Symmetric Encryption from Cyclic Codes over Non-Chain Rings

Abstract

This paper introduces a novel encryption scheme constructed over the finite v, uv = vu = 0. Inspired by the principles of the one-time pad cryptosystem, the proposed method employs a unique, random key of equal length to the plaintext, ensuring theoretical perfect secrecy. A key feature of this design is its resistance to ciphertext-only attacks, as multiple plaintexts may map to the same ciphertext under different key instances. To assess the scheme's security against quantum adversaries, we model the key-recovery process and analyze its complexity under Grover's quantum search algorithm, which offers a quadratic speed-up compared to classical brute-force techniques. Experimental simulations in Python, using NumPy and Matplotlib, illustrate the performance gap between classical and quantum search across rings with varying cardinalities. The results reveal that while brute-force attacks quickly become infeasible as the key space grows, Grover's algorithm maintains computational viability. Overall, this study highlights the potential of integrating algebraic ring structures with post-quantum cryptographic analysis, offering a promising avenue for secure communication in quantum-aware security environments.