Visual Cryptography Schemes (VCS) based on the "XOR" operation (XVCS) exhibit significantly smaller pixel expansion and higher contrast compared to those based on the "OR" operation. Moreover, the "XOR" operation appears to possess superior qualities, as it effectively operates within a binary field, while the "OR" operation merely functions as a ring with identity. Despite these remarkable attributes, our understanding of XVCS remains limited. Especially, we have done little about the noise in the reconstructed image up to now. In this paper, we introduce a novel concept called Static XVCS (SXVCS), which completely eliminates the noise in the reconstructed image. We also demonstrate that the equivalent condition for perfect white pixel reconstruction is simply the existence of SXVCS. For its application, we naturally propose an efficient method for determining the existence of XVCS with perfect white pixel reconstruction. Furthermore, we apply our theorem to $(2,n)$-XVCS and achieve the optimal state of $(2,n)$-XVCS.

翻译：基于“异或”（XOR）操作的视觉密码方案（XVCS）相较于基于“或”（OR）操作的方案，具有显著更小的像素扩展和更高的对比度。此外，XOR操作表现出更优越的特性，因为它能在二进制域内有效运行，而OR操作仅作为一个带单位元的环。尽管这些特性引人注目，我们对XVCS的理解仍然有限，尤其是在重构图像中的噪声问题方面迄今进展甚微。本文提出一种名为静态XVCS（SXVCS）的新概念，可完全消除重构图像中的噪声。我们还证明了完美白色像素重构的等价条件即为SXVCS的存在性。在其应用层面，我们自然提出了一种用于判定具备完美白色像素重构能力的XVCS存在性的高效方法。此外，我们将该定理应用于(2,n)-XVCS，并实现了(2,n)-XVCS的最优状态。