秘密共享方案将秘密分成一组共享，并在符合条件的参与者之间分配它们，每个参与者都可以共享一个秘密。共享技术允许参与者的任何合格子集恢复秘密。在（t，n）阈值秘密共享方案中，秘密以份额的形式在n个参与者之间分配，这样每个参与者都恰好拥有一个份额。个人分享并没有透露任何秘密。的大小参与者的任意子集吨以上（吨≤ Ñ）可以结合其股份并计算秘密，而尺寸的任意子集<吨无法做到这一点。本文提出了一种可验证的（t，n）阈值秘密图像共享（VSIS）方案。在所提出的方案，秘密图像之间共享Ñ参与者的意图，如果吨以上（吨≤ Ñ）参与者协作，则秘密图像可以成功地计算出来。但是，任何小于t参与者一无所获。该方案利用基于多项式的秘密共享和XOR运算来构造份额并恢复秘密映像。我们的方案的主要优点在于，它以整数（而不是以前的SIS方案中生成的图像矩阵）形式显示公共份额，比秘密图像小得多。它还会生成与秘密图像大小相同的公共共享图像。因此，公共共享可以在公共网络上有效地传输并有效地存储在存储器中。该方案适用于灰度图像和彩色图像。椭圆曲线密码术（ECC）的使用使参与者可以选择自己的秘密阴影并独立计算伪份额（整数）。因此，整个通信可以安全地在公共渠道上进行。伪共享对参与者和组合者均可以验证。较小的公共份额和椭圆曲线密码系统的组合使该方案非常适合资源受限的设备。相比之下，公共共享图像可以安全地与云服务提供商（CSP）存储。

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An efficient verifiable ( t , n )-threshold secret image sharing scheme with ultralight shares

A secret sharing scheme partitions a secret into a set of shares and distributes them among the eligible participants, with each participant receiving one share of the secret. The sharing technique allows any qualified subset of participants to recover the secret. In (t,n)-threshold secret sharing schemes, the secret is distributed among n participants in the form of shares, such that every participant holds exactly one share. Individual share reveals nothing about the secret. Any subset of participants of size t or more (t ≤ n) can combine their shares and compute the secret, while any subset of size < t is not able to do so. This paper proposes a verifiable (t,n)-threshold secret image sharing (VSIS) scheme. In the proposed scheme, a secret image is shared among n participants with an intention that if t or more (t ≤ n) participants collaborate, then the secret image can be computed successfully. Still, any less than t participants get nothing. The scheme makes use of polynomial-based secret sharing and XOR operations to construct the shares and recover the secret image. Our scheme’s main advantage is that it presents the public shares as integer numbers (not image matrices produced in previous SIS schemes), much smaller than the secret image. It also generates a public share-image of the size the same as that of the secret image. Thus, the public shares can be efficiently transferred over the public network and efficiently stored in memory. The scheme applies to both grayscale and color images. The use of Elliptic Curve Cryptography (ECC) enables the participants to choose their own secret shadows and compute the pseudo shares (integer numbers) independently. Hence the entire communications can take place safely on public channels. The pseudo shares are verifiable to the participants as well as the combiner. The combination of small public shares and the elliptic curve cryptosystem makes this scheme ideal for resource-constrained devices. In contrast, public share-image can be safely stored with a Cloud Service Provider (CSP).