A versatile and tunable vectorial holography is demonstrated based on single-layer single-material liquid crystal superstructures. This novel approach advances the process from scalar to vectorial ...holography, opening new opportunities for advanced cryptography, super‑resolution imaging, and many other tunable photonic applications.
In the paper, we present a new method to study the differential properties of addition modulo 2 n using the formulas of coefficients of sum of 2-adic integers.
To improve the efficiency of lattice-based cryptography in practical applications, the optimization technology of polynomial multiplication in lattice-based cryptography is proposed. The polynomial ...coefficients are stored in a ping-pong structure to improve the bandwidth. By eliminating pre-scale operations, 10.5% of modular multiplication operations and 16.7% of storage space are saved. The structure based on look-up table shift register and three-input adder is adopted to reduce the logical resource occupation. The pipeline structure with optional stages is designed to make the butterfly module in polynomial multiplication meet the timing requirements of different cryptographic hardware systems. The evaluation results show that the maximum frequency of low-area, balanced and high-performance implementations of the optimized butterfly unit can reach 150, 250 and 350 MHz, respectively. Compared with the existing implementation technologies, the optimized hardware implementation can achieve higher operating fr
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