Among various post-quantum cryptography (PQC) proposed by researchers, lattice-based cryptography is considered to be one of the most promising post-quantum public key cryptography systems. It has significant advantages over other PQC schemes in terms of security, computational efficiency, and versatility in designing public key encryption, digital signatures, and cryptographic negotiation protocols. Efficient implementations of the number theoretic transform (NTT) operations are crucial for many lattice-based encryption algorithms. This article presents an NTT hardware acceleration structure based on SRAM in-memory computing technology, which optimizes the key butterfly structure in the NTT algorithm by improving the 6T-SRAM array structure and incorporating near-memory computing structures. Compared with existing technologies, this accelerator can significantly reduce area and power consumption.

Combinatorial optimization problems (COPs) are notoriously difficult to solve for classic Von-Neumann computers, which are ubiquitous in various domains. As a state-of-the-art hardware acceleration scheme for COPs, Ising machines are one of the promising research directions for the next generation of computing, but still suffer from the low solution accuracy and speed due to the high complexity of the fully-connected Ising model. In this work, a novel parallel tempering processing architecture (PTPA) is proposed with the modified parallel tempering algorithm, aimed at reducing search time and improving the solution quality. Several techniques are developed to further reduce hardware overhead and enhance parallelism, including the independent pipelined spin update architecture, approximated probability equations, and compact random number generators. Its prototype is implemented on FPGA with eight replicas, each replica containing 1,024 fully-connected spins and at most 64 concurrent update spins. The proposed design achieves an average cut accuracy of 99.43% within 1ms solution time on various G-set problems. Compared with the CPU-based parallel tempering implementation, it enhances the speed of solving the max-cut problems by 5,160 times.

Combinatorial optimization problems (COPs) are prevalent in various domains and present formidable challenges for modern computers. Searching for the ground state of the Ising model emerges as a promising approach to solve these problems. Recent studies have proposed some annealing processing architectures based on the Ising model, aimed at accelerating the solution of COPs. However, most of them suffer from low solution accuracy and inefficient parallel processing. This article presents a novel parallel tempering processing architecture (PTPA) based on the fully-connected Ising model to address these issues. The proposed modified parallel tempering algorithm supports multi-spin concurrent updates per replica and employs an efficient multi-replica swap scheme, with fast speed and high accuracy. Furthermore, an independent pipelined spin update architecture is designed for each replica, which supports replica scalability while enabling efficient parallel processing. The PTPA prototype is implemented on FPGA with 8 replicas, each with 1,024 fully-connected spins. It supports up to 64 spins for concurrent updates per replica and operates at 200 MHz. Different concurrency strategies are considered to further improve the efficiency of solving COPs. In the test of various G-set problems, PTPA achieves 3.2× faster solution speed along with 0.27% better average cut accuracy compared to a state-of-the-art FPGA-based Ising machine.