In the literature of secret sharing, the property of essential secret sharing scheme ensures that no set of participants, missing at least one essential participant, should be able to get any information regarding the secret. However, there are essential secret image sharing schemes available in the literature in which we have shown mathematically as well as through experiments that any $k$ or more non-essential participants together can get information about the secret image. It is true that in most of these schemes, preprocessing steps such as random permutations or chaotic maps are used on the secret image to avoid this problem. But that will surely introduce an overhead to the schemes. Moreover, the security of these schemes mainly depends on the preprocessing step and not on the secret sharing schemes. However, our proposed $(t,k,n)$-ESIS scheme for grayscale images over the finite field $\mathrm{GF}\left(p^m\right)$ does not require any preprocessing step to secure the scheme. Though, the proposed scheme over $\mathrm{GF}\left(p^m\right)$ with $p^m>2^8$ is little lossy, it has the advantage over most of the ESIS schemes in the sense that the scheme works fine, even if the number of participants is more than 255. Most importantly, our proposed scheme over $\mathrm{GF}\left(2^8\right)$ is completely lossless. Moreover, our proposed scheme, does not have the limitations such as different size of shadows, concatenation of sub-shadows, use of derivative polynomials etc. Finally, our scheme has reduced share size and work fine without any preprocessing steps on secret image, making our scheme efficient.

在秘密共享的文献中，基本秘密共享方案的属性可确保任何一组参与者（至少缺少一个基本参与者）都无法获得有关该秘密的任何信息。但是，文献中提供了一些基本的秘密图像共享方案，我们在数学上以及通过实验表明，任何$ķ$或更多非必要参与者可以一起获得有关秘密图像的信息。的确，在大多数这些方案中，对秘密图像使用了诸如随机置换或混沌映射之类的预处理步骤来避免此问题。但这肯定会给方案带来开销。而且，这些方案的安全性主要取决于预处理步骤，而不取决于秘密共享方案。但是，我们建议$（Ť，ķ，ñ）$-ESIS方案用于有限域上的灰度图像 $\mathrm{GF}（p^{米}）$不需要任何预处理步骤即可确保方案安全。虽然，提议的方案$\mathrm{GF}（p^{米}）$ 与 $p^{米}>2^8$ 损失很小，即使参与者人数超过255，它在大多数ESIS方案上都可以正常工作，因此具有优势。最重要的是，我们提出的方案 $\mathrm{GF}（2^8）$是完全无损的。此外，我们提出的方案没有诸如阴影大小不同，子阴影级联，使用导数多项式等限制。最后，我们的方案减小了共享大小，并且无需对秘密图像进行任何预处理就可以很好地工作，我们的计划高效。