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Abstract
Polarization encryption has long been shown to allow simultaneous encryption of 2D images, but with scarce practical implementations or commercial applications to date. Nevertheless, a possible vector for its use in market products may be additive manufacturing (AM). As more complex and diversified technologies use AM in their production chains, intellectual property (IP) protection of shared data is becoming increasingly crucial. Many AM techniques rely on optical systems, therefore, it is essential to analyze the prospects of safeguarding AM processes using advances in optical secrecy. This work demonstrates the use of polarization encoding by employing liquid crystals for physical layer security. We examine the encoding of the information in a signal’s polarization state and show that linear transformations of polarization can be used to encrypt and decrypt data. We further demonstrate the use of off-the-shelf liquid crystal displays (LCD) in a low-cost commercial resin 3D printer to build a "polarization decryptor". The proposed system does not require any software modification and in hardware only the replacement of the printer’s LCD masking screen. This technique provides a promising methodology to secure part of the supply chain for AM operations.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Additive manufacturing (AM) has gained widespread adoption in the past few years spanning a wide range of applications: from advanced biomedical modules [1] to print-at-home action figures [2], to the manufacturing of inter-die optical wire bonds [3]. As a result of the growing AM market, the cost of 3D printers today has reached those of conventional paper and ink printers, with quality reaching and exceeding some of the best 3D printing technologies available less than a decade ago [4]. However, as the number of manufacturers and suppliers increases, the supply chain for AM systems becomes more vulnerable [5]. Particularly, many low-cost AM systems now feature Wi-Fi, Ethernet, and Bluetooth connections, and have access to cloud-based resource sharing. A consequence of this is that the privacy of data exchanged with 3D printers is at risk. This is especially true when manufacturers offer cloud platforms for users to upload and manage printing tasks, often free of charge [5,6].
A specific technology that has seen an increase in market reach is the Liquid Crystal Displays (LCD) ultraviolet (UV) lithography printer, a consequence of the present low cost of LCDs. The technology consists of a UV light source that is masked using an LCD, allowing light to only expose specific areas in a layer of resin on top of the display. Multiple layers can be subsequently processed to build a structure in three dimensions. In this work, we show how replacing the original LCD with a modified Liquid Crystal (LC) doublet, i.e. a sandwich of two sequential LC arrays, enables an operation to be carried out in the physical layer. This can be done without additional modifications to the printer’s hardware or its firmware.
In this paper, we will first discuss the vulnerabilities that arise from exchanging plain text manufacturing files with 3D printers. We then formally discuss the characteristics of information encoded in the polarization state of light , and how two sequential rotations of the polarization state over orthogonal directions can be interpreted as an encoding operation. We then , through simulations, demonstrate how the aforementioned encoding permits operations that maintain secrecy. Following, we will describe the methodology to build a polarization-based decryptor using off-the-shelf LCDs and show its use in a 3D printing process. We finally present the results of our implementation, discuss its limitations, and propose mechanisms to improve its performance. Despite multi-layered LCDs having been recently developed to enhance the contrast on high dynamic range TV screens [7,8], to the best of our knowledge, this is the first time a sandwiched layered LC array is reported as a mechanism to perform encryption operations.
2. Threat model
A typical AM process starts with a designer that defines a 3D model using CAD software. This 3D model is the designer’s intellectual property (IP) and may include information that must be kept secret. For example, in a health implant, a 3D part contains information about the physical description of a patient’s body and diagnostics; or the design may follow a precisely engineered topology that is not intended to be disclosed to parties in the manufacturing process chain. The final design is saved as a 3D file, ready for sharing, often following STL format specifications (an acronym for stereolithography). The manufacturing operator uses the STL file to generate a Computer Aided Manufacturing (CAM) file consisting of a list of instructions specific to the 3D printer(s) to be used. Finally, the list of instructions is uploaded to the printer, and the part is manufactured. In LCD-based AM processes, the CAM file contains a list of images consisting of cross-sections (slices) from the original part, hence we further refer to it as the ’slice file’. In said process, any number of data protection schemes can be used to ensure privacy at any-time information is shared. Nevertheless, it is always necessary that in the final manufacturing step, the information processed by the hardware (the printer) is not encrypted to, evidently, be able to fabricate the part. Worth noting is that reconstructing the original IP from the plain text CAM files is trivial and requires only knowledge of the manufacturing process specifications. Researchers have even found that side-channel analysis of fused deposition printers allows the reconstruction of CAM files [9], and from them retrieve the original IP.
The threat model in this work, illustrated in Fig. 1, assumes a malicious AM systems manufacturer or 3D printing service provider (SP), that may gain access to a slice file and can reconstruct the original IP for counterfeiting using the CAM information shared with the printer. A malicious party may gain access to the plain text slice file directly from a tampered printer or from information-sharing services that provide an exchange of CAM files (i.e. 3D parts online marketplaces).
Fig. 1. (a) A malicious 3D printer or a malicious marketplace of CAM files may provide multiple access points of plain-text Slice Files that render AM IP vulnerable. Printers with online access to marketplaces generate direct vulnerabilities being capable of sharing disclosed information directly. (b) 3D model before and after digital encryption after being manufactured on an LCD-based 3D printer. The area encrypted includes the bounding box of the model, generating as a consequence a box with randomly printed voxels when encrypted.
We propose protecting the IP by encrypting digitally the physical description of the part in the slice file, i.e. the voxels that compose the part, in lieu of (or in addition to) the digital files, and carrying decryption in the physical domain during the printing process. In this configuration only after printing, the intended 3D part is revealed, and the printer’s hardware and software have only access to the protected slice file, guaranteeing that the original IP is protected. This configuration, when combined with a strong cryptography system during encryption, such as a block cipher in a mode that guarantees IND-CPA (indistinguishable under chosen plain-text attacks) [10], guarantees the secrecy of the information (the part’s design).
3. Polarization encryption using liquid crystal arrays: working principle
In this section we discuss the mechanism that allows encryption / decryption in the physical layer. The use of LCs for encryption was initially described using Spatial Light Modulators (SLM) [11] that employ phase [12–14] or polarization [15,16–18] to encode information. When an incoherent light source is used, such as light-emitting diodes (LEDs), conventional optical phase encryption techniques cannot be immediately used. Yet, a simplified analysis of polarization encoding becomes available [19], and phase retrieval techniques may still be used to allow phase encoding with an incoherent source [20]. Recent LC security applications include the development of re-configurable polarizing filters for ciphering [21], the use of and dynamic focus encryption in the fractional Fourier domain [22]. The analytical study of polarization encryption is well described in the literature [23], information being encoded in four orthogonal states, namely vertical, horizontal, right hand circular and left hand circular. [16].
We hereby provide a simplified analysis of the operations performed by a back-to-back LC doublet for rotation between only the vertical and horizontal polarization (s and p) using Jones matrices. When few information is available about the liquid crystal, Jones matrices have been shown to approximate well the bulk effect in the system’s polarization state [24]. Let the ket $|{\varphi }\rangle$ denote the state of polarization of an electromagnetic wave propagating in $\hat {z}$ given by Eq. (1):
We are only concerned with linearly polarized states, so we can simplify this system by removing the quarter waveplates. In this case, the state of polarization of the generator will have the two electric field components in phase and can be set to be aligned to one of the coordinate axes. We prepare the input polarization state so that it is aligned with the x-axis, namely
By setting an analyzer to be aligned with the y-axis, the system in Eq. (2) may be described to include two LC transformation matrixes as Eq. (4)
where $T_{i}$ is the Jones matrix of the $i^{th}$ LC layer. A liquid crystal can be described as a material with two different indexes of refraction along orthogonal directions, namely its ordinary and extraordinary axes. The orientation of the axes can be modified using an applied voltage. Of interest to this work, in a twisted nematic LC, a wave propagating in the z-direction can be modeled as a rotation and a propagation matrix. Using only the two axes orthogonal to the main propagation direction, such a system may be described by the Jones matrix [26]:This is a rotation matrix over a differential angle $\delta \theta$ and propagation over a layer thickness $dz$, with $n_o$ and $n_e$, the ordinary and extraordinary refractive indices, respectively and $k_{0}$ the free space wave-number. When N layers of nematic fluid are used to generate a total angle of rotation of $\theta$, we can model the total propagation matrix as
Using this expression, we calculate the four possible permutations of the LC doublet, as represented in Fig. 2, where the resulting output is reported for each state. It’s evident that the system is equivalent to an exclusive OR (XOR) operation, assuming the input bits are transformed into the state of each of the LC layers (i.e. a binary one into a $\pi /2$ polarization rotation or $0b1 \xrightarrow {} \theta =\pi /2$). Most importantly, each transformation is linear, and they can be used as prototypes for operators in a group (particularly, the Galois Field of order 2) in a cryptographic algorithm.
Fig. 2. Four states for the Liquid Crystal doublet. LC cells are represented in dark purple, with the orientation of the extraordinary axis in bright purple.
4. Implementation
As described in Section 3, the polarization rotation operation, when applied to a space with only two orthogonal states, can be understood as a binary XOR. Therefore, we may use it to run a stream cipher (e.g. in the output of a block cipher in the correct mode of operation). For this work, we implement an encryption system using the Advanced Encryption Standard [27] of 128 bits in counter (CTR) mode. For data encryption, we directly modified a slice file to encrypt an area of selected printing layers, following the process described in Section 1 of the Supplement 1. For decryption, we substitute the final XOR of the algorithm with the modified LC doublet sandwiched between two linear polarization filters (PF), as is represented in Fig. 3. One of the LC arrays is driven by the original printer board while the second one is directly connected to the user’s computer. The interface to the second LC array is a standard MIPI display serial interface (DSI) driven by an HDMI/MIPI-DSI converter board.
Fig. 3. Schematic of the proposed encryption and decryption mechanism. The file is first encrypted digitally, and upon printing, the modified printer with an LC doublet performs an operation equivalent to an XOR when changing the polarization state of light (or a sum in GF-2). PF: Linear polarizing filters.
We built the LC doublet using commercial off-the-shelf low-cost components. We target a Creality LCD resin 3D printer (LD-002R), hence we use a compatible LCD (SHARP LS055R1SX04). Standard LCDs are manufactured as a sandwich consisting of a white backlight, a linear polarizer (in $\hat {x}$), a liquid crystal array, and a final polarizer (in $\hat {y}$). Additional layers can include Fresnel lenses, quarter waveplates, gratings, and antireflective layers to maximize the display performance. The LC cell itself is an array with three individual windows per pixel, each consisting of a twisted nematic liquid crystal cell and a unique color filter.
To build the LC doublet, we removed the backlight and gratings from two LCDs, remove the output polarizer filter from one and the input polarizer from the second, then stack both together and mount them on the printer’s body as depicted in Fig. 4(a). The process is described in further detail in the documentation in [29]. The resulting system can be operated to display an image in the first LC array, and selectively invert each pixel using the second, as is illustrated in Fig. 4(b) and 4(c), in which a full image is inverted using the LC doublet. To correct for small misalignments between layers (that generates a Moiré pattern in the output [30]) we add a diffuser on top of the LC doublet.
Fig. 4. (a) Liquid Crystal doublet mounted on the LCD-SLA Creality LD-002R printer body. The printer is shown without its resin basin. (b) An optical image of Marie Curie [28] displayed in the LC doublet when the first array shows the image while the second is fully black, or (c) white, a case in which image inversion occurs.
5. Results
5.1 Simulations
We simulate the 4 states of the LC doublet using Finite-Differences in Time-Domain (FDTD) in Ansys Lumerical. To test the device’s performance, the Transverse Electric (TE) polarization fraction of an injected TE polarized wave was measured across the entire device. We used two liquid crystal cells modeled as a $5 \mu m$ thick layer of Merck TL-216 with anisotropic permittivity calculated using a Cauchy approximation for wavelengths between $[450-656] nm$ [31], and linearly extrapolating outside this range.
The index alteration induced by the electric field across the LC is simulated as a parametric rotation of the permittivity tensor. Furthermore, the simulations assume the two LC cells are separated by a $5 \mu m$ thick Silicon Oxide ($SiO_{2}$) layer, and light is injected from the bottom of the stack. The role of $SiO_{2}$ is only to serve as a transparent structural layer to separate the two cells. This would typically be a conductive oxide to serve as a ground connection to the LC array. We simulate the transmission between $360 nm$ and $780 nm$ wavelengths and compute the inner product with the light emission of a commercial UV LED (Thorlabs M405L4). The resulting TE polarization fraction for all states is plotted in Fig. 5. The TE polarization fraction is equivalent to the binary operation XOR when a s-polarization filter is added to the output, or XNOR when for a p-polarization one.
Mismatch through the LC array and elliptical states generate fluctuations in the TE polarization fraction. As seen in the polarization fraction spectrum plotted in Fig. 6(a) for the $\langle {y}|J_{\pi /2} \vert J_{\pi /2}|{x}\rangle$ operation, different wavelengths reach a complete rotation of the polarization state at different positions along the LC doublet. To reduce this effect, we can physically rotate the second LC array by 90 degrees so that, when the cell is active, the output extraordinary axis of the first LC matches that of the input of the second LC. Such rotation allows for a much more homogeneous response across the spectrum as shown in Fig. 6(b). It is also a necessary step to ensure a good contrast when the light source used for exposure is broadband. This approach is, however, not practical when using off-the-shelf LCDs for which the shape of each LC cell is rectangular (and not squared). This would generate a pixel mismatch when building the doublet stack. For completeness, Fig. S1 in Supplement 1 shows the other three operations.
Fig. 6. TE polarization fraction spectrum for aligned LC doublet (a) and rotated by $\pi$/2 (b) for the $\langle {y}|J_{\pi /2} \vert J_{\pi /2}|{x}\rangle$ operation. The onsets show the corresponding RGB values of the output using channels 640 nm, 540 nm, and 400 nm respectively.
5.2 Implementation using off-the-shelf components
We first analyzed the light polarization in the output for the $J _{\pi /2} | J _{\pi /2}$ and $J _{\pi /2} | J _0$ states using a power meter and a polarization filter as an analyzer. The measured transmittance of the system for different angles $\chi$ in the analyzer is shown in Fig. 7. The two measurements obey an expected $sin^{2}$ behavior for polarized light. However, it is clear that the contrast between the two orthogonal states (for $\chi =0$ and $\chi =\pi /2$) is significantly different. For the $J _{\pi /2} | J _{\pi /2}$ transformation, the off-angle lower amplitude is 3.73 times (−5.72 dB) smaller than its maximum value. In comparison, the $J _{\pi /2} | J _0$ the off angle is 22.34 times (−13.49 dB) smaller than its maximum value. The low contrast in the $J_{\pi /2} \vert J_{\pi /2}$ operation is an indication of elliptical polarization in the output, which in practice translates into a lower light intensity contrast when switching to said state. This is a disadvantage since the $\langle {y}| J_{\pi /2} \vert J_{\pi /2} |{x}\rangle$ state, which should show as dark, will have a relatively higher optical power intensity transmitted at the output.
Fig. 7. (a) Schematic of the liquid crystal doublet tested, and (b) transmittance in the visible spectrum for different analyzer angles and for two states in the output LC array, when the first LC remains as $J_{\pi /2}$ (on).
Furthermore, to test the assembled setup, we encrypted a section of ‘3DBenchy’, a model used as a standard 3D printing benchmark. Only a square area in the central region of the 3D model was encrypted, to show the ability to protect specific parts of a model. This, for example, allows the creation of partially locked 3D models that can only be fully printed with the use of a key. The effect of the low contrast of the $\langle {y}|J_{\pi /2} \vert J_{\pi /2} |{x}\rangle$ state is evident as shown in Fig. 8(a). As can be seen, some of the pixels outside of the boat’s hull are not completely off. We digitally set a lower resolution for the screens to reduce the effect of misalignment between the LC arrays and to allow determining the changes with the naked eye.
Fig. 8. Optical image of a slice of an LCD 3D printing process of a modified 3D Benchy model when the correct key is used to decrypt (a), and when an incorrect one is used (b), while using a white LED source as backlight.
Since we are using an AES engine in the counter mode, we used the layer number as the counter during the encryption and decryption process to make sure that each layer is encrypted differently. This renders the system resistant to chosen plain text attacks. We further allow for n layers to be encrypted using the same counter (i.e. the counter c=l mod (n), where l is the layer number) to make an easier visualization of the system performance. Despite the correct modification/decryption and retrieval of the original slice plaintext, the low contrast for the $\langle {y}| J_{\pi /2} \vert J_{\pi /2} |{x}\rangle$ transformations results in the pixels that undergo this transformation not being completely dark as they are supposed to. Therefore, during the printing process, large portions of undesired resin are exposed, prohibiting high-resolution printing at this stage. An application where the LC doublet is integrally manufactured, instead of assembled from modified off-the-shelf components should enable strict control of the LC cells. This would help ensure that the polarization in the output is correctly rotated to avoid the elliptical states that generate noise in the current application. This normally requires only the correct calculation of the cell thickness, reducing the distance between the two layers of LC arrays (here limited by the $SiO_2$ protective layer in each LCD) and using LC cells laid with orthogonal extraordinary axes to implement the corrections discussed in 4.1.
The 3D printing slice files modified in this work were generated with Chitubox up to version 1.6.5.1, newer versions include additional encryption mechanisms in the data that render the file harder to read. The analysis of an approach to target newer files is however beyond the scope of interest of this paper.
6. Conclusions
In this work, the ability to encrypt data using light polarization is demonstrated and applied in an additive manufacturing process. Using twisted nematic pairs in an LC array, we generate a linear (invertible) transformation in the polarization state of light that results from the rotation of the extraordinary axis of the LC cells. We have proven that the use of two sequential LC arrays allows the encryption or decryption of large images when the transformation occurs as the last computation of a cryptographic system, namely an AES-128 engine. We proposed the use of such transformations in systems that currently employ LCDs, and we specifically demonstrated its application in LCD UV lithography 3D printers.
In such printers, the photosensitive 3D resin printing process uses an LCD as a mask. Our threat model assumes an untrusted 3D printer manufacturer or a tampered printer, that seeks unauthorized access to the 3D part’s IP when said part is sent for printing. The proposed methodology uses commercial off-the-shelf components to build an LC doublet consisting of a [PF - LC - LC - PF] sandwich that replaces the original printer’s LCD. We’ve demonstrated how the resulting unit can decrypt data that was previously encrypted in a 3D part’s voxels. Furthermore, protecting the entire portion isn’t necessary; rather, the technique allows for the protection of the specific regions where relevant IP exist. However, we were not able to effectively print new parts in the modified setup due to the significant reduction in the total transmitted optical power when using the LC doublet. Additionally, one of the operations ($1\bigoplus 1=0, or \langle {y}| J_{\pi /2} \vert J _{\pi /2} |{x}\rangle$) has a significant dark transmission leakage that causes enough noise for the layers to be incorrectly exposed during printing. We discussed additional polarization corrections to prevent this phenomena.
Other applications of decrypting LC doublets may include streaming of video information with partial protection of data and spatial light polarization encryption in free space communication networks. The transformations presented here use only two orthogonal states of polarization, but in practice, a larger number of states, including circular ones, can be employed to generate a larger ciphertext space.
Acknowledgments
Part of work presented in this report used resources from the Core Technologies Platform at New York University Abu Dhabi.
Disclosures
The authors declare no conflicts of interest.
Data availability
All data used in this project, including example files and code used to modify the OBJ slice file, are available in [29].
Supplemental document
See Supplement 1 for supporting content.
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