  In this paper, we introduce a symmetric-key Latin square image cipher (LSIC)
for grayscale and color images. Our contributions to the image encryption
community include 1) we develop new Latin square image encryption primitives
including Latin Square Whitening, Latin Square S-box and Latin Square P-box ;
2) we provide a new way of integrating probabilistic encryption in image
encryption by embedding random noise in the least significant image bit-plane;
and 3) we construct LSIC with these Latin square image encryption primitives
all on one keyed Latin square in a new loom-like substitution-permutation
network. Consequently, the proposed LSIC achieve many desired properties of a
secure cipher including a large key space, high key sensitivities, uniformly
distributed ciphertext, excellent confusion and diffusion properties,
semantically secure, and robustness against channel noise. Theoretical analysis
show that the LSIC has good resistance to many attack models including
brute-force attacks, ciphertext-only attacks, known-plaintext attacks and
chosen-plaintext attacks. Experimental analysis under extensive simulation
results using the complete USC-SIPI Miscellaneous image dataset demonstrate
that LSIC outperforms or reach state of the art suggested by many peer
algorithms. All these analysis and results demonstrate that the LSIC is very
suitable for digital image encryption. Finally, we open source the LSIC MATLAB
code under webpage https://sites.google.com/site/tuftsyuewu/source-code.
