Multi-Probability Hash-based Random Number Generator for Post-Quantum Cryptography

The security of a cryptographic system depends on the reliability and irreversibility of random numbers. Secure Hash Algorithm-3 (SHA-3) is widely utilized in cryptography due to its robust security, computational efficiency, and versatile hashing capabilities. SHA-3 and discrete sampling are vital components in post-quantum cryptography, providing essential defense against quantum computing attacks. This paper presents a multi-probability random number generator for lattice-based post-quantum cryptography. The design utilizes a cascaded Keccak core and single-stage registers to build a SHA-3 module. Random numbers with different probability distributions are generated through variable binomial sampling, rejection sampling, and Gaussian sampling. The proposed design consumes 11520 LUTs and 3252 FFs at the frequency of 300MHz on the Xilinx UltraScale+ FPGA, achieving a throughput rate of 14.4Gbps. The ASIC evaluation indicates a hardware overhead of 68.5 kGE (NAND2) under the 40nm process. Compared with similar designs, our design demonstrates 11% and 27% frequency and throughput improvements under the same hardware resources, respectively.