Secure Encryption Over Eisenstein-Jacobi Integers From <i>w</i>-Cyclic Codes

Ensuring secure communication in the digital era is of paramount importance. This study introduces a novel encryption model that combines w-cyclic codes with the one-time pad (OTP) method over Eisenstein-Jacobi integers, achieving information-theoretic security. The method constructs a finite ring over Eisenstein-Jacobi integers, generates one-time keys from w-cyclic codewords, and uses these keys to encrypt messages, guaranteeing each key is used only once. Multiple plausible ciphertexts are produced for each plaintext, making unauthorized decryption infeasible. Key findings show that the scheme provides high computational efficiency and robust resistance to cryptographic attacks, outperforming existing code-based and public-key systems. Security scales with prime selection, as longer codewords and keys increase protection. The algebraic structure of Eisenstein-Jacobi integers enables efficient key generation and encryption operations, making the model suitable for critical security applications. Existing OTP and cyclic code-based encryption systems are typically limited to binary fields or specific rings, constraining key diversity and scalability. By extending OTP to w-cyclic codes over Eisenstein-Jacobi integers, the proposed model overcomes these limitations, providing a larger key space and more complex encryption structure. Code-based encryption, including cyclic codes, offers quantum-resistant security. This feature aligns the proposed OTP model with post-quantum cryptography (PQC). This work demonstrates that combining cyclic codes with OTP creates an unbreakable and practical encryption framework, providing resistance against both conventional and quantum attacks.