A Novel (k,n) Secret Sharing Scheme from Quadratic Residues for Grayscale Images

TL;DR

This paper introduces a secure grayscale image encryption method combining quadratic residue-based encryption with Shamir's secret sharing, enabling flexible reconstruction with high image quality and strong security guarantees.

Contribution

It presents a novel $(k,n)$ secret sharing scheme for grayscale images that integrates quadratic residue encryption with polynomial-based sharing, enhancing security and image quality.

Findings

Scheme is provably secure.

Reconstructed images maintain high quality.

Flexible threshold for secret reconstruction.

Abstract

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.