Minimal-Polynomial-Based Lightweight Cryptography for IoT and Wireless Hardware: Security Analysis and FPGA Implementation

This paper proposes a lightweight polynomial-based encryption architecture for resource-constrained IoT and wireless communication hardware. Instead of substitution boxes, the method uses key-dependent polynomial multiplication with minimal polynomials over finite fields. Plaintext rows are XORed with secret keys and a nonce-dependent pseudorandom mask and multiplied by a minimal polynomial; multiplication by a complementary factor recovers the message exactly. A security analysis shows that, because the transformation is linear over $\mathrm{GF}\left(2\right)$, reuse of the same key and polynomial allows for known- and chosen-plaintext key recovery; per-message nonce masking is therefore required. Software experiments (four message lengths, 100 trials) verified lossless decryption. The encryption time of the key-assisted method was comparable to that of SPECK64/128 at the same implementation level, whereas AES-128 was faster for long messages, and the avalanche ratio of the proposed method (0.070) was well below the value of about 0.5 obtained by the reference ciphers. On a Xilinx Artix-7 FPGA, the proposed core used 1211 LUTs and 205 registers without block RAM or DSPs and reached 154.1 MHz, compared with 2305 LUTs and 2733 registers for an iterative AES-128 core. The method is a compact, S-box-free polynomial processing layer rather than a stand-alone replacement for standard ciphers.