一种基于 Weyl 定理的数字图像加密传输方法*

摘要

针对数字图像如何更好地在网络中进行安全传输的问题，需要研究一种高质量的加密和解密算法，使得加密图像以不可见隐藏方式嵌入叠加到非加密图像中，并且使得提取后的加密图像与原图像具有较好的一致性，因此提出了一种基于Weyl定理的数字图像保密传输方法。该方法首先依据Weyl定理分析了矩阵奇异值对图像扰动的影响，进而建立了图像保密数学模型并给出图像加密和解密求解；然后根据算子公式编写了图像嵌入合成、图像提取的M atlab程序；最后得到肉眼不能识别微弱变化的合成图像，并比较了加密图像处理前后矩阵数据差异大小。该方法最终得到加密图像处理前后矩阵数据差异较小的结论，验证了基于Weyl定理的图像保密算法的优越性，达到了加密图像能够隐藏在一般图像中安全传输而不被识别出的效果，也可供其他多媒体信息进行保密传输时参考使用。%About digital images how to be transmitted safely in internet is a big question ,which needs one kind of better algorithm to encrypt and decrypt them .Confidential image is inserted and superimposed in non confidential image with the hidden mode ,and also the confidential image restored out is identical to the original image .Here one kind of digital image confidential transmission method based on Weyl theory is proposed .First the influence of image disturbance is analyzed in ac‐cordance with Weyl theory .Then image confidential model is constructed and the solving of image encryption and decryption is deduced .Second the Matlab program about image synthesis and restoration is written by the operator equation .Last syn‐thetic image can be got which has the slight change unseen .Furthermore ,the difference of matrix data about the confidential image and the restored image is also compared .Finally the superiority of the image confidential algorithm based on Weyl the‐ory is verified by the small difference of the confidential image and the restored image .So the effect has been got that one confidential image can be transmitted safely with the hidden mode in a common image but can't be identified .This method can also be used in other kinds of multimedia information's confidential transmission .