PQES: Post-quantum encryption and signature scheme based on FFT-accelerated polynomial ring lattice for IoT devices

With the rapid advancement of quantum computing, traditional public-key cryptosystems (e.g., RSA and ECC) are facing severe threats from quantum attacks (e.g., Shor’s algorithm). To address the demand for efficient and secure communication in resource-constrained scenarios such as the Internet of Things (IoT), this paper proposes an integrated quantum-resistant encryption and signature scheme based on polynomial ring lattices and accelerated by the Fast Fourier Transform (FFT). The scheme combines the Ring Learning With Errors (Ring-LWE) and Ring-LWE-Short Integer Solution (Ring-SIS) problems, optimizing operations over the polynomial ring $Z_q\left[x\right]/(x^N+1)$ to significantly reduce key and ciphertext sizes. Additionally, FFT techniques are introduced to accelerate polynomial multiplication, while finite field FFT and floating-point error correction mechanisms address precision issues. Experimental results demonstrate that for polynomial degrees $N\ge 1024$, the encryption time is reduced by 23% compared to CRYSTALS-Kyber, with a 35% decrease in memory consumption. Moreover, Our signature verification mechanism demonstrates significantly lower resource consumption compared to both CRYSTALS-Dilithium and Falcon implementations under equivalent security parameters, making it suitable for low-overhead verification on edge devices and efficient signing on servers.