SISS‐CSA: Secret image sharing scheme with ciphertext‐based share authentication for malicious model

Abstract

AbstractWe 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.