  A new grayscale image encryption algorithm based on $(k,n)$ threshold secret
sharing is proposed. The scheme allows a secret image to be transformed into
$n$ shares, where any $k \le n$ shares can be used to reconstruct the secret
image, while the knowledge of $k-1$ or fewer shares leaves no sufficient
information about the secret image and it becomes hard to decrypt the
transmitted image. In the proposed scheme, the pixels of the secret image are
first permuted and then encrypted by using quadratic residues. In the final
stage, the encrypted image is shared into n shadow images using polynomials of
Shamir scheme. The proposed scheme is provably secure and the experimental
results shows that the scheme performs well while maintaining high levels of
quality in the reconstructed image.
