Fig. 1. Concept of the multiuser SPI security framework. N plaintexts are compositely encrypted and transparently transmitted to all users by the composite SPI Fourier encryption. Simultaneously, three types of key sets Ψ, Φ, and Ω are encapsulated into the metasurface for key distribution. After receiving the bucket signal, users access the metasurface to acquire their own secret keys to decrypt different plaintexts. The private {Ψ} and {Φ} sets represent the 2N decomposed keys from Λ, a pair of which corresponds to the plaintext and authenticating information for each user. Ω denotes a common key set for authentication.

Fig. 2. Schematic of the Fourier SPI encryption. The host digitally processes I1∼I9 and configures a Fourier SPI optical path, where a digital micromirror device (DMD) and Fourier structured light are presented. To improve the efficiency of the following key processing, the initial conditions of chaos instead of the generated masks are encapsulated.

Fig. 3. Schematic of regional encryption. (a) Texture information and spacing distribution of pixels can be scrambled by whitening and permutation, whereas (b) permutation-only encryption still can reveal the content information.

Fig. 4. Flowchart for generating different whitening masks Wkm×n by chaos.

Fig. 5. Schematic of diffusion encryption.

Fig. 6. Design concept of OFDM-assisted key management. (a) Connecting role of key management between SPI encryption and multiple users. (b) Keys are separately processed by OFDM-like coding and RSA, zoned as the private channel and public channel, which are further physically confused by polarization and etched into the metasurface.

Fig. 7. Design principle of the OFDM-assisted key management. (a) Flowchart of OFDM-like coding. (b) Time-frequency diagram of S. (c) 2D parameter optimization of nanobricks, in which the upper region of the red dashed line represents the RPRE of long-polarized light and the lower region indicates that of the short-polarized light. (d) Simulated Rl and Tl. The Malus metasurface is designed to operate in the reflective mode. (e) Four states of the unit cell, where “1” and “0” denote the positive and negative states of the private (public) channel of the metasurface, respectively. (f) Top view of the prototype captured by a scanning electron microscopy with scale bar of 200 nm.

Fig. 8. Optical setup of the proposed scheme. (a) Setup of the multiuser SPI encryption framework and decryption mechanism. (b) Configuration of key distribution.

Fig. 9. Synergetic authentication mechanism. The red dashed box shows the retrieving process of I9, whereas the blue dashed box displays the retrieving process of the token by the OFDM-assisted key management.

Fig. 10. Attacking results from a deep differential attack. G. T., D. V., and C. V. denote ground truth, the legal decrypted version, and cracked version, respectively. Ex. Att. and In. Att. mean the external and internal attacking results from Eve and internal user, respectively. The attack mode is only directed toward the pertinent stages of SPI encryption. The measures unrelated to encryption, such as steganography and holography, are assumed to be prior-known by default. SCU is the abbreviation of Sichuan University and is used with the permission of Sichuan University.

Fig. 11. Error tolerance analysis. (a) Recovered token display under the recognition errors occurring with different ratios. (b) BER performance of OFDM-like coding and the raw token.

Fig. 12. Numerical assessment of bucket signal o and Idiffuse3m×3n of SPI encryption. (a) Intensity sequence. (b) Visual randomness assessment of the sampled intensity sequence. (c) Histogram of Idiffuse3m×3n. (d) Correlation test of Idiffuse3m×3n.