In this paper, we introduce a symmetric-key Latin square image cipher (LSIC) for grayscale and color image encryption. Our main contributions include (1) we propose new Latin square image encryption primitives including Latin Square Whitening, Latin Square S-box and Latin Square P-box; (2) we develop probabilistic image encryption by embedding random noise into the least significant bit-plane of images; and (3) we design a new loom-like 2D substitution-permutation network maintaining good confusion and diffusion properties with extra error tolerance. Theoretical analysis and simulation results show that the proposed method has many desired properties of a secure cipher, shows robustness against different attack models, and outperforms state of the art suggested by many peer algorithms. Open-source implementation can be found on the webpage https://sites.google.com/site/tuftsyuewu/source-code. © 2014 Elsevier Inc. All rights reserved.