Method for realizing physical unclonable function (PUF) based on window comparator

Abstract

The invention provides a method for realizing a physical unclonable function (PUF) based on a window comparator, and belongs to the field of physical unclonable function design. The response bit of the physical unclonable function is obtained by judging the relative proximity degree of two physical quantities X1 and X2 to be compared, when the absolute value of the difference between the two physical quantities is smaller than or equal to a threshold value delta, the output response bit is' 0 '(or bit' 1 '), and when the absolute value of the difference between the two physical quantities is larger than the threshold value delta, the output response bit is' 1 '(or bit' 0 '). Result swing and bit flipping of noise and rising and falling of absolute magnitude comparison are avoided; according to the method, the security of the PUF is improved, the bit error rate is obviously reduced, the modeling resistance is safer, the response bit nonuniformity caused by factors such as drifting in the PUF can be eliminated, or the uniformity of the response bit is purposefully regulated and controlled, and the more flexible PUF response bit regulation and control capability is realized on the premise of lower hardware cost.

Description

Technical Field

[0001] The present invention relates to the field of physical unclonable function design, and in particular to a physical unclonable function (PUF) design based on a window comparator circuit. Background Art

[0002] In today's connected world, the widespread deployment of various IoT devices at the edge has driven a massive demand for cloud-edge interaction. However, most of these edge devices are deployed in unmanned environments, such as streets, warehouses, courtyards, and unmanned facilities. Because these environments are vulnerable to external attacks and interference, devices distributed across these unmanned environments become the weakest and most vulnerable nodes in the entire IoT security system. To address potential security risks, the use of physically unclonable functions (PUFs) has been proposed for applications such as user authentication and key generation. As a physical entity, a PUF can perform externally undetectable and mathematically unpredictable black-box processing on a given input (a challenge signal, C), transforming it into an output (a response signal, R). The PUF's input-output mapping (a challenge-response pair, CRP) serves as a "fingerprint" of the physical entity and can be used to verify the legitimate identity of the device or user. In the actual verification process, the CRP is binary. The PUF first registers with the cloud in a secure environment: the cloud sends a sufficient number of different challenges, collects the responses returned by the PUF, and establishes a CRP library for the PUF entity on the cloud. In an insecure environment, before the PUF requests to establish communication with the cloud, the cloud randomly selects a small number of challenges from the established CRP library and sends them to the PUF. The cloud then compares the response results of the PUF entity with the existing results in the library. If the match exceeds a judgment threshold (such as 95%), the PUF is considered to be legitimate.

[0003] Because the "fingerprint" is determined solely by physical differences and manufacturing variations within the PUF, and because it is tamper-resistant, unmodelable, collision-resistant, and reproducible, PUF is widely considered the most suitable solution for addressing edge security needs. Researchers have proposed traditional CMOS device solutions, such as Arbiter-PUFs based on delay arbiters and RO-PUFs based on ring oscillators, as well as novel non-volatile NVM device solutions, such as RRAM-PUFs based on resistive random access memory, MRAM-PUFs based on magnetic random access memory, and FeFET-PUFs based on ferroelectric transistors.

[0004] However, since the above PUF generally relies on a comparator to generate the final 1-bit response signal when generating CRP, the two physical quantities input to the comparator are generally analog quantities (current, voltage, etc.), and in the PUF, all kinds of random physical quantities X obey the normal distribution X~N(n,p) rather than the uniform distribution X~U(a,b). Therefore, the random physical quantities have a higher statistical probability of tending to the average value μ=E(X)=np, and the variance σ 2 =np(1-p) is small, the two random physical quantities being compared are quite close, which can lead to reliability issues such as PUF being easily interfered with. Specifically, the rail-to-rail characteristics of the comparator itself can amplify the influence of noise in the previous stage, causing the comparator output to change under non-ideal conditions such as external signal interference and environmental changes. This is known as a response bit flip, resulting in the inability to stably reproduce CRP and the failure of user identity verification, among other serious reliability issues. Therefore, achieving a more reliable PUF circuit design with a low bit error rate is of great significance. Summary of the Invention

[0005] To address the above-mentioned problems in the existing technologies, this paper proposes a method for implementing a low-error-rate physically unclonable function (PUF) based on a window comparator circuit, achieving a more stable CRP generation method at a lower hardware cost. Compared to traditional CMOS-based or NVM-based PUFs, this paper overcomes the need to use a comparator to compare two physical quantities with similar values, replacing absolute size comparisons with relative range comparisons, significantly improving the stability of the PUF response bits.

[0006] The technical solutions of the present invention are as follows:

[0007] A method for implementing a physical unclonable function (PUF) based on a window comparator circuit is characterized in that a response bit Response of the physical unclonable function is obtained by judging the relative proximity of two physical quantities X1 and X2 to be compared. When the absolute value of the difference between the two physical quantities is less than or equal to a proximity threshold δ, that is, δ≥X1-X2≥-δ, the output response bit is "0" (or bit "1"). When the absolute value of the difference between the two physical quantities is greater than the proximity threshold δ, that is, X1-X2>δ or X1-X2<-δ, the output response bit is "1" (or bit "0"), thereby avoiding the result swing and bit flipping of the absolute magnitude comparison under noise and fluctuation. The method for implementing a PUF using a window comparator circuit includes the following steps:

[0008] 1) Two different random physical quantities X1 and X2 are obtained by inputting the challenge signal and the internal fluctuation of the PUF;

[0009] 2) These two physical quantities are used as the two inputs of the window comparator and the threshold voltage V ref For comparison, V ref The size of is δ;

[0010] 3) The window comparator outputs a "1" or "0" response bit according to two different situations: the two inputs are close (δ≥X1-X2≥-δ) and the two are far away (X1-X2>δ or X1-X2<-δ).

[0011] Furthermore, the proximity threshold δ is a dimensionless number that is always greater than zero. Its value is determined based on the probability of "1" and "0" bits in the PUF's output response. Based on the actual ratio of "1" and "0" bits in the PUF's output response, δ can be adjusted until the ratio meets the actual requirements of the PUF application (in most cases, the ratio is required to be 50%, that is, the proximity threshold is adjusted to ensure that the output probabilities of "1" and "0" are roughly the same).

[0012] Furthermore, when the two different random physical quantities X1 and X2 obtained by inputting the challenge signal and the internal fluctuation of the PUF are voltages, X1 and X2 are first input to the positive and negative input terminals of the differential operational amplifier respectively. At this time, the output of the operational amplifier is proportional to X1-X2; then the output is simultaneously input to the positive input terminal of comparator 1 and the negative input terminal of comparator 2 in the window comparator, and a positive threshold voltage V is input to the negative terminal of comparator 1. ref , and the negative threshold voltage -V is input to the positive terminal of comparator 2 ref Finally, the outputs of comparator 1 and comparator 2 are connected as the final response bit output port; therefore, the two comparators will compare X1-X2 with the threshold ±V ref Two absolute size comparisons are performed to implement indirect range proximity comparison and obtain more stable output response bits.

[0013] Furthermore, when the two different random physical quantities X1 and X2 obtained by inputting the challenge signal and the internal fluctuation of the PUF are currents, they are first fed through two resistors with the same feedback resistance R f After the trans-impedance amplifier (TIA) converts the current signal into a voltage signal, X1 and X2 are input to the positive and negative input terminals of the differential operational amplifier respectively. At this time, the output of the operational amplifier is proportional to X1-X2; the output is then input to the positive input terminal of comparator 1 and the negative input terminal of comparator 2 in the window comparator at the same time, and the positive threshold voltage V is input to the negative terminal of comparator 1. ref , and the negative threshold voltage -V is input to the positive terminal of comparator 2 refFinally, the outputs of comparator 1 and comparator 2 are connected as the final response bit output port; therefore, the two comparators will compare X1-X2 with the threshold ±V ref Two absolute size comparisons are performed to implement indirect range proximity comparison and obtain more stable output response bits.

[0014] The technical effects of the present invention are as follows:

[0015] 1. This invention is fundamentally different from existing PUF circuits based on current-sensing amplifiers or voltage comparators. It utilizes the characteristics of a window comparator to implement relative range comparison, avoiding the need to frequently compare the absolute values ​​of two similar values ​​in traditional PUF designs and resolving the reliability issue of response bit flips caused by absolute comparison.

[0016] 2. The proximity comparison scheme proposed in this invention helps improve the security of PUFs. This is because the results of absolute comparison can be used to model the PUF. For example, if X1>X2, X2>X3, then X1>X3, which could potentially pose a security risk. However, proximity comparison further conceals information about magnitude relationships, making it impossible to infer proximity relationships of unknown random physical quantities based on existing proximity results. This significantly reduces the bit error rate and provides greater security against modeling.

[0017] 3. The window comparator for the adjacent comparison of the present invention can freely set the threshold voltage by changing V ref The size of can effectively control the proportion of "1" and "0" bits in the output response bits, which can be further used to eliminate the response bit unevenness caused by factors such as drift in the PUF, or to purposefully control the uniformity of the response bits, achieving more flexible PUF response bit control capabilities at a lower hardware cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0019] Figure 1 Schematic diagram of the principle of physical unclonable function PUF;

[0020] Figure 2 This is a schematic diagram of the circuit design for absolute comparison using a comparator in a common PUF.

[0021] Figure 3 Schematic diagram of the unstable bit distribution corresponding to absolute comparison and adjacent comparison;

[0022] Figure 4This is a schematic diagram of a window comparator circuit structure provided according to an embodiment of the present invention, which is composed of a transimpedance amplifier, a differential operational amplifier, and a window comparator module, and implements a proximity comparison operation between two input currents.

[0023] Figure 5 The reliability simulation results of the PUF achieved through absolute comparison and the reliability simulation results of the PUF achieved through proximity comparison using the window comparator circuit proposed in the present invention are shown. DETAILED DESCRIPTION

[0024] The present invention will be further clearly and completely described below through specific embodiments, with reference to the accompanying drawings. Although specific embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. Rather, these embodiments are provided to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0025] Figure 1 This diagram illustrates the operation of a physical unclonable function (PUF). As a physical entity, it processes the input challenge signal and converts it into a response signal for input. The PUF's challenge-response pair (CRP) can be used as its unique identification code for subsequent hardware security requirements. The complexity of PUF design makes it difficult to predict and model the CRP relationship. Furthermore, the CRP relationships between PUFs of the same type are distinct and unique, ensuring the collision resistance of the CRP relationship as a PUF fingerprint.

[0026] Common PUF circuit designs such as Figure 2 As shown, the input challenge vector interacts with the unpredictable fluctuations inside the PUF (such as resistance fluctuations) to obtain multiple random physical quantities (such as current, voltage, etc.), and a selector randomly selects two of them for size comparison, and directly outputs a response bit "1" or "0" based on the absolute size. Although this method is simple and intuitive, since the two physical quantities to be compared are close, when the PUF environment changes or there is large external noise interference, the original size relationship will be reversed, resulting in a flip of the response bit and a higher bit error rate. Figure 4 The bit error rate caused by this absolute size comparison scheme is shown in (a) and (b) of the Monte Carlo simulation. The average bit error rate in 1000 simulations is 4.61%, and in the worst case it reaches 6.5%, which will bring obvious PUF reliability problems. The origin of this problem can be seen from Figure 3 (a) Understand. Assume that the current of the two columns selected by the column selector MUX is I A and I B , the expected on-state current of the device at the read voltage is Ion , the number of devices in the on state in one column is N, and the number of devices in the on state in the two columns selected by the selector MUX is N A and N B When the switching ratio is large enough, the difference between the two currents of the comparator's positive and negative inputs is:

[0027] ΔI=I A -I B =(N A -N B )I on

[0028] Since the number of devices in the on state in a column N can be considered as the sum of the results of an independent random experiment for each device in n rows, N follows a binomial distribution. When the array size n is large, the normal distribution approximation is μ=E(X)=np,σ 2 =np(1-p). Therefore, in the formula (N A -N B )~N(0,2np(1-p)) obeys normal distribution, where p=0.5, Figure 3 (a) in (N A -N B ) is represented by the horizontal axis (X1-X2), and its distribution ΔI satisfies ΔI~N(0,2np(1-p)), with the mean located at X1-X2 = 0. When n is small, the variance is small, and many currents to be compared are located near the mean of the normal distribution, resulting in a higher proportion of unstable response bits. Figure 3 The proximity comparison in (b) avoids this problem. In this case, the current to be compared is located away from the mean value with the highest normal distribution density, but is located on both sides with lower probability. In this case, the two physical quantities to be compared are less likely to be close to each other. The window comparator will generate a response bit based on proximity (within the range defined by the two positive and negative thresholds) or distance (outside the range defined by the two positive and negative thresholds), avoiding the comparison of neighboring values ​​and improving the reliability of the PUF.

[0029] Further, in Figure 3 In (b), the value of the proximity threshold δ can be adjusted according to the ratio of "1" and "0" output by the PUF, or it can be solved by looking up a table based on the mathematical principle of normal distribution. Since the probability of each unit in the array being in the on state and the off state is 50%, (N A -N B )~N(0,2np(1-p)) obeys normal distribution, which can be transformed into standard normal distribution according to Z=(X-μ) / σ. The N corresponding to the 25% and 75% integral intervals can be obtained by looking up the Z-score table. A -N B The neighboring threshold is located at (where p = 1 / 2 is the probability that each unit in the array outputs "1", Z 0.75,N(0,1) is a standard normal integral constant), and the proximity threshold set at this position ensures that the proportions of the middle and the left and right sides are both 50%, that is, the uniformity and symmetry of the output response bits "1" and "0".

[0030] exist Figure 4 (a) shows an embodiment based on current window comparison. After the PUF outputs the simulated current value, two currents to be compared I are obtained through the selector MUX. A and I B , they serve as the input of a pair of identical transimpedance amplifiers TIA, whose non-inverting input terminals are grounded. The current can be proportionally amplified to V A =R f I A and V B =R f I B , and then perform subtraction and amplification operations through the subsequent differential operational amplifier to obtain V out =α(V A -V B )=αR f (I A -I B ). Finally, the two voltage comparators of the window comparator module are respectively compared with the positive and negative threshold voltages ±V ref By absolute comparison, we get V out With V ref The comparison results and V out with -V ref The comparison result of the two comparators can be further short-circuited to achieve the "OR" operation. out |=α|V A -V B |>V ref , that is, V out >V ref or V out <-V ref , there is always a high level output in comparator 1 or 2, which causes the final window comparator output to be pulled high, that is, the response bit is "1"; if |V out |=α|V A -V B |≤V ref , that is, V ref ≥V out ≥-V ref , comparator 1 or 2 both output a low level, resulting in the final window comparator output being pulled down to a low level, i.e., the response bit is "0". Figure 4(b) shows an embodiment based on voltage window comparison. Compared with the embodiment based on current window comparison, it omits the transimpedance amplifier and directly compares the proximity relationship of two voltages.

[0031] Since the threshold voltage V ref The embodiment of the present invention can flexibly adjust V according to the needs. ref The size of the output response bits can be further adjusted to control the ratio of "1" and "0" (for example, 60% or 75% of the output "1"), thus avoiding PUF response uniformity issues. At the same time, proximity comparison blurs the magnitude relationship between the two physical quantities, making it impossible to infer the proximity of X1 and X2 or X2 and X3 from the proximity of X1 and X3, thus avoiding potential security risks such as modeling attacks that PUFs may face.

[0032] Figure 5 (c) and (d) demonstrate the bit error rate brought about by the neighboring comparison scheme of the embodiment of the present invention through Monte Carlo simulation. The average bit error rate in 1000 simulations is 0.65%, and in the worst case it is only 1%. Compared with the absolute comparison scheme, the bit error rate is reduced by 7.1 times and 6.5 times, respectively, significantly improving the CRP reproducibility of the PUF and the stability of the response bit.

[0033] This embodiment fully and in detail explains the principles and methods of implementing a proximity comparison PUF based on a window comparator. Compared with PUFs based on absolute comparison, it has a significantly lower bit error rate and greater anti-modeling security. It also achieves more flexible PUF response bit control capabilities at a lower hardware cost.

[0034] The window comparator circuit implemented in the PUF of the present invention can further perform pairwise comparisons between the input challenge signal and multiple different random physical quantities obtained from the PUF's internal fluctuations. This can include simultaneously outputting multiple response bits for CRP generation through parallel comparison, or converting multiple response bits into a single response bit through a step-by-step comparison process for use in the PUF's CRP generation process. This invention proposes a CRP generation method using a window comparator circuit to implement proximity comparison. PUF designs using other window comparator circuits to implement proximity comparison are also within the scope of the present invention.

[0035] Finally, it should be noted that the purpose of disclosing the embodiments is to facilitate a further understanding of the present invention. However, those skilled in the art will appreciate that various substitutions and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the contents disclosed in the embodiments, and the scope of protection claimed by the present invention shall be determined by the scope defined in the claims.

Claims

1. A method for implementing a physical unclonable function PUF based on a window comparator circuit, characterized in that: The response bit of the physical unclonable function is obtained by judging the relative proximity of the two physical quantities X1 and X2 to be compared. When the absolute value of the difference between the two physical quantities is less than or equal to the proximity threshold δ, that is, δ≥X1-X2≥-δ, the output response bit is "0" (or bit "1"), and when the absolute value of the difference between the two physical quantities is greater than the proximity threshold δ, that is, X1-X2>δ or X1-X2<-δ, the output response bit is "1" (or bit "0"); the method comprises the following steps: 1) Two different random physical quantities X1 and X2 are obtained by inputting the challenge signal and the internal fluctuation of PUF; 2) These two physical quantities are used as the two inputs of the window comparator and the threshold voltage V ref For comparison, V ref The size of is δ; 3) The window comparator outputs a "1" or "0" response bit according to two different situations: the two inputs are close (δ≥X1-X2≥-δ) and the two are far away (X1-X2>δ or X1-X2<-δ).

2. The method for implementing a physical unclonable function PUF based on a window comparator circuit according to claim 1, characterized in that: The proximity threshold δ is a dimensionless number that is always greater than zero, and its size is adjusted and determined according to the required ratio of the PUF output response bits "1" and "0".

3. The method for implementing a physical unclonable function PUF based on a window comparator circuit as claimed in claim 2, characterized in that: The proportion of PUF output response bits "1" and "0" is 50% each.

4. The method for implementing a physical unclonable function PUF based on a window comparator circuit according to claim 1, characterized in that: When the two different random physical quantities X1 and X2 obtained by inputting the challenge signal and the internal fluctuation of the PUF are voltages, X1 and X2 are first input to the positive and negative input terminals of the differential operational amplifier, respectively. At this time, the output of the operational amplifier is proportional to X1-X2; then the output is simultaneously input to the positive input terminal of comparator 1 and the negative input terminal of comparator 2 in the window comparator, and a positive threshold voltage V is input to the negative terminal of comparator 1. ref , and the negative threshold voltage -V is input to the positive terminal of comparator 2 ref Finally, the outputs of comparator 1 and comparator 2 are connected as the final response bit output port; therefore, the two comparators will compare X1-X2 with the threshold ±V ref Two absolute size comparisons are performed to implement indirect range proximity comparison and obtain output response bits.

5. The method for implementing a physical unclonable function PUF based on a window comparator circuit according to claim 1, characterized in that: When the two different random physical quantities X1 and X2 obtained by inputting the challenge signal and the internal fluctuation of the PUF are currents, they are first passed through two feedback resistors R f After the transimpedance amplifier TIA converts the current signal into a voltage signal, X1 and X2 are respectively input to the positive and negative input terminals of the differential operational amplifier. At this time, the output of the operational amplifier is proportional to X1-X2; the output is then simultaneously input to the positive input terminal of comparator 1 and the negative input terminal of comparator 2 in the window comparator, and a positive threshold voltage V is input to the negative terminal of comparator 1. ref , and the negative threshold voltage -V is input to the positive terminal of comparator 2 ref Finally, the outputs of comparator 1 and comparator 2 are connected as the final response bit output port; therefore, the two comparators will compare X1-X2 with the threshold ±V ref Two absolute size comparisons are performed to implement indirect range proximity comparison and obtain output response bits.

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