In this paper, we propose a new color secret image sharing based on homogeneous linear recursion (HLR). Merits of the previous related schemes, such as no pixel expansion, no code book required, no public image, lossless recovery, and high resolution are maintained in the proposed scheme, simultaneously. In addition, it has smaller shadow images and less complex calculations compared to related works. Besides, there are three methods for reconstruction that make it more convenient. Also, the RGB components of the secret image are processed in one step and there is no need to repeat the process of the scheme for each color channel that makes the process faster and more convenient.

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In this paper, we present two verifiable multi-secret sharing schemes, including a linear multi-secret sharing scheme with public access structure and a threshold (t, n) scheme based on the learning with errors (LWE) problem. The first scheme is a linear multi-secret sharing scheme in which a number of secrets is distributed by a dealer among a set of participants according to the access structure corresponding to each secret. This scheme has the advantages of the earlier ones and it also has many practical applications compared to previous schemes including a multi-use verifiable multi-secret sharing scheme in which the secret reconstruction is according to the dealer’ s preassigned order. In addition, the security of the scheme has been proven in the standard model. This scheme is based on the hard problems in number theory and therefore is not secure against quantum attacks. The second scheme presented in this paper is a lattice-based secret sharing scheme. In this scheme, which is a threshold (t, n) multi-secret sharing scheme, the presence of at least t participants is required for the reconstruction of the secret. The security of this scheme is based on the difficulty of the LWE problem and so it is resistant against quantum attacks.

Secret sharing is the process of distributing a secret among n shareholders, in such a way that only a subset of them can recover the secret, while unauthorized subsets, referred to as dishonest shareholders, cannot access the secret. During the secret reconstruction phase, when shareholders present their shares, a dishonest shareholder or shareholders can always obtain the secret exclusively by presenting fake shares, thus leaving the honest shareholders with nothing but a fake secret. Detecting cheating is crucial for achieving a fair secret reconstruction. In this paper, it has been proposed a cheating-detecting secret sharing scheme that utilizes polynomial coefficients for cheat detection in secret reconstruction. It is leveraged the invertibility property of polynomial coefficients in the z_q field to detect cheat and employ relationships that follow a linear equation.

in visual secret sharing, the secret image is transformed into several share images and distributed among different people. The share images do not contain any information about the original image, and these images are similar to the noise image. When needed, the original image can be retrieved in the presence of all stakeholders and by stacking the share images. In this regard, the appearance of noisy images may attract the attention of the attackers. To solve this problem, meaningful visual secret sharing was presented. In this article, a method for sharing the image with meaningful shares is introduced. There are a number of hyper parameters in the proposed algorithm. To improve performance, an attempt has been made to determine these hyper parameters using a genetic algorithm. The cost function of the genetic algorithm is the difference between the two values of the correct number of bits of the recovered image and the original image and the correct number of integer bits between the cover image and the shares. The proposed method was evaluated using PSNR, MSE, BCR criteria and presented good results on different images with different number of shares.

A Publicly Verifiable Secret Sharing (PVSS) scheme, as introduced by Stadler, has a feature where anyone, besides the participants, can verify the validity of the shares distributed by the dealer. Schoenmakers added a new feature, by providing a proof of correctness of the shares released by the players in the reconstruction process. This protocol is claimed to be an improvement on Stadler's and Fujisaki-Okamoto's, both in efficiency and in the type of intractability assumptions. However, Young-Yung improved Schoenmakers' PVSS, using a Discrete-Log instead of a Decision Diffie-Hellman. In this paper, a new PVSS is presented, having an intrinsic difference with its predecessors, that is, the participants can prove the validity of their given shares, implicitly, proving their membership by a zero-knowledge protocol. This feature prevents cheaters from participating in the reconstruction process to gain valid shares. Hence, the new proposed PVSS is more secure than previous ones. Besides, the dealer only sends the amount of commitments limited to the threshold value, regardless of the number of shareholders; this leads to a more dynamic protocol.

Protecting valuable data along the Cyber Security is the one of the strategic issues of cyber defense. The secret sharing scheme is an attractive branch of advanced cryptography that has extremely important role in cyber defense and for the preservation of documents and confidential information against threats such as robbery and unauthorized accesses. In the secret sharing schemes, for increasing security shareholders present a shadow image instead of the genuine share while they are recovering secret images. Thus each shareholder is able to share several images with others by having only one portion of image.In this paper, we define and design a new generating function that by replacing with the Hou Zheng Feng and et.al's generating function, can improved it. Since the new generating function is one-way and hard problem, hence increased the security of improved scheme. Also, with implementation and performing the new scheme again, our revised scheme will be more efficient respect to previous scheme according to the analysis and speed of computations.