Shadow images generated from Shamir’s polynomial-based secret image sharing (SSIS) may leak the original secret image information, which causes a significant risk. The occurrence of this risk is closely related to the basis of secret image sharing, Shamir’s polynomial. Shamir’s polynomial plays an essential role in secret sharing, but there are relatively few studies on the power and order number of Shamir’s polynomial. In order to improve the security and effectiveness of SSIS, this paper mainly studies the utility of two parameters in Shamir’s polynomial, order number and power. Through the research of this kind of utility, the choice of order number and power can be given under different security requirements. In this process, an effective shadow image evaluation algorithm is proposed, which can measure the security of shadow images generated by SSIS. The user can understand the influence rule of the order number and power in SSIS, so that the user can choose the appropriate order number and power according to different security needs.

中文翻译：

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秘密图像共享中订单号和权力的价值

从Shamir的基于多项式的秘密图像共享（SSIS）生成的阴影图像可能会泄漏原始的秘密图像信息，从而造成重大风险。这种风险的发生与秘密图像共享（Shamir多项式）的基础密切相关。Shamir多项式在秘密共享中起着至关重要的作用，但是关于Shamir多项式的幂和阶数的研究相对较少。为了提高SSIS的安全性和有效性，本文主要研究Shamir多项式中两个参数的实用性：阶数和幂。通过对这种实用工具的研究，可以在不同的安全要求下给出订货号和功率的选择。在此过程中，提出了一种有效的阴影图像评估算法，可以衡量SSIS生成的阴影图像的安全性。用户可以在SSIS中了解订单号和电源的影响规则，以便用户根据不同的安全需求选择合适的订单号和电源。