Shamir给出了一种基于拉格朗日插值的密码学分存方案,该文将其思想引入到图像信息安全处理当中,提出了用动直线进行多幅图像分存的方法,并阐述了这一算法的数学基础.此外,在进行图像分存时考虑了更多的原始图像,采用高次有理曲线进行图像分存计算,并分析比较了基于拉格朗日插值的分存算法和基于动直线的分存算法在多幅图像分存上的异同,指出了基于拉格朗日插值的图像分存算法在实际应用中存在的问题.最后,给出了采用动直线进行图像分存的实验结果.

Shamir gave the (t,n)-Threshold Secret Sharing Scheme of cryptography based on Lagrange interpolation. In this paper, the authors introduce it into image sharing and give a new kind of algorithm for image sharing based on moving lines. The mathematical scheme of moving lines is presented in this paper. Hereby, when an image is shared, the authors consider more original images, compute with rational curves of high degree, compare the differences between Lagrange interpolation and moving lines on image sharing of many frames, and give the application fault of Lagrange interpolation with high degree in image sharing. Finally, some experimental results for image sharing based on moving lines are presented.

本文研究得到国家自然科学基金(No.19671003)和国家973高科技项目基金(No.G1998030608)资助.