A novel chaotic map based on Euler number namely Euler Map (EMAP) is suggested for image encryption algorithms (IEAs). The chaotic behavior of EMAP is appreciated with bifurcation analysis and Lyapunov Exponent (LE). The LE is the best due to the ultimate and most stable characteristic in case compared with the literature. A two-stage IEA, permutation and diffusion, is used to demonstrate the successful performance of EMAP, and this is how the success of EMAP is verified. The IEA with EMAP is examined in secure cryptanalyses and computational complexity. Some results are validated with the state of the arts. In the comparison, the suggested EMAP-based IEA stands out due to the diversity and complexity performance. It achieves a cropped image having minimum loss, a good operation time of 0.2297s and a low computational complexity. Therefore, the proposed EMAP can be applied to realistic systems.