In this paper, we propose three novel image encryption algorithms. Separable moments and parallel computing are combined in order to enhance the security aspect and time performance. The three proposed algorithms are based on TKM (Tchebichef-Krawtchouk moments), THM (Tchebichef- Hahn moments) and KHM (Krawtchouk-Hahn moments) respectively. A novel chaotic scheme is introduced, which allows for the encryption steps to run si multaneously. The proposed algorithms are tested under several criteria and the experimental results show a remarkable resilience against all well-known attacks. Furthermore, the novel parallel encryption scheme exhibits a drastic improvement in the time performance. The proposed algorithms are compared to the state-of-the-art methods and they stand out as a promising choice for reliable use in real world applications.