Essential Secret Image Sharing Scheme With Flexible Reconstruction, Reduced Share Storage Costs, and Faster Shares Generation

ABSTRACT We propose a Essential Secret Image Sharing scheme using Linear Homogeneous Recurrence Relation and polynomials for sharing a grayscale or color secret image in the semihonest model. In our scheme, the dealer generates essential and nonessential shares of a secret image. A combiner needs shares to reconstruct the secret image, where at least are essential shares. Unlike most state‐of‐the‐art schemes restricting to be equal to , our scheme also allows for . This merit makes reconstruction possible even if up to essential shares are unavailable. Additionally, compared to state‐of‐the‐art schemes, our scheme offers substantial reductions in share sizes—by factors formed from , , , and . Thus, with this reduced size of shares, leading to reduced share storage costs, our scheme has a broader range of applications, including those with limited budgets. Moreover, in cases where , the shares generation period in our scheme, during which an adversary can potentially steal the secret image from the dealer, is at least 42% shorter than that in the state‐of‐the‐art scheme supporting .