A Novel (k,n) Secret Sharing Scheme from Quadratic Residues for Grayscale Images
This work addresses secure image transmission for applications like digital media, but it is incremental as it builds on existing secret sharing methods.
The paper tackles the problem of securely sharing grayscale images by proposing a (k,n) threshold secret sharing scheme using quadratic residues and Shamir polynomials, achieving provable security and high-quality reconstructed images in experiments.
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.