<p>Algebraic structures are highly effective in designing symmetric key cryptosystems; however, if the key space is not sufficiently large, such systems become vulnerable to brute-force attacks. To address this challenge, our research focuses on enlarging the key space in symmetric key schemes by integrating the non-chain ring with a four-dimensional chaotic system. While chaotic maps offer significant potential for data processing, relying solely on them does not fully leverage their operational advantages. Therefore, it is essential to incorporate algebraic structures that enhance the complexity of the scheme. In the proposed technique, four-dimensional chaotic sequences are employed for image pixel permutation, diffusion, and exclusive-or operations. The scheme is further strengthened against chosen and known plaintext attacks by incorporating pixel values during the exclusive-or operation, where images are XORed with hashed images and keys generated from chaotic sequences. The effectiveness of the technique, its resilience to various forms of attack, and its feasibility for practical implementation are demonstrated through extensive testing and a comprehensive security analysis.</p>