Abstract In traditional secret image sharing schemes, shareholders have similar situations, and to recover the secret image, they must be present as many as the threshold. However, in scenarios where the shareholders occupy different positions, essential and non‐essential, the use of essential secret image sharing schemes becomes necessary. This article presents a novel verifiable essential secret image sharing scheme based on LWEs that incorporates Bloom filters and hash functions for verification purposes. The proposed scheme for a secret image does not require any pre‐processing. The shadow images of both essential and non‐essential shareholders are of the same size, eliminating the need for concatenating sub‐shadows. Furthermore, shadow images for essential and non‐essential shareholders are produced simultaneously in a single step. The scheme is also quantum safe thanks to the use of quantum‐resistant primitives. The experimental results confirm the security and efficiency of the proposed scheme.

Abstract Steganography and secret sharing are schemes to increase the security of private information against attackers. Steganography emphasizes secrecy while secret sharing distributes the secret key in shares that are conditionally classified to reconstruct the original secret. This paper introduces a counting‐based secret sharing scheme that aims to reduce the computational complexity for longer keys, thereby providing a practical steganographic approach for efficient sharing. The scheme integrates counting‐based secret sharing with integer wavelet transform (IWT) and steganography. The subscriptions created using the Hamming code are embedded in the cover image. Using this method, IWT significantly reduces the occurrence of common rounding errors. As a result, secret key extraction becomes very accurate and eliminates the need to access the original images. This design, using secret sharing based on counting, not only has simplicity and efficiency, but also features such as flexibility, scalability, and lack of central authority. In addition, high‐quality steganography was obtained for keys with lengths of 64, 256, 512, 1024, and 3072, showing an average PSNR=80.11 in different color images. This outstanding performance makes it a highly efficient alternative to previous designs, representing a groundbreaking contribution with significant public interest in the field.

In multi‐secret sharing (MSS) scheme, a dealer distributes multiple secrets among a set of participants, each of them according to an access structure. In this study, the authors propose a novel linear MSS with computational verifiability that provide many functions for practical applications in comparison with the previous works focusing on MSS schemes in the general scenario. This scheme has the same advantages as previous schemes; moreover, it is verifiable and multi‐use secret sharing. Furthermore, in this scheme the secret reconstruction is according to the dealer's preassigned order. Also, they prove the security of the authors’ scheme in the standard model.

Abstract A new multistage secret‐sharing scheme based on the homogeneous linear feedback shift register is proposed. This scheme has few public outputs, a new simple construction, and different techniques for the reconstruction phase. Moreover, based on the semantic security of the underlying encryption scheme, we prove the computational security of our scheme in the standard model. Copyright © 2016 John Wiley & Sons, Ltd.