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 .

Abstract We propose a novel secret image sharing scheme with ciphertext‐based share authentication (SISS‐CSA) for sharing grayscale and color secret images in the malicious model. In SISS‐CSA, the dealer and each participant, individually acting as a combiner, can identify each invalid share received from the malicious participant(s) before using it to reconstruct the secret image. This capability, which most comparable schemes lack, prevents reconstructing an incorrect secret image. In SISS‐CSA, the asymptotic time complexities of operations executed by the dealer in the shares generation phase and executed by each combiner in the secret image reconstruction phase are and , respectively. Here, is the number of grayscale values in the secret image, is the number of generated shares, and is the threshold number of shares required for reconstructing the secret image. These asymptotic time complexities and the size of additional information each combiner stores for identifying invalid share(s) are comparatively lesser than those in the state‐of‐the‐art schemes. Furthermore, we obtain a maximum of reduction in the size of additional information each combiner stores for share authentication using the ciphertext‐based share authentication compared to using the standard SHA‐256. To the best of our knowledge, none of the related share authentication approaches achieves this much reduction. We prove the properties of SISS‐CSA using theoretical analysis. We also provide experimental results validating the implications of theoretical analysis corresponding to asymptotic time complexities and the random nature of shares.

Abstract Researchers have put forward many variations of schemes for secret image sharing on grounds of visual cryptography and polynomials. The authors of this paper put forward a novel scheme for sharing multiple secret images with perfect reconstruction and authentication for cheating prevention. The perfect reconstruction of all shared secret images is obtained by applying polynomial‐based encryption and decryption, and one‐time authentication is done for all shared secret images by stacking the intelligible shares created by using extended visual cryptography. Properties' analysis, experimental results and comparisons are given to exhibit the potency of the scheme.