Revisiting silk: a lens-free optical physical unclonable function

For modern security, devices, individuals, and communications require unprecedentedly unique identifiers and cryptographic keys. One emerging method for guaranteeing digital security is to take advantage of a physical unclonable function. Surprisingly, native silk, which has been commonly utilized in everyday life as textiles, can be applied as a unique tag material, thereby removing the necessary apparatus for optical physical unclonable functions, such as an objective lens or a coherent light source. Randomly distributed fibers in silk generate spatially chaotic diffractions, forming self-focused spots on the millimeter scale. The silk-based physical unclonable function has a self-focusing, low-cost, and eco-friendly feature without relying on pre-/post-process for security tag creation. Using these properties, we implement a lens-free, optical, and portable physical unclonable function with silk identification cards and study its characteristics and reliability in a systemic manner. We further demonstrate the feasibility of the physical unclonable functions in two modes: authentication and data encryption.


Supplementary Note 1. Optical simulations for a single fiber
A two-dimensional beam propagation method (BPM) built in a commercial software (RSoft, Synopsys, USA) was used to investigate the self-focusing phenomena of a single fiber. A grid size of 5 nm was used in the simulation to produce numerically stable results. A plane wave with a 645 nm-wavelength was used as the light source. The boundary conditions were the transparent boundary conditions. An absorption coefficient of 0.02 was applied to the fiber media shown in Fig. 2a to realize the opaque fiber. A programmable language (MATLAB, Mathworks, USA) was exploited to generate the simulation domains with different nanohole densities of 0, 5, and 10%. The domain for the random hole was defined as a 25000 × 25000 blank matrix. One element of the matrix was present at 1 nm. Thus, the dimensions of the blank matrix were 25 µm × 25 µm. The diameters of all the nanoholes were set to 25 nm. The generated holes, which had 25 diameter elements, were located in the domain with arbitrary center positions. The located holes were recorded as '1' in the matrix. To check the density of the hole, the ratios of 1 and 0 were calculated for every generation. In addition, we used feedback to avoid the overlapping of each nanohole ( Supplementary Fig. 25). Supplementary   Fig. 3 shows one of the generated single fibers with nanofibrillar structures. The refractive indices of the background, microfiber, and nanoholes were 1, 1.6, and 1, respectively.

Supplementary Note 2. Theoretical analyses of the fiber bundle for PUF applications
Three-dimensional BPM simulations were performed using commercial software (RSoft, Synopsys, USA) to analyze the lens-free imaging features in the fiber bundle geometries. A commercial programmable language (MATLAB, Mathworks, USA) was used to produce random fiber media with three densities: 70, 80, and 90%. The domain for the random fiber was defined as a 1000 × 1000 blank matrix. One element of the matrix was 1 μm. The overall size of the fiber bundle domain was fixed at 1×1 mm 2 . The fiber bundles consisted of 30 µmwide fibers. The virtual rectangular fiber, which had 30 elements for width and an infinite length, was defined to fill the domain. The virtual fiber was generated in a domain with an arbitrary center position and angle. The located fiber was recorded as '1' in the matrix. To check the density of the fibrous medium, ratios of 1 and 0 were calculated for every generation.
The boundary conditions were the transparent boundary conditions. To validate the statistical approach, we repeated the generation of a random fibrous medium. All of the generated fiber bundle media are shown in Supplementary Fig. 6. The generation method for a fiber bundle is shown in Supplementary Fig. 26. The geometrical parameters (i.e., average diameters and number of holes) in each medium were analyzed. To calculate the average diameter of the medium, the diameter of the circle was calculated by dividing the total hole area by the number.
The geometrical statistical results confirmed the consistency of the generated fiber bundle media. To simplify the computation, the refractive index of all fibers was set to 1.6, and all fibers were assumed to be opaque by introducing an absorption coefficient of 0.02. Image simulations were conducted to confirm the unique responses from randomly generated fibrous media ( Supplementary Fig. 7). Three light sources (i.e., red, green, and blue) were launched from three incident angles, i.e., −15°, 0°, and 15°, for CRPs. Without a cut-off process, the simulated images did not exhibit remarkably focused spots. The cut-off process provided apparent and unique focal spots at far distances, such as 0.8 and 1.0 mm, in the red, green, and blue images. Based on this result, colored lights from different incident angles could serve as true random seeds for PUF applications. The colored images in Fig. 1d were also produced using this simulation.

Supplementary Note 3. Measurement setup for the self-focusing effect
Supplementary Fig. 4 exhibits the optical image of the measurement setup for observing the self-focusing feature of native silks under an incoherent light source. Three solid-state LEDs (LED625L, LED525L, LED470L, Thorlabs, Inc., Germany) produced red, green, and blue light, and a native silk fabric was mounted between the glass slides to ensure the flatness of the silk fabric. A 1x objective lens (i.e., relay lens; 30 mm focal length f/4, Thorlabs, Inc., Germany) transferred the focal spots generated by the silk fabric to a commercial image sensor (IMX226, Sony, Japan). The image sensor was a chromatic sensor that separated colored lights. To capture the focal spots using silk depending on the distance, a single-axis motorized stage (CMA-25PP, Newport, USA) was used, which was controlled by a motion controller (ESP-300, Newport, USA). The images were obtained with a movement step of 10 μm. The obtained results are shown in Figs. 2g and 2h.

Supplementary Note 4. Conversion method of the response to bitstream
MATLAB (Mathworks, Inc., USA) was used for image processing and bit extraction. The captured images had a three-color space composed of red, green, and blue. For image processing, the image was decomposed using three channel images. Next, each image was exploited to generate bitmaps. To equalize the LED illumination, the original and blurred images were subtracted from each other through a Gaussian filter. Moreover, a binning process was performed to reduce the peak/edge noise ( Supplementary Fig. 23). An image size of 2048 × 2048 was binned to an image size of 32 × 32 pixels. A threshold was applied to the binned image for digitization of the data. Finally, von Neumann debiasing was conducted in each bit column stream (i.e., 32 × 1 bits). Von Neumann debiasing follows the following rule. (i) If a pair of bits in sequence were 00 or 11, the pair of bits moved to the 2 nd pass extractor. (ii) If the pair of bits were 01 or 10, the bit pair moved to a debiased bit sequence. (iii). Reconsidering the bits in the 2 nd pass extractor, the bit pairs were again grouped into pairs. (iv) If the first and second pairs were different (i.e., 0011 or 1100), the bit pairs in the 2 nd pass extractor were maintained ( Supplementary Fig. 24). If the number of debiased column bits was more than four bits, the first four bits were extracted. Otherwise, the processing moved to the adjacent bit column sequence and extracted four bits. This process was repeated until 64 bits were collected.

Au nanoparticles
Optical (metallic) 40× lens camera [4] Thermoplastic materials Optical (organic) 2.8× lens camera [5] Supplementary Table 1. Summary of various optical PUF devices in terms of their materials and objective lens specifications. All reported optical PUFs adopted lens elements to distinguish random seeds in the PUF response. The original data has noise bit elements due to the edges of the peak point. Binning was performed to cluster the bits into a unit of a predetermined dimension so that the noise at the edge had a smaller influence than the peak signal. Supplementary Fig. 24 | Process of von Neumann debiasing. An illustration of von Neumann debiasing. The extracted bit sequence was biased at '0' because the number of peak points was smaller than whole domain. Thus, 2 pass von Neumann debiasing extraction was used to increase the uniformity of the bit sequence.
Supplementary Fig. 25 | Generation of random nanofibrillar structures. An illustration of the generation of random nanofibrillar structures in a single microfiber. A flow chart of random fiber generation (top) and a typical example (bottom). To confirm the density of the random fibers, the ratio of white and black areas was checked at every generation. Also, feedback was conducted to avoid any overlapping of the random holes.
Supplementary Fig. 26 | Generation of random fibrous medium. An illustration of the random fibrous medium generation. A flow chart of the random fiber bundle generation (top) and a typical example (bottom). To confirm the density of the random fibrous medium, the ratio of the white and black areas was checked at every generation.