wherein, The encoding steps are performed according to a publicly agreed-upon protocol.

19. The method of claim 18, wherein, The publicly agreed-upon agreement includes a limited number of exchange actions.

20. The method of claim 19, wherein, The decoding step is performed by exhaustively trying all of the finite number of swap actions.

21. A system for performing verification, the system being configured to perform the method of claim 1, the system comprising: Laser source; Entangled photon sources; One or more single-photon detectors; One or more photonic chaotic chips that provide physical one-way functions; One or more photon arrival time measuring devices; One or more photon frequency measurement devices; and Public databases of correlation measurement results.

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