An efficient essential secret sharing: Application to gray and color images

Abstract

A Secret Sharing Scheme (SSS) is a cryptographic primitive used to share secrets, such that the secret can be revealed only when a specified number of shares are available. Due to varying levels of importance or hierarchy among shareholders, some shareholders may be deemed essential for secret recovery. This concept is addressed by essential secret sharing. The essential SSSs designed for sharing secret images suffer from various limitations, including different shadow image sizes for essential and non-essential shareholders, large share sizes, preprocessing requirements, the need for concatenating sub-shadows, constraints on image type, and pixel expansion. To address these issues, we propose an essential SSS based on simple linear algebra. This scheme is both perfect and ideal. We then leverage this scheme to develop a perfect and ideal essential secret image sharing (SIS) scheme that accommodates essential participants. We further modify the scheme to reduce the share sizes by a factor of k, which makes it efficient. It is applicable for gray as well as color images. Our approach relies on simple operations like matrix addition, multiplication, and inversion. Our scheme supports color images and offers lossless recovery. It overcomes the limitations present in existing SIS schemes. We have discussed experimental results for the gray and color images. Furthermore, all schemes presented in this article are quantum secure.