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Abstract
We present an experimental analysis of optical Physically Unclonable Functions enhanced using plasmonic metal nanoparticles in a Silicon on Insulator based integrated structure. We experimentally demonstrate the behavior of possible configurations of simple PUF structures defined only by the nanoparticle distribution. The devices show a promising response when tested with transverse magnetic polarized light. This response offers an easy-to-implement methodology to enhance the behavior of previously proposed optical PUFs. We additionally make a comprehensive analysis of the power, thermal, and polarization stability of the devices for possible side-channels attacks to the systems.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
1.1 Physical One-way functions
One-way functions (OWF) are defined as problems easy to compute but hard to invert. These are essential features for the construction of important cryptographic elements such as pseudorandom generators, message authentication codes, and hashing functions. In information theory, OWFs are based on problems considered to be hard (meaning an algorithm cannot solve them in polynomial time), such as the large prime factorization problem, and most cryptography developments are supported on this concept. Moreover, it has been demonstrated the ability to use complex and unpredictable physical systems as OWF [1–3]. The inherent hardness to make physical copies of such systems grants their classification as Physically Unclonable Functions (PUF).
In electronics, PUFs have been typically implemented using delay lines in circuits that are often configured to form ring oscillators (in which the resonances highly depend on the delay line fabrication) [4], or by using the random behavior of static random access memories [5] or memristors [6]. Optical PUFs (OPUFs), use complex nonlinear behaviors in optical devices to generate physical OWF. In fact, some of the first PUFs developed were optical systems, designed to reflect light in unique hard-to-replicate patterns in currency [7] or to modify its wavefront phase pattern to encode information [1,8]. In the field of integrated optics, modern OPUFs have been experimentally demonstrated using different principles including small non-traditional variations of the device geometry [9], cascaded interferometers [10,11], scattering of light from inhomogeneous media [2], the uncontrollable nature of material growth in heterogeneous structures [12], and non-linear interactions in specialized integrated devices [13]. Of interest in this work, gold nanoparticles (Au NPs) have previously been used for optical authentication as part of phase-encoded structures [14] and to generate polarization-dependent specular patterns for authentication [15,16]. We have previously proposed and numerically studied the application of plasmonic resonance sites on silicon integrated devices to generate PUFs [17]; the present work provides an experimental verification of the latter study.
1.2 Plasmonic Enhanced Optical PUF (peo-PUF)
The concept of enhancing the distinctive response of OPUFs using metal nanoparticles is based on the synergy of two physical phenomena: light propagation in integrated silicon resonators and surface plasmons arising from the metal nanoparticles (NPs) randomly placed along the resonator. Light itself, while confined to a resonance cavity, is more subject to non-linear phenomena such as the Kerr effect, Raman scattering, two-photon absorption, etc., given the high-power density that can be reached inside of the cavity. The presence of metal nanoparticles allows the excitation of surface plasmon polariton (SPP) waves that alter the cavity’s optical behavior based on the specific location of the metal NP. This is a promising characteristic given the difficulty to place the NPs in specific locations on the surface of the disk, and consequently, the probability to fabricate two identical devices is negligible.
Nevertheless, the surface waves in the metal NPs have higher power confinement and not all the light is coupled back to the silicon cavity, instead, it scatters out from the device. This limits the number of particles that can be placed on top of the structure to maintain a measurable response. For illustration, in Fig. 1, we show the mentioned phenomena by placing a 40 nm diameter Au sphere on a disk resonator’s surface. The response was simulated using FDTD in Lumerical.
Fig. 1. a) Transmission spectra of simulation of disk resonator, b) schematic of the disk resonator structure with Au NP, and c) simulated electric field distribution (without NP)
In this work, we test the assumption that the introduction of metal NPs to generate plasmonic resonance centers is sufficient to generate OPUFs. We test this by measuring simple resonating structures with random distributions of minimum amounts of Au NPs. Arguably, the processes cannot be replicated. The addition of Au NPs is sufficient to generate weak PUFs, as described in [18], and exhibits only some of the requirements of a strong PUF. Additionally, testing their behavior against different experimental conditions shows their stability and gives hints into possible side-channels attacks. The simplicity of the selected plasmonic-enhanced silicon structure is used to assert the possibility of expanding the method to generate more unique behaviors. This is in particular useful when more complex systems and interrogation methods are used.
2. Methodology
2.1 Fabrication
OPUFs were fabricated on a silicon on insulator (SOI) wafer using e-beam lithography and reactive ion etching. Fabrication was carried by a third-party foundry (Applied Nanotools Inc., Edmonton, CA). Each OPUF consists of a disk resonator with the diameter specified in Table 1. The inputs and outputs bus waveguides employ either evanescent or direct coupling to inject light to the disk resonator.
Table 1. PUF device characteristics
Disks that use evanescent coupling have a gap of 200 nm and have one input and two output buses, namely the through and drop ports. All bus waveguides have a cross-section of $w = 500\; nm$ by $h = 220\; nm$, and air cladding. At $\lambda = 1550\; nm$, they support one transverse electric (TE) mode with calculated effective and group indices of ${n_{e,TE}} = 2.385$ and ${n_{g,TE}} = 4.42$, respectively; and one transverse magnetic (TM) mode with ${n_{e,TM}} = 1.583$ and ${n_{g,TM}} = 3.527$. Two chips including four copies of each design were tested before and after casting 40 nm Au NPs on top of them. The device's dimensions represent standard sizes used in integrated silicon, as are the dimensions of the Au NPs. Note however that the 40 nm Au NPs are thick enough to generate significant absorption. We set this dimension as an upper boundary to make sure they can be resolved without difficulty during characterization.
The casting of the Au NPs was carried inside a cleanroom facility. The surface of the chip was cleaned with Acetone, Isopropanol, and DI water and dehydrated for 4 minutes at 200°C, then the surface was functionalized with hexamethyldisilazane to increase its adhesion with the NPs. Finally, 1 ml of 40nm Au NPs suspended on a 0.1 mM Phosphate Buffered Saline (PBS) solution was cast on the surface at 70°C for 2 minutes then dried up using nitrogen. The magnification shown in Fig. 2 cannot resolve the individual nanoparticles, yet areas where the NPs form clusters can still be discriminated as encircled in Fig. 2 b).
Fig. 2. SEM images of all tested device configurations. a) 10.5µm disk resonator, b) 30.5 µm disk resonator and c) a 30.5 µm disk resonator with evanescent field coupling.
2.2 Measurements
The wavelength insertion loss of the devices was measured between 1530 and 1570 nm using a tunable laser source (Keysight 8164B) with a 10 mW output power. The transmitted power was measured using an InGaAs-based power meter (Keysight N7744A). The polarization was adjusted using a manual fiber-stress-based polarization controller and fixed as either TE or TM using a standard ring resonator structure as a reference. All devices were measured under standard lab environment conditions (average of 23°C, RH 40-50%) and independent devices were tested in a reduced period to reduce environmental effects on the function behavior. Only the TM polarized input condition is used to characterize the peo-PUF behavior, given that surface plasmon excitation in the upper surface of the silicon structure mainly exists for this mode [19]. All measurements and data processing scrips are available in Dataset 1, Ref. [20]. For illustration, the waveguide mode distribution for both polarization states is plotted in Fig. 3 with a Au NP of 40 nm diameter (simulated using Lumerical MODE).
Fig. 3. Electric field intensity for the TE (left) and TM (right) mode of a waveguide a) without Au NPs and b) with a Au NP in its surface.
In addition to the spectral analysis of the device's responses, we studied the impact of different parameters on its stability, namely thermal effects, input power attenuation, and polarization state as follows:
- • The thermal stability of the device was tested using a thermal controller (Thorlabs TC200) and an inverted thermoelectric cooler (Thorlabs TECF1S) while varying the temperature of the chip from 25°C to 30°C.
- • The input power stability was analyzed by introducing input power losses with a variable optical attenuator (Keysight N7762A). The power was varied between 0dB and -20dB. Measurements were carried with the chip heated to 30°C.
- • The polarization stability was measured using a polarimeter (Thorlabs PAX1000IR2) connected to the device as described in the schematic in Fig. 4(a). The polarization state of the input to the device under test (DUT) is set to TM using a standard ring resonator response and set as a reference state of polarization (SOP) in the polarimeter. Then, the input polarization was rotated in controlled steps until the orthogonal state (TE polarization), in both the azimuthal and the elliptical directions as depicted in Fig. 4(b). The measurements reported correspond to a device of design type 2.
Fig. 4. a) Polarization response test setup with a tunable Laser Source (LS), manual Polarization Controllers (PC), a Polarimeter (PM), and an optical Power Detector (PD), and b) Poincare sphere with the polarization states measured (below 10° from TM, the polarization was measured in steps of 2°, not shown).
The birefringent nature of high-index contrast rectangular waveguides also means they cannot support circular polarization states. However, we still check the two orthogonal trajectories of the polarization transitions to make sure that we cover any possible input polarization state. This includes possible circular intermediate states even if these are decomposed into the TE and TM modes once coupled to the waveguide.
2.3 Data analysis
We analyzed the OPUF behavior using its continuous-wave frequency response to the TM polarization mode. To define Challenge-Response Pairs (CRPs), we built a vector with random permutations of the wavelengths at which the measured spectrum was numerically sampled and built sets of 128 features in length. The different wavelengths at which the response is sampled correspond to the ‘challenge’, and the output amplitude to the ‘response’ of the CRP. The spectral response of the device is subsampled to 1001 samples to reduce the dependence between neighboring responses. This is equivalent to a challenge size and usable space of 210 and 1001 symbols, respectively.
For each device, we test 1000 different CRPs to compute the average device response. Each device behavior was measured in terms of the following metrics, defined in the Supplement 1 and following previous work in optical PUFs [10,17]:
- • Fractional Euclidean Distance (ED)
- • Fractional Loose Hamming Distance (LHD), unless stated otherwise we use a Loose parameter $L = 0.15$
- • Fractional Bitwise Hamming Distance (BHD), extracting 3 bits per CRP.
Evaluation also includes small variations in the measurement conditions, e.g. the lab temperature, and any small shifts in frequency in the overall free spectral range (FSR) of any resonance harmonics. Therefore, we analyze all devices using their raw response and the numerically shifted (in frequency) response to align them so that we optimize the correlation between the two compared spectrums. The correlation coefficients for all OPUFs datasets before and after shifting their spectra for one set of measurements of devices with Au NPs are tabulated in Table 2. Here, the response correlation coefficient of two devices i and $j$, is calculated as
where Ri,k is the optical transmission of the device at a given wavelength λk, N is the number of features, µi is the average transmission of the ith device, and σi is its standard deviation.
Table 2. Correlation coefficients of peo-PUF datasets
As required for a device to work as PUFs, in most cases, a low correlation was found between identical devices. Nevertheless, it is worth noting the observed increment in their cross-correlation after we shift the spectrum. Some of these shifts are as small as 45 pm. This is mostly related to the governing linear resonances of the disks, that are still present in the device response with Au NPs. Note that the spectrum is shifted compared to the first device tested, therefore it is reasonable that some of the correlations decrease between pairs that exclude this device (e.g. ${\rho _{2,3}}$ for design 3). This is a good indication of the linear independence of the response of each devices, despite the common background response for each set. The corresponding covariance values are available in Fig. S1 in Supplement 1.
3. Results
3.1 Inter device response without nanoparticles
Here we compare all combinations of pairs of devices with reference to the same design without nanoparticles. Experiments were performed for both polarization states before and after shifting the spectrum to maximize the correlation between the responses. Figure 5 shows a single pair LHD comparisons for each of the three design types for TE and TM polarizations. Table 3 tabulates the average metrics for all the comparisons; these are equivalent to the uniqueness for the LHD and BHD metrics as defined in the Supplement 1.
Table 3. Average Inter distance metrics with no AU NP enhancement.a
We first investigated the performance of the devices without Au nanoparticles. The computed HD for the TE response is in general low for device designs 1 and 2. This is expected due to the confinement of the mode inside the waveguide that makes it less susceptible to possible noise from changes in the air cladding or imperfections in the walls of the silicon structures. The higher HD for the TM mode is a direct consequence of the opposite case, given the higher intensity of the mode located on the surface of the waveguides. In contrast, device design three shows the opposite behavior; this results from the higher evanescent field coupling between the waveguide and the resonant cavity. The lower coupling of the TE mode means a lower signal-to-noise ratio, whereas, for the TM mode, the characteristic response of the device is highly dependent on the well-coupled resonance frequencies in the cavity, hence a low HD when the devices are identical. In practice, one can safely assert that the response of all devices cannot be used as unclonable functions given the high similarity between them.
3.2 Plasmonic-enhanced response
Figure 6 shows the two fractional LHD metrics for one device of each design type with Au nanoparticles. The optical coupling into the chip and the polarization state was scrambled and realigned to add noise between multiple measurements to determine the intra-HD. As shown in blue color in Fig. 6 and as tabulated in Table 4, overall, the intra-HD shows good replicability. The deviation from a perfect identical response is related to the high sensitivity of the response to polarization changes, as will be further discussed. For device type three, however, this can be expected to arise from the evanescent field coupling which brings the cavity response closer to the noise level.
Table 4. Average intra metrics for all devices with Au NPa
The average inter-distance metrics computed for the peo-PUFs are listed in Table 5. The averaged values for LHD and BHD are equivalent to their uniqueness ${u_{LHD}}$ and ${u_{BHD}}$, respectively. The high standard deviation for device design 3 shows that some devices still have significantly similar behavior. This can be sorted by increasing the number of nanoparticles, however at the cost of increasing the overall optical losses.
Table 5. Average inter metrics for all devices with Au NPa
The relatively large standard deviation of the HD indicates a larger probability of authentication errors, with decisions thresholds of 0.18, 0.11 and 0.31 for the three types of devices, respectively. Values for False Rejection Rate (FRR) were computed numerically by comparing CRPs from two independent measurements of the same device. It is performed for all devices on the chip. The False Acceptance Rate (FAR) was computed from a pairwise comparison of devices with identical dimensions located on the same chip. Resulting Values for FAR and FRR are plotted in Fig. 7.
To test the effect of changes in the input challenge, we compare the LHD between two independent measurements of the same device. One device is queried with a challenge that is subject to a predefined number of bit flips. This allows for experimental analysis of the diffusion of the PUF [21]. It results in an average LHD of 0.34, 0.33, and 0.25, for device designs 1, 2, and 3, respectively, independent of the number of bits changed. This shows a good diffusion, despite not reaching the HD = 0.5 expected from ideal uncorrelated responses. The LHD distribution for all devices and a different number of bits changed is plotted in Fig. S2 in Supplement 1.
3.3 Input Optical Power Stability
We test input optical power stability only for device with Au NP type two. There are no significant changes in the response of the peo-PUF under power attenuation by 20 dBm where the laser input power was set as 10 mW. In general, there is a good linear response through all the power attenuation limits. We reduce the Loose HD threshold to 3% (L=0.03) for the data plotted in Fig. 8, to bring the analysis closer to the noise level. The average fractional LHD and BHD obtained are 0.0313 ± 0.039 and 0.0395 ± 0.017, respectively.
Fig. 8. HD for variable power attenuation, a) histogram of all computed distance and b) distance against power attenuation
Although the results here suggest good stability in terms of power attenuation, we acknowledge that the excitation with higher power density would render additional non-linear phenomena. In turn, this should generate a larger entropy in the device behavior. In this work, we do not study further such phenomena given recent results [9] that propose high power input pulses as a viable option for the generation of OPUFs.
3.4 Thermal stability
We test the temperature stability only for device type two. There is a large variation in the response upon modifying the chip temperature. About 10% of the resulting HD is a consequence of the spectrum shift, which we can correct for. However, we are not accounting for any phenomena different from this linear shift. Consequently, it directly increases the entropy in the device’s response. The data shown in Fig. 9 is taken after shifting the spectrum to maximize its correlation to the reference one (T=25°C). The average LHD and BHD across the tests carried are 0.205 ± 0.087 and 0.293 ± 0.060, respectively (calculated after correcting the temperature-induced spectral shift).
Fig. 9. Intra HD under temperature variations, a) histogram of all measured temperatures and b) HD against temperature.
3.5 Polarization stability
The spectral response of the device was measured with TM polarization in the input and rotated for subsequent measurements. The spectral response at every polarization state was then compared to both the quasi-TM and the quasi-TE modes and the LHD computed for each case; the results are plotted in Fig. 10. This figure shows the Poincaré spheres cross-sections with the different polarization states tested for all device types. The intensity component (Stokes’s parameter S0) was replaced by the computed Loose Hamming Distance. The angular components correspond to the state of polarization in the reference polarimeter. Since the polarization was rotated, modifying either the azimuthal component (Stokes’s parameters S1 and S2) or the elliptical component (Stokes’s parameters S1 and S3), but not both, all the HD measurements lie in one of the shaded planes.
Fig. 10. LHD Poincare spheres for a) device design 1, b) device design 2, and c) device design 3, only the two octants around which the polarization was measured are shown.
Both the TM LHD (LHD measured comparing to the TM response) and the TE LHD show a cardioid-like distribution for both the azimuthal and elliptical polarization changes. Nevertheless, the TM LHD grows beyond 0.2 within a $\pi /10$ rotation of the polarization (in either the azimuthal or the elliptical components) for device types one and two. Whereas, the TE LHD only goes beyond this threshold after around $\pi /2$ for all device types. This can be read as the TM response being very sensitive to small variations in the polarization state for device types one and two in contrast to their TE response. The dissimilar behavior of device type three is a consequence of the evanescent field coupling with the resonant cavity, largely dominated by the TM mode.
A direct consequence of the large sensitivity of the polarization state for device types one and two is that a modification of the input polarization state (by a possible attacker) can quickly render the device unusable as a PUF. However, the possibility of implementing compact integrated polarization filters [22,23] on a chip maintains the usefulness of the studied devices.
4. Conclusions
In this work, we presented a plasmonics-enhanced silicon photonic resonance disk to generate physical unclonable functions. The device employs randomly distributed gold nanoparticles on an integrated silicon resonance cavity. This results in variations in the device’s spectral response that are hard to replicate arising from the plasmonic resonances of the different Au NPs distributions. We measured three disk resonator types before and after adding nanoparticles. As a result, we have shown that the level of entropy added to the response allows for its use as an OPUF. Furthermore, we used the TM0 mode as our target state given its stronger interaction with the Au NPs on the silicon surface. This is expected from the larger mode confinement in the surface and the nature of the surface plasmon polariton wave. The similarity between devices of the same type was computed as the fractional Hamming Distance between series of Challenge-Response Pairs. For all device types, we reached levels of uniqueness (inter-device distances) that are beyond a 30% threshold. This is achieved while maintaining intra device distances below the same level, which renders the peo-PUF approach useful. In conclusion, the plasmonic generation of randomness is proven applicable for simple linear devices; hence, the same approach can be used to modify other types of more complex silicon constructions. This conclusion should still apply within the test boundaries asserted in this study.
The peo-PUF presented satisfies the requirements of a weak-PUF [18]. Namely, a small number of CRPs, stable, unpredictable response, and it is impractical to manufacture two devices with the same response. Moreover, they satisfy some requirements of strong PUFs, namely unfeasibility to manufacture two PUFs with the same response and querying the functions reveal only the response to the queried input. This is true even though the challenge-response space is small. In practice the PUF is vulnerable to an attacker who is targeting to store a complete enough look-up table of its responses.
The approach presented in this work is robust against physical attacks to replicate the devices. In practice, using scanning and transmission electron microscopy or atomic force microscopy, one could identify and characterize the exact geometry and position of the nanoparticles. However, doing so induces changes in the diffusion of the particles on its surrounding substrate as well as generates atomic dislocations (sputter) [24] that will modify the PUF response. As shown in section 3.3, the power stability of the devices shows a low probability of using the input optical intensity as a side-channel to affect the performance of the device. The analysis presented in Supplement 1 shows a significant change in a device response after carrying SEM characterization of the chips, supporting this assertion, even though it remains unchanged when the device is characterized using AFM. Nonetheless, a real device will have a cladding layer that will render either measurement technique impractical.
In contrast, the high thermal and polarization sensitivity show that these parameters need to be carefully controlled to maintain the PUFs within usable limits. The use of evanescent field coupled cavities allows a lower sensitivity on the polarization state at a cost of superior noise in the response. Long term stability of the proposed peo-PUFs needs to be tested given that gold nanoparticles may diffuse through the silicon matrix and the device response change outside of its working limits.
Funding
NYUAD Center for Cybersecurity (CCSAD).
Acknowledgments
This research was in part carried using resources from the Core Technologies Platform at NYUAD. We especially acknowledge the support of Nikolaos Giakoumidis for his instrumentation support and Dr. James Weston for his guidance for system characterization. The NYUAD Center for Cybersecurity (CCSAD) is acknowledged for the partial funding for this project.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper and scripts in Matlab to process the data are available in Dataset 1, Ref. [20].
Supplemental document
See Supplement 1 for supporting content.
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