Though there have been many research works carried out on the grayscale secret image sharing schemes, there is not sufficient research work available on the field of color secret image sharing schemes, especially on the lossless secret image sharing schemes. In the current work, we propose a new lossless secret color image sharing scheme with small shadow size. We directly deal with the three components of the intensities of the RGB values of each color pixel of the secret image. Using a mathematical transformation, we first embed the RGB intensity values of each secret pixel as an element of a suitably chosen finite field F. Then the whole mathematical operations are carried over the finite field F to generate shares using $k-1$ degree polynomials in the polynomial ring $F[x]$. Unlike most of the image sharing schemes, we do not have the preprocessing stage in which the secret image is transferred into random image either by using Arnold Cat map or by using some chaotic maps to avoid residual image effect. From experimental simulations, it is evident that the measure of randomness of the shares generated using our algorithm is same as that of the shares generated using the preprocessing stage in which Arnold Cat map or chaotic map is used, resulting our scheme simpler and efficient. Moreover, our scheme produces shares having smaller size than the secret image. Finally the recovery of the secret image by the qualified set of participants is lossless.

尽管已经有许多关于灰度秘密图像共享方案的研究工作，但是在彩色秘密图像共享方案领域，尤其是无损秘密图像共享方案领域，没有足够的研究工作。在当前的工作中，我们提出了一种新的无损秘密彩色图像共享方案，具有较小的阴影大小。我们直接处理秘密图像每个颜色像素的RGB值强度的三个分量。使用数学变换，我们首先嵌入每个秘密像素的RGB强度值作为适当选择的有限域的元素˚F。然后整个数学运算在有限域F上进行以使用$ķ--\mathrm{1个}$ 多项式环中的次数多项式 $F[X]$。与大多数图像共享方案不同，我们没有预处理阶段，在该阶段中，通过使用Arnold Cat映射或通过使用一些混沌映射将秘密图像转换为随机图像，以避免残留图像效果。从实验模拟中可以明显看出，使用我们的算法生成的股票的随机性度量与使用Arnold Cat映射或混沌映射的预处理阶段生成的股票的随机性度量相同，从而使我们的方案更加简单有效。而且，我们的方案产生的共享文件的大小小于秘密映像的共享文件的大小。最后，合格的一组参与者对秘密映像的恢复是无损的。